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Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Basic Skills Project

2010-11-29T12:57:20Z

MariaFayloga: /* Example 2 */

For the Basic Skills Project, Group 9 plans on focusing on Inequalities.

We will give several worked out examples to cover all cases of questions concerning this topic.

Also, we will include tips & tricks for how to solve more difficult problems and possible references related to the topic.

<pre>Let's work with Group 10 for the group project :D -- Ellen</pre>

=What is an inequality?=

A way to remember what Inequalities are is:

<pre>A statement indicating that the value of one quantity or expression is not equal to another, as in x ≠ y</pre>

''Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005''

What that basically means is:

* When an equation is < or > or ≤ or ≥ than something.
** E.g. x + 1 ≤ 3

=Linear Inequalities=

The only difference between solving linear inequalities and solving linear equations is that '>' or '<' replaces the '=' sign.

Also, if you multiply or divide by a negative number, you have to change the sign around.

====Example 1====

Solve -2x > 2

we start by dividing both sides by -2 to solve the inequality

x < -1

====Example 2====
Solving linear inequalities is almost exactly like solving linear equations.

* Solve x + 3 < 0.

If they'd given "x + 3 = 0", we would know how to solve: we would have subtracted 3 from both sides. The same applies here.

x < -3

Then the solution is:

x < –3

====Example 3====

* Solve x – 4 > 0.

If they'd given "x – 4 = 0", then we would can solve by adding four to each side. The same applies here.
x >= 4

Then the solution is: x > 4

====Example 4====

* Solve 2x < 9.

If they had given "2x = 9", we would have divided the 2 from each side.

x <= 9/2

Then the solution is: x < 9/2

====Example 5====

* Solve (2x – 3)/4 < 2.
First, multiply through by 4. Since the "4" is positive, we don't have to flip the inequality sign:

(2x – 3)/4 < 2
(4) × (2x – 3)/4 < (4)(2)
2x – 3 < 8
2x < 11
x < 11/2 = 5.5
====Example 6====

* Solve 10 < 3x + 4 < 19.

This is what is called a "compound inequality". It works just like regular inequalities, except that it has three "sides". So, for instance, when we go to subtract the 4, I will have to subtract it from all three "sides".

=10 < 3x + 4 < 19
=6 < 3x < 15
=2 < x < 5
====Example 7====
* Solve 5x + 7 < 3(x + 1).

First we multiply through on the right-hand side, and then solve as usual:

5x + 7 < 3(x + 1)
5x + 7 < 3x + 3
2x + 7 < 3
2x < –4
x < –2

=Tips=
If x ≥ y then 1/x ≤ 1/y

=Quadratic Inequalities=
references:

http://www.purplemath.com/modules/ineqquad.htm

http://www.analyzemath.com/Inequalities_Polynomial/quadratic_inequalities.html

====Example 1====

Solve <math>x^2-2x-15>0</math>

Treat it like a normal quadratic equation and find the zeroes
* <math>x^2-2x-15=0</math>
<math>(x-5)(x+3)=0</math>
x-5=0 or x+3=0
x=5 or -3

The zeroes divide the number line into three regions

[[File:Crappy_number_line_thing_1.png]]

For region x>5, check for a number greater than 5 (eg.6).
*<math>(6)^2-2(6)-15>0</math>
9>0
All x-values greater than 5 will work.

For region x<-3, check for a number less than -3 (eg.-4).
*<math>(-4)^2-2(-4)-15>0</math>
9>0
All x-values less than -3 will work.

*Show answer using interval notation
<math>(-infinity,-3)U(5,infinity)</math>

====Example 2====

Solve <math>3x^2>-x+4</math>

Make one side equal to zero
*<math>3x^2+x-4>0</math>

Find the zeroes using the quadratic formula and factor

*(3x+4)(x-1)>0
3x+4=0 or x-1=0
x=<math>-(4/3)</math> or 1

For region x><math>-(4/3)</math>, check for a number less than <math>-(4/3)</math> (eg.-2).
*<math>3(-2)^2+(-2)-4>0</math>
6>0
All x-values less than <math>-4/3</math> will work.

For region x>1, check for a number greater than 1 (eg.4).
*<math>3(4)^2+(4)-4>0</math>
48>0
All x-values greater than 1 will work.

*Show values that produce an answer greater than 0 using interval notation
<math>(-infinity, -4/3)U(1,+infinity)</math>

=Videos teaching Inequality=

Video 1. http://www.khanacademy.org/video/inequalities?playlist=Algebra%20I%20Worked%20Examples
- This video touches upon the concept of inequality and has a basic word problem solved.

Video 2. http://www.khanacademy.org/video/interpreting-inequalities?playlist=Algebra%20I%20Worked%20Examples
- This video is about interpreting inequalities in word problems.

Video 3. http://www.khanacademy.org/video/solving-inequalities?playlist=Algebra%20I%20Worked%20Examples
- This video is about solving basic problems regarding inequalities.

Video 4. http://www.khanacademy.org/video/inequalities-using-addition-and-subtraction?playlist=ck12.org%20Algebra%201%20Examples
- This video solves random question about inequalities with addition and subtraction.

Video 5. http://www.khanacademy.org/video/inequalities-using-multiplication-and-division?playlist=ck12.org%20Algebra%201%20Examples
- This video solves random question about inequalities with multiplication and division

Video 6. http://www.khanacademy.org/video/quadratic-inequalities?playlist=Algebra
- This video explains quadratic Inequalities.

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Basic Skills Project

2010-11-29T12:45:24Z

MariaFayloga:

For the Basic Skills Project, Group 9 plans on focusing on Inequalities.

We will give several worked out examples to cover all cases of questions concerning this topic.

Also, we will include tips & tricks for how to solve more difficult problems and possible references related to the topic.

<pre>Let's work with Group 10 for the group project :D -- Ellen</pre>

=What is an inequality?=

A way to remember what Inequalities are is:

<pre>A statement indicating that the value of one quantity or expression is not equal to another, as in x ≠ y</pre>

''Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005''

What that basically means is:

* When an equation is < or > or ≤ or ≥ than something.
** E.g. x + 1 ≤ 3

=Linear Inequalities=

The only difference between solving linear inequalities and solving linear equations is that '>' or '<' replaces the '=' sign.

Also, if you multiply or divide by a negative number, you have to change the sign around.

====Example 1====

Solve -2x > 2

we start by dividing both sides by -2 to solve the inequality

x < -1

====Example 2====
Solving linear inequalities is almost exactly like solving linear equations.

* Solve x + 3 < 0.

If they'd given "x + 3 = 0", we would know how to solve: we would have subtracted 3 from both sides. The same applies here.

x < -3

Then the solution is:

x < –3

====Example 3====

* Solve x – 4 > 0.

If they'd given "x – 4 = 0", then we would can solve by adding four to each side. The same applies here.
x >= 4

Then the solution is: x > 4

====Example 4====

* Solve 2x < 9.

If they had given "2x = 9", we would have divided the 2 from each side.

x <= 9/2

Then the solution is: x < 9/2

====Example 5====

* Solve (2x – 3)/4 < 2.
First, multiply through by 4. Since the "4" is positive, we don't have to flip the inequality sign:

(2x – 3)/4 < 2
(4) × (2x – 3)/4 < (4)(2)
2x – 3 < 8
2x < 11
x < 11/2 = 5.5
====Example 6====

* Solve 10 < 3x + 4 < 19.

This is what is called a "compound inequality". It works just like regular inequalities, except that it has three "sides". So, for instance, when we go to subtract the 4, I will have to subtract it from all three "sides".

=10 < 3x + 4 < 19
=6 < 3x < 15
=2 < x < 5
====Example 7====
* Solve 5x + 7 < 3(x + 1).

First we multiply through on the right-hand side, and then solve as usual:

5x + 7 < 3(x + 1)
5x + 7 < 3x + 3
2x + 7 < 3
2x < –4
x < –2

=Tips=
If x ≥ y then 1/x ≤ 1/y

=Quadratic Inequalities=
references:

http://www.purplemath.com/modules/ineqquad.htm

http://www.analyzemath.com/Inequalities_Polynomial/quadratic_inequalities.html

====Example 1====

Solve <math>x^2-2x-15>0</math>

Treat it like a normal quadratic equation and find the zeroes
* <math>x^2-2x-15=0</math>
<math>(x-5)(x+3)=0</math>
x-5=0 or x+3=0
x=5 or -3

The zeroes divide the number line into three regions

[[File:Crappy_number_line_thing_1.png]]

For region x>5, check for a number greater than 5 (eg.6).
*<math>(6)^2-2(6)-15>0</math>
9>0
All x-values greater than 5 will work.

For region x<-3, check for a number less than -3 (eg.-4).
*<math>(-4)^2-2(-4)-15>0</math>
9>0
All x-values less than -3 will work.

*Show answer using interval notation
<math>(-infinity,-3)U(5,infinity)</math>

====Example 2====

Solve <math>3x^2>-x+4</math>

Make one side equal to zero
*<math>3x^2+x-4>0</math>

Find the zeroes using the quadratic formula and factor

*(3x+4)(x-1)>0
3x+4=0 or x-1=0
x=<math>(-4/3)</math> or 1

The zeroes divide the number line into three regions

<insert some kind of number line drawing here>

For region x><math>(-4/3)</math>, check for a number greater than <math>(-4/3)</math> (eg.-2).
*<math>3(-2)^2+(-2)-4>0</math>
6>0
All x-values greater than <math>-4/3</math> will work.

For region x<-3, check for a number less than -3 (eg.-4).
*(3x+4)(x-1) =(3(-2)+4)((-2)-1)

*Show answer using interval notation
<math>(-infinity,-3)U(5,infinity)</math>

=Videos teaching Inequality=

Video 1. http://www.khanacademy.org/video/inequalities?playlist=Algebra%20I%20Worked%20Examples
- This video touches upon the concept of inequality and has a basic word problem solved.

Video 2. http://www.khanacademy.org/video/interpreting-inequalities?playlist=Algebra%20I%20Worked%20Examples
- This video is about interpreting inequalities in word problems.

Video 3. http://www.khanacademy.org/video/solving-inequalities?playlist=Algebra%20I%20Worked%20Examples
- This video is about solving basic problems regarding inequalities.

Video 4. http://www.khanacademy.org/video/inequalities-using-addition-and-subtraction?playlist=ck12.org%20Algebra%201%20Examples
- This video solves random question about inequalities with addition and subtraction.

Video 5. http://www.khanacademy.org/video/inequalities-using-multiplication-and-division?playlist=ck12.org%20Algebra%201%20Examples
- This video solves random question about inequalities with multiplication and division

Video 6. http://www.khanacademy.org/video/quadratic-inequalities?playlist=Algebra
- This video explains quadratic Inequalities.

File:Crappy number line thing 1.png

2010-11-29T12:44:49Z

MariaFayloga:

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Basic Skills Project

2010-11-29T12:41:20Z

MariaFayloga:

For the Basic Skills Project, Group 9 plans on focusing on Inequalities.

We will give several worked out examples to cover all cases of questions concerning this topic.

Also, we will include tips & tricks for how to solve more difficult problems and possible references related to the topic.

<pre>Let's work with Group 10 for the group project :D -- Ellen</pre>

=What is an inequality?=

A way to remember what Inequalities are is:

<pre>A statement indicating that the value of one quantity or expression is not equal to another, as in x ≠ y</pre>

''Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005''

What that basically means is:

* When an equation is < or > or ≤ or ≥ than something.
** E.g. x + 1 ≤ 3

=Linear Inequalities=

The only difference between solving linear inequalities and solving linear equations is that '>' or '<' replaces the '=' sign.

Also, if you multiply or divide by a negative number, you have to change the sign around.

====Example 1====

Solve -2x > 2

we start by dividing both sides by -2 to solve the inequality

x < -1

====Example 2====
Solving linear inequalities is almost exactly like solving linear equations.

* Solve x + 3 < 0.

If they'd given "x + 3 = 0", we would know how to solve: we would have subtracted 3 from both sides. The same applies here.

x < -3

Then the solution is:

x < –3

====Example 3====

* Solve x – 4 > 0.

If they'd given "x – 4 = 0", then we would can solve by adding four to each side. The same applies here.
x >= 4

Then the solution is: x > 4

====Example 4====

* Solve 2x < 9.

If they had given "2x = 9", we would have divided the 2 from each side.

x <= 9/2

Then the solution is: x < 9/2

====Example 5====

* Solve (2x – 3)/4 < 2.
First, multiply through by 4. Since the "4" is positive, we don't have to flip the inequality sign:

(2x – 3)/4 < 2
(4) × (2x – 3)/4 < (4)(2)
2x – 3 < 8
2x < 11
x < 11/2 = 5.5
====Example 6====

* Solve 10 < 3x + 4 < 19.

This is what is called a "compound inequality". It works just like regular inequalities, except that it has three "sides". So, for instance, when we go to subtract the 4, I will have to subtract it from all three "sides".

=10 < 3x + 4 < 19
=6 < 3x < 15
=2 < x < 5
====Example 7====
* Solve 5x + 7 < 3(x + 1).

First we multiply through on the right-hand side, and then solve as usual:

5x + 7 < 3(x + 1)
5x + 7 < 3x + 3
2x + 7 < 3
2x < –4
x < –2

=Tips=
If x ≥ y then 1/x ≤ 1/y

=Quadratic Inequalities=
references:

http://www.purplemath.com/modules/ineqquad.htm

http://www.analyzemath.com/Inequalities_Polynomial/quadratic_inequalities.html

====Example 1====

Solve <math>x^2-2x-15>0</math>

Treat it like a normal quadratic equation and find the zeroes
* <math>x^2-2x-15=0</math>
<math>(x-5)(x+3)=0</math>
x-5=0 or x+3=0
x=5 or -3

The zeroes divide the number line into three regions

<insert some kind of number line drawing here>

For region x>5, check for a number greater than 5 (eg.6).
*<math>(6)^2-2(6)-15>0</math>
9>0
All x-values greater than 5 will work.

For region x<-3, check for a number less than -3 (eg.-4).
*<math>(-4)^2-2(-4)-15>0</math>
9>0
All x-values less than -3 will work.

*Show answer using interval notation
<math>(-infinity,-3)U(5,infinity)</math>

====Example 2====

Solve <math>3x^2>-x+4</math>

Make one side equal to zero
*<math>3x^2+x-4>0</math>

Find the zeroes using the quadratic formula and factor

*(3x+4)(x-1)>0
3x+4=0 or x-1=0
x=<math>(-4/3)</math> or 1

The zeroes divide the number line into three regions

<insert some kind of number line drawing here>

For region x><math>(-4/3)</math>, check for a number greater than <math>(-4/3)</math> (eg.-2).
*<math>3(-2)^2+(-2)-4>0</math>
6>0
All x-values greater than <math>-4/3</math> will work.

For region x<-3, check for a number less than -3 (eg.-4).
*(3x+4)(x-1) =(3(-2)+4)((-2)-1)

*Show answer using interval notation
<math>(-infinity,-3)U(5,infinity)</math>

=Videos teaching Inequality=

Video 1. http://www.khanacademy.org/video/inequalities?playlist=Algebra%20I%20Worked%20Examples
- This video touches upon the concept of inequality and has a basic word problem solved.

Video 2. http://www.khanacademy.org/video/interpreting-inequalities?playlist=Algebra%20I%20Worked%20Examples
- This video is about interpreting inequalities in word problems.

Video 3. http://www.khanacademy.org/video/solving-inequalities?playlist=Algebra%20I%20Worked%20Examples
- This video is about solving basic problems regarding inequalities.

Video 4. http://www.khanacademy.org/video/inequalities-using-addition-and-subtraction?playlist=ck12.org%20Algebra%201%20Examples
- This video solves random question about inequalities with addition and subtraction.

Video 5. http://www.khanacademy.org/video/inequalities-using-multiplication-and-division?playlist=ck12.org%20Algebra%201%20Examples
- This video solves random question about inequalities with multiplication and division

Video 6. http://www.khanacademy.org/video/quadratic-inequalities?playlist=Algebra
- This video explains quadratic Inequalities.

File:14csb4g.png

2010-10-20T05:42:30Z

MariaFayloga: uploaded a new version of "File:14csb4g.png"

File:14csb4g.png

2010-10-20T05:38:00Z

MariaFayloga: uploaded a new version of "File:14csb4g.png"

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Homework 4

2010-10-20T05:34:53Z

MariaFayloga: /* Problem 3 */

Q1: Ellen

Q2: Kazi

Q3: Maria

Q4: Ali

Q5: Edith

==Problem 1==
'''Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?
* Tosh owns a cat,
* Bianca owns a frog that she loves,
* Jaela owns a parrot which keeps calling her "darling, darling",
* Jun owns a snake, don't mess with him,
* Suzan is the name of the frog,
* The cat is named Jun,
* The name by which they call the turtle is the name of the woman whose pet is Tosh,
* Finally, Suzan's mother's pet is Bianca.'''

---

From this question we can derive several general things:
* There are 5 people with 5 pets, and the pets cannot be named after their owners.
* One of the following 4 people are Suzan's mother: Tosh, Jun, Jaela or Bianca. (It cannot be Suzan herself)
* Be careful not to assume that Tosh and Jun are male.

From the clues we can see that:

* Tosh owns a cat - Jun
* Bianca owns a frog - Suzan
* Jaela owns a parrot - Tosh or Bianca
* Jun owns a snake - Tosh or Bianca
* Suzan owns a turtle (by elimination, the rest is given in the clues) - Jaela or Jun (Name of the woman whose pet is Tosh)

Suzan owns a turtle which:
* cannot be named Bianca, because Bianca is the name of Suzan's mother's pet
* cannot be named Jun, because that is the cat's name
* cannot be named Tosh, because the name of the turtle is the name of the woman whose pet is Tosh, and a pet cannot be named after its owner.

Hence, by elimination, the turtle is called Jaela.

"The name by which they call the turtle is the name of the woman whose pet is Tosh".
The turtle is called Jaela, therefore Jaela (the person) must own Tosh.
Jaela owns a parrot, therefore the parrot must be Tosh.

The only pet name left is Bianca. Therefore, by elimination, the name of the snake is Bianca.

"Suzan's mother's pet is Bianca". Hence, Suzan's mother must be Jun.

==Problem 2==
'''Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?'''

==Problem 3==
'''Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:
* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.'''

''Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).''

'''Adam'''
*cannot be:

the catcher unless he dislikes himself

an outfielder because it says he's either part of the battery or infield

shortstop

right or centre fielder because he's married

2nd baseman because he's already married and can't be engaged to Ed's sister

'''Ed'''
*cannot be the second baseman unless he is in an incestuous relationship and is engaged to his own sister

'''Mathieu'''
*cannot be the centre fielder because he is the shortest

''*only person that can be right fielder according to information given
''

'''Hassan'''
*cannot be an outfielder because it says he's either part of the battery or infield

third baseman

second baseman

catcher

right or centre fielder because he's married

'''Ed'''
*cannot be:

right

left

centre

(outfielder)

*because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman

'''Charles'''
*cannot be:

an outfielder because it says he's either part of the battery or infield

since he cannot be right or centre fielder, it means that he's married

2nd baseman because he's already married and can't be engaged to Ed's sister

pitcher since he won $20 from him at a poker game

'''Pascal'''
*cannot be:

shortstop

second baseman

catcher

right fielder

centre fielder

pitcher since he won $20 from him at a poker game

*because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman

'''Bobo'''
*cannot be:

second baseman

catcher

third baseman

shortstop

right fielder because he is the only person who can be centre fielder

''*only person that can be centre fielder according to information given
''

'''Sung'''
*is still married and, therefore, cannot be engaged to Ed's sister (yet)-->cannot be 2nd baseman
*cannot be right or centre fielder because he's married

'''Jason'''
*cannot be:

right fielder

centre fielder

*because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman
[[File:14csb4g.png‎ ]]

Using the information given, it can be concluded that only

Pascal and Sung can be the left fielder

Adam, Charles, Ed, Hassan, Pascal, and Sung can be the 1st baseman

Adam, Charles, and Sung can be the 3rd baseman

Charles, Ed, Hassan, and Sung can be the shortstop

Adam, Hassan, and Sung can be the pitcher

Charles and Sung can be the catcher

''Sung can be any of the remaining positions'', but Ed can only be the 1st baseman or the shortstop. Pascal can only be the left fielder or the 1st baseman. Charles is the only other person that can be the catcher.

If Sung is the shortstop, that means that Ed would have to be the 1st baseman, Pascal would have to be the left fielder, and Charles would have to be the catcher.
This leaves Hassan as the only person that can be the pitcher and Adam as the 3rd baseman.

* Adam is the third baseman
* Bobo is the centre fielder
* Charles is the catcher
* Ed is the first baseman
* Hassan is the pitcher
* Jason is the second baseman
* Mathieu is the right fielder
* Pascal is the left fielder
* Sung is the shortstop

==Problem 4==
'''Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?'''

==Problem 5==
'''Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.'''

*On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.
*On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.
*On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.
*In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.
*The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.
*No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

S = Salesman

D = Neighbour's dog

C = Construction Workers

Confirmed:

Sat: S

Sun: D

Mon: S+C

Tues: ?

Wed: S+D

Thurs: ?

Fri: ?

Sat: C

Sun: D

Important!

== //No one of the three noisemakers was quiet for three consecutive days

== //No pair of them made noise on more than one day during Homer's vacation

--> Then it means that there could be a pair of construction workers + dog on a certain day

// The construction worker has to bother Homer on Thursday .

// From above information, the salesman has to come by on Friday (as the last confirmed date he came by is Wednesday) as he can't come by on Thursday.

// The last time the dog barks is on Sunday so the dog has to bark on a day not past Thursday. But the above information states on pair makes noise for more than a day so the dog has to bark on Thursday. It will work as the construction workers and dog didn't combine their forces for any time in the confirmed information.

Chart:

Sat: S

Sun: D

Mon: S+C

Tues: ? ==> REST!!

Wed: S+D

Thurs: ? ==> C+D

Fri: ? ==> S

Sat: C

Sun: D

Then with all the combined information, the holiday day where Homer gets to sleep in has to be Tuesday.

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Homework 4

2010-10-20T04:12:21Z

MariaFayloga:

Hi guys, please choose whichever Q you want to do.

Q1: Ellen

Q2:

Q3: MF (Do I have to show how I got the answers?) - yeap.
OMG that was so fun! I totally didn't just die a little inside...

Q4:

Q5: Edith

==Problem 1==
'''Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?
* Tosh owns a cat,
* Bianca owns a frog that she loves,
* Jaela owns a parrot which keeps calling her "darling, darling",
* Jun owns a snake, don't mess with him,
* Suzan is the name of the frog,
* The cat is named Jun,
* The name by which they call the turtle is the name of the woman whose pet is Tosh,
* Finally, Suzan's mother's pet is Bianca.'''

Tosh owns a cat - Jun

Bianca owns a frog - Suzan

Jaela owns a parrot - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Jun owns a snake - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Suzan owns a turtle - Jaela or Jun (Name of the woman whose pet is Tosh)

==Problem 2==
'''Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?'''

==Problem 3==
'''Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:
* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.'''

''Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).''

'''Adam'''
*cannot be:

the catcher unless he dislikes himself

an outfielder because it says he's either part of the battery or infield

shortstop

right or centre fielder because he's married

2nd baseman because he's already married and can't be engaged to Ed's sister

'''Ed'''
*cannot be the second baseman unless he is in an incestuous relationship and is engaged to his own sister

'''Mathieu'''
*cannot be the centre fielder because he is the shortest

''*only person that can be right fielder according to information given
''

'''Hassan'''
*cannot be an outfielder because it says he's either part of the battery or infield

third baseman

second baseman

catcher

right or centre fielder because he's married

'''Ed'''
*cannot be:

right

left

centre

(outfielder)

*because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman

'''Charles'''
*cannot be:

an outfielder because it says he's either part of the battery or infield

since he cannot be right or centre fielder, it means that he's married

2nd baseman because he's already married and can't be engaged to Ed's sister

pitcher since he won $20 from him at a poker game

'''Pascal'''
*cannot be:

shortstop

second baseman

catcher

right fielder

centre fielder

pitcher since he won $20 from him at a poker game

*because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman

'''Bobo'''
*cannot be:

second baseman

catcher

third baseman

shortstop

right fielder because he is the only person who can be centre fielder

''*only person that can be centre fielder according to information given
''

'''Sung'''
*is still married and, therefore, cannot be engaged to Ed's sister (yet)-->cannot be 2nd baseman
*cannot be right or centre fielder because he's married

'''Jason'''
*cannot be:

right fielder

centre fielder

*because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman

Using the information given, it can be concluded that only

Pascal and Sung can be the left fielder

Adam, Charles, Ed, Hassan, Pascal, and Sung can be the 1st baseman

Adam, Charles, and Sung can be the 3rd baseman

Charles, Ed, Hassan, and Sung can be the shortstop

Adam, Hassan, and Sung can be the pitcher

Charles and Sung can be the catcher

''Sung can be any of the remaining positions'', but Ed can only be the 1st baseman or the shortstop. Pascal can only be the left fielder or the 1st baseman. Charles is the only other person that can be the catcher.

If Sung is the shortstop, that means that Ed would have to be the 1st baseman, Pascal would have to be the left fielder, and Charles would have to be the catcher.
This leaves Hassan as the only person that can be the pitcher and Adam as the 3rd baseman.

* Adam is the third baseman
* Bobo is the centre fielder
* Charles is the catcher
* Ed is the first baseman
* Hassan is the pitcher
* Jason is the second baseman
* Mathieu is the right fielder
* Pascal is the left fielder
* Sung is the shortstop

==Problem 4==
'''Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?'''

==Problem 5==
'''Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.'''

*On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.
*On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.
*On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.
*In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.
*The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.
*No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

S = Salesman

D = Neighbour's dog

C = Construction Workers

Confirmed:

Sat: S

Sun: D

Mon: S+C

Tues: ?

Wed: S+D

Thurs: ?

Fri: ?

Sat: C

Sun: D

Important!

== //No one of the three noisemakers was quiet for three consecutive days

== //No pair of them made noise on more than one day during Homer's vacation

--> Then it means that there could be a pair of construction workers + dog on a certain day

// The construction worker has to bother Homer on Thursday .

// From above information, the salesman has to come by on Friday (as the last confirmed date he came by is Wednesday) as he can't come by on Thursday.

// The last time the dog barks is on Sunday so the dog has to bark on a day not past Thursday. But the above information states on pair makes noise for more than a day so the dog has to bark on Thursday. It will work as the construction workers and dog didn't combine their forces for any time in the confirmed information.

Chart:

Sat: S

Sun: D

Mon: S+C

Tues: ? ==> REST!!

Wed: S+D

Thurs: ? ==> C+D

Fri: ? ==> S

Sat: C

Sun: D

Then with all the combined information, the holiday day where Homer gets to sleep in has to be Tuesday.

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Homework 4

2010-10-20T04:10:46Z

MariaFayloga:

Hi guys, please choose whichever Q you want to do.

Q1: Ellen

Q2:

Q3: MF (Do I have to show how I got the answers?) - yeap.

Q4:

Q5: Edith

==Problem 1==
'''Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?
* Tosh owns a cat,
* Bianca owns a frog that she loves,
* Jaela owns a parrot which keeps calling her "darling, darling",
* Jun owns a snake, don't mess with him,
* Suzan is the name of the frog,
* The cat is named Jun,
* The name by which they call the turtle is the name of the woman whose pet is Tosh,
* Finally, Suzan's mother's pet is Bianca.'''

Tosh owns a cat - Jun

Bianca owns a frog - Suzan

Jaela owns a parrot - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Jun owns a snake - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Suzan owns a turtle - Jaela or Jun (Name of the woman whose pet is Tosh)

==Problem 2==
'''Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?'''

==Problem 3==
'''Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:
* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.'''

''Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).''

'''Adam'''
*cannot be:

the catcher unless he dislikes himself

an outfielder because it says he's either part of the battery or infield

shortstop

right or centre fielder because he's married

2nd baseman because he's already married and can't be engaged to Ed's sister

'''Ed'''
*cannot be the second baseman unless he is in an incestuous relationship and is engaged to his own sister

'''Mathieu'''
*cannot be the centre fielder because he is the shortest

''*only person that can be right fielder according to information given
''

'''Hassan'''
*cannot be an outfielder because it says he's either part of the battery or infield

third baseman

second baseman

catcher

right or centre fielder because he's married

'''Ed'''
*cannot be:

right

left

centre

(outfielder)

*because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman

'''Charles'''
*cannot be:

an outfielder because it says he's either part of the battery or infield

since he cannot be right or centre fielder, it means that he's married

2nd baseman because he's already married and can't be engaged to Ed's sister

pitcher since he won $20 from him at a poker game

'''Pascal'''
*cannot be:

shortstop

second baseman

catcher

right fielder

centre fielder

pitcher since he won $20 from him at a poker game

*because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman

'''Bobo'''
*cannot be:

second baseman

catcher

third baseman

shortstop

right fielder because he is the only person who can be centre fielder

''*only person that can be centre fielder according to information given
''

'''Sung'''
*is still married and, therefore, cannot be engaged to Ed's sister (yet)-->cannot be 2nd baseman
*cannot be right or centre fielder because he's married

'''Jason'''
*cannot be:

right fielder

centre fielder

*because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman

Using the information given, it can be concluded that only

Pascal and Sung can be the left fielder

Adam, Charles, Ed, Hassan, Pascal, and Sung can be the 1st baseman

Adam, Charles, and Sung can be the 3rd baseman

Charles, Ed, Hassan, and Sung can be the shortstop

Adam, Hassan, and Sung can be the pitcher

Charles and Sung can be the catcher

''Sung can be any of the remaining positions'', but Ed can only be the 1st baseman or the shortstop. Pascal can only be the left fielder or the 1st baseman. Charles is the only other person that can be the catcher.

If Sung is the shortstop, that means that Ed would have to be the 1st baseman, Pascal would have to be the left fielder, and Charles would have to be the catcher.
This leaves Hassan as the only person that can be the pitcher and Adam as the 3rd baseman.

* Adam is the third baseman
* Bobo is the centre fielder
* Charles is the catcher
* Ed is the first baseman
* Hassan is the pitcher
* Jason is the second baseman
* Mathieu is the right fielder
* Pascal is the left fielder
* Sung is the shortstop

==Problem 4==
'''Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?'''

==Problem 5==
'''Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.'''

*On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.
*On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.
*On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.
*In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.
*The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.
*No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

S = Salesman

D = Neighbour's dog

C = Construction Workers

Confirmed:

Sat: S

Sun: D

Mon: S+C

Tues: ?

Wed: S+D

Thurs: ?

Fri: ?

Sat: C

Sun: D

Important!

== //No one of the three noisemakers was quiet for three consecutive days

== //No pair of them made noise on more than one day during Homer's vacation

--> Then it means that there could be a pair of construction workers + dog on a certain day

// The construction worker has to bother Homer on Thursday .

// From above information, the salesman has to come by on Friday (as the last confirmed date he came by is Wednesday) as he can't come by on Thursday.

// The last time the dog barks is on Sunday so the dog has to bark on a day not past Thursday. But the above information states on pair makes noise for more than a day so the dog has to bark on Thursday. It will work as the construction workers and dog didn't combine their forces for any time in the confirmed information.

Chart:

Sat: S

Sun: D

Mon: S+C

Tues: ? ==> REST!!

Wed: S+D

Thurs: ? ==> C+D

Fri: ? ==> S

Sat: C

Sun: D

Then with all the combined information, the holiday day where Homer gets to sleep in has to be Tuesday.

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Homework 4

2010-10-20T04:02:23Z

MariaFayloga: /* Problem 3 */

Hi guys, please choose whichever Q you want to do.

Q1: Ellen

Q2:

Q3: MF (Do I have to show how I got the answers?) - yeap.

Q4:

Q5: Edith

==Problem 1==
'''Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?
* Tosh owns a cat,
* Bianca owns a frog that she loves,
* Jaela owns a parrot which keeps calling her "darling, darling",
* Jun owns a snake, don't mess with him,
* Suzan is the name of the frog,
* The cat is named Jun,
* The name by which they call the turtle is the name of the woman whose pet is Tosh,
* Finally, Suzan's mother's pet is Bianca.'''

Tosh owns a cat - Jun

Bianca owns a frog - Suzan

Jaela owns a parrot - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Jun owns a snake - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Suzan owns a turtle - Jaela or Jun (Name of the woman whose pet is Tosh)

==Problem 2==
'''Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?'''

==Problem 3==
'''Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:
* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.'''

''Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).''

Adam
-cannot be:
the catcher unless he dislikes himself
an outfielder because it says he's either part of the battery or infield
shortstop
right or centre fielder because he's married
2nd baseman because he's already married and can't be engaged to Ed's sister

Ed
-cannot be the second baseman unless he is in an incestuous relationship and is engaged to his own sister

Mathieu
-cannot be the centre fielder because he is the shortest
'''-only person that can be right fielder according to information given'''

Hassan
-cannot be an outfielder because it says he's either part of the battery or infield
-cannot be
third baseman
second baseman
catcher
-cannot be right or centre fielder because he's married

Ed
-cannot be:
right
left
centre
(outfielder)
-because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman

Charles
-cannot be:
an outfielder because it says he's either part of the battery or infield
since he cannot be right or centre fielder, it means that he's married
2nd baseman because he's already married and can't be engaged to Ed's sister
pitcher since he won $20 from him at a poker game

Pascal
-cannot be:
shortstop
second baseman
catcher
right fielder
centre fielder
pitcher since he won $20 from him at a poker game
-because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman

Bobo
-cannot be:
second baseman
catcher
third baseman
shortstop
right fielder because he is the only person who can be centre fielder
'''-only person that can be centre fielder according to information given'''

Sung
-is still married and, therefore, cannot be engaged to Ed's sister (yet)-->cannot be 2nd baseman
-cannot be right or centre fielder because he's married

Jason
-cannot be:
right fielder
centre fielder
-because he's still a bachelor cannot have two legitimate children-->cannot be catcher or third baseman

Using the information given, it can be concluded that only

Pascal and Sung can be the left fielder

Adam, Charles, Ed, Hassan, Pascal, and Sung can be the 1st baseman

Adam, Charles, and Sung can be the 3rd baseman

Charles, Ed, Hassan, and Sung can be the shortstop

Adam, Hassan, and Sung can be the pitcher

Charles and Sung can be the catcher

''Sung can be any of the remaining positions'', but Ed can only be the 1st baseman or the shortstop. Pascal can only be the left fielder or the 1st baseman. Charles is the only other person that can be the catcher.

If Sung is the shortstop, that means that Ed would have to be the 1st baseman, Pascal would have to be the left fielder, and Charles would have to be the catcher.
This leaves Hassan as the only person that can be the pitcher and Adam as the 3rd baseman.

* Adam is the third baseman
* Bobo is the centre fielder
* Charles is the catcher
* Ed is the first baseman
* Hassan is the pitcher
* Jason is the second baseman
* Mathieu is the right fielder
* Pascal is the left fielder
* Sung is the shortstop

==Problem 4==
'''Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?'''

==Problem 5==
'''Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.'''

*On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.
*On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.
*On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.
*In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.
*The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.
*No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

S = Salesman

D = Neighbour's dog

C = Construction Workers

Confirmed:

Sat: S

Sun: D

Mon: S+C

Tues: ?

Wed: S+D

Thurs: ?

Fri: ?

Sat: C

Sun: D

Important!

== //No one of the three noisemakers was quiet for three consecutive days

== //No pair of them made noise on more than one day during Homer's vacation

--> Then it means that there could be a pair of construction workers + dog on a certain day

// The construction worker has to bother Homer on Thursday .

// From above information, the salesman has to come by on Friday (as the last confirmed date he came by is Wednesday) as he can't come by on Thursday.

// The last time the dog barks is on Sunday so the dog has to bark on a day not past Thursday. But the above information states on pair makes noise for more than a day so the dog has to bark on Thursday. It will work as the construction workers and dog didn't combine their forces for any time in the confirmed information.

Chart:

Sat: S

Sun: D

Mon: S+C

Tues: ? ==> REST!!

Wed: S+D

Thurs: ? ==> C+D

Fri: ? ==> S

Sat: C

Sun: D

Then with all the combined information, the holiday day where Homer gets to sleep in has to be Tuesday.

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Homework 4

2010-10-20T03:12:57Z

MariaFayloga:

File:14csb4g.png

2010-10-20T03:11:58Z

MariaFayloga:

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Homework 4

2010-10-20T03:11:28Z

MariaFayloga:

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Homework 4

2010-10-20T01:53:32Z

MariaFayloga:

Hi guys, please choose whichever Q you want to do.

Q1: Ellen

Q2:

Q3: MF (Do I have to show how I got the answers?)

Q4:

Q5:

==Problem 1==
'''Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?
* Tosh owns a cat,
* Bianca owns a frog that she loves,
* Jaela owns a parrot which keeps calling her "darling, darling",
* Jun owns a snake, don't mess with him,
* Suzan is the name of the frog,
* The cat is named Jun,
* The name by which they call the turtle is the name of the woman whose pet is Tosh,
* Finally, Suzan's mother's pet is Bianca.'''

Tosh owns a cat - Jun

Bianca owns a frog - Suzan

Jaela owns a parrot - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Jun owns a snake - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Suzan owns a turtle - Jaela or Jun (Name of the woman whose pet is Tosh)

==Problem 2==
'''Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?'''

==Problem 3==
'''Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:
* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.'''

''Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).''

* Adam is the third baseman
* Bobo is the centre fielder
* Charles is the catcher
* Ed is the first baseman
* Hassan is the pitcher
* Jason is the second baseman
* Mathieu is the right fielder
* Pascal is the left fielder
* Sung is the shortstop

==Problem 4==
'''Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?'''

==Problem 5==
'''Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.'''

*On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.
*On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.
*On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.
*In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.
*The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.
*No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

Course:MATH110/Archive/2010-2011/003/Homework/4

2010-10-20T01:48:44Z

MariaFayloga:

Here are the problems to work on for this week. These are harder than those of last week, I suggest making sure you try them before Tuesday night, especially if you split the work among yourselves, some might be a bit easier and some might need more than one brain to figure them out, so watch out, you've been warned.

==Problem 1==
Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?
* Tosh owns a cat,
* Bianca owns a frog that she loves,
* Jaela owns a parrot which keeps calling her "darling, darling",
* Jun owns a snake, don't mess with him,
* Suzan is the name of the frog,
* The cat is named Jun,
* The name by which they call the turtle is the name of the woman whose pet is Tosh,
* Finally, Suzan's mother's pet is Bianca.

==Problem 2==
Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?

==Problem 3==
Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:
* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.

''Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).''

==Problem 4==
Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?

==Problem 5==
Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.

On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.

On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.

On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.

In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.

The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.

No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

__NOTOC__

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Homework 4

2010-10-20T01:43:12Z

MariaFayloga:

Hi guys, please choose whichever Q you want to do.

Q1: Ellen

Q2:

Q3: MF

Q4:

Q5:

==Problem 1==
'''Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?
* Tosh owns a cat,
* Bianca owns a frog that she loves,
* Jaela owns a parrot which keeps calling her "darling, darling",
* Jun owns a snake, don't mess with him,
* Suzan is the name of the frog,
* The cat is named Jun,
* The name by which they call the turtle is the name of the woman whose pet is Tosh,
* Finally, Suzan's mother's pet is Bianca.'''

Tosh owns a cat - Jun

Bianca owns a frog - Suzan

Jaela owns a parrot - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Jun owns a snake - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Suzan owns a turtle - Jaela or Jun (Name of the woman whose pet is Tosh)

==Problem 2==
'''Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?'''

==Problem 3==
'''Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:
* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.'''

''Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).''

* Adam is the third baseman
* Bobo is the centre fielder
* Charles is the catcher
* Ed is the first baseman
* Hassan is the pitcher
* Jason is the second baseman
* Mathieu is the right fielder
* Pascal is the left fielder
* Sung is the shortstop

==Problem 4==
'''Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?'''

==Problem 5==
'''Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.'''

*On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.
*On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.
*On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.
*In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.
*The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.
*No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Homework 4

2010-10-20T01:20:10Z

MariaFayloga: /* Problem 3 */

Hi guys, please choose whichever Q you want to do.

Q1: Ellen

Q2:

Q3: MF

Q4:

Q5:

==Problem 1==
'''Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?
* Tosh owns a cat,
* Bianca owns a frog that she loves,
* Jaela owns a parrot which keeps calling her "darling, darling",
* Jun owns a snake, don't mess with him,
* Suzan is the name of the frog,
* The cat is named Jun,
* The name by which they call the turtle is the name of the woman whose pet is Tosh,
* Finally, Suzan's mother's pet is Bianca.'''

Tosh owns a cat - Jun

Bianca owns a frog - Suzan

Jaela owns a parrot - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Jun owns a snake - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Suzan owns a turtle - Jaela or Jun (Name of the woman whose pet is Tosh)

==Problem 2==
'''Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?'''

==Problem 3==
'''Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:
* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.'''

''Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).''

==Problem 4==
'''Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?'''

==Problem 5==
'''Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.'''

*On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.
*On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.
*On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.
*In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.
*The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.
*No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Homework 4

2010-10-20T00:55:56Z

MariaFayloga: /* Problem 3 */

Hi guys, please choose whichever Q you want to do.

Q1: Ellen

Q2:

Q3: MF

Q4:

Q5:

==Problem 1==
'''Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?
* Tosh owns a cat,
* Bianca owns a frog that she loves,
* Jaela owns a parrot which keeps calling her "darling, darling",
* Jun owns a snake, don't mess with him,
* Suzan is the name of the frog,
* The cat is named Jun,
* The name by which they call the turtle is the name of the woman whose pet is Tosh,
* Finally, Suzan's mother's pet is Bianca.'''

Tosh owns a cat - Jun

Bianca owns a frog - Suzan

Jaela owns a parrot - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Jun owns a snake - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Suzan owns a turtle - Jaela or Jun (Name of the woman whose pet is Tosh)

==Problem 2==
'''Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?'''

==Problem 3==
'''Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:
* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.'''

''Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).''

* Bobo is the centre fielder
* Jason is the second baseman
* Mathieu is the right fielder

==Problem 4==
'''Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?'''

==Problem 5==
'''Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.'''

*On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.
*On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.
*On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.
*In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.
*The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.
*No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?

Course:MATH110/Archive/2010-2011/003/Groups/Group 09/Homework 4

2010-10-19T04:28:04Z

MariaFayloga:

Hi guys, please choose whichever Q you want to do.

Q1: Ellen

Q2:

Q3: MF

Q4:

Q5:

==Problem 1==
'''Five persons named their pets after each other. From the following clues, can you decide which pet belongs to Suzan's mother?
* Tosh owns a cat,
* Bianca owns a frog that she loves,
* Jaela owns a parrot which keeps calling her "darling, darling",
* Jun owns a snake, don't mess with him,
* Suzan is the name of the frog,
* The cat is named Jun,
* The name by which they call the turtle is the name of the woman whose pet is Tosh,
* Finally, Suzan's mother's pet is Bianca.'''

Tosh owns a cat - Jun

Bianca owns a frog - Suzan

Jaela owns a parrot - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Jun owns a snake - Bianca or Tosh (Bianca if Jaela is Suzan's mother)

Suzan owns a turtle - Jaela or Jun (Name of the woman whose pet is Tosh)

==Problem 2==
'''Bohao, Stewart, Dylan, Tim and Chan are the five players of a basketball team. Two are left handed and three right handed, Two are over 2m tall and three are under 2m, Bohao and Dylan are of the same handedness, whereas Tim and Chan use different hands. Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. If you know that the one playing centre is over 2m tall and is left handed, can you guess his name?'''

==Problem 3==
'''Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:
* Adam does not like the catcher,
* Ed's sister is engaged to the second baseman,
* The centre fielder is taller than the right fielder,
* Hassan and the third baseman live in the same building,
* Pascal and Charles each won $20 from the pitcher at a poker game,
* Ed and the outfielders play cards during their free time,
* The pitcher's wife is the third baseman's sister,
* All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
* Pascal, Adam and the shortstop lost $100 each at the race track,
* The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
* Sung is in the process of getting a divorce,
* The catcher and the third baseman each have two legitimate children,
* Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
* The shortstop, the third baseman and Bobo all attended the fight,
* Mathieu is the shortest player of the team,
Determine the positions of each player on the baseball team.'''

''Note: On a baseball team there are three outfielders (right, centre and left), four infielders (first baseman, second baseman, third baseman and shortstop) and the battery (pitcher and catcher).''

==Problem 4==
'''Six players - Petra, Carla, Janet, Sandra, Li and Fernanda - are competing in a chess tournament over a period of five days. Each player plays each of the others once. Three matches are played simultaneously during each of the five days. The first day, Carla beats Petra after 36 moves. The second day, Carla was again victorious when Janet failed to complete 40 moves within the required time limit. The third day had the most exciting match of all when Janet declared that she would checkmate Li in 8 moves and succeeded in doing so. On the fourth day, Petra defeated Sandra. Who played against Fernanda on the fifth day?'''

==Problem 5==
'''Homer finally had a week off from his job at the nuclear power plant and intended to spend all nine days of his vacation (Saturday through the following Sunday) sleeping late. But his plans were foiled by some of the people who work in his neighbourhood.

On Saturday, his first morning off, Homer was wakened by the doorbell; it was a salesman of magazine subscriptions.

On Sunday, the barking of the neighbour's dog abruptly ended Homer's sleep.

On Monday, he was again wakened by the persistent salesman but was able to fall asleep again, only to be disturbed by the construction workers next door.

In fact, the salesman, the neighbour's dog and the construction workers combined to wake Homer at least once each day of his vacation, with only one exception.

The salesman woke him again on Wednesday; the construction workers on the second Saturday; the dog on Wednesday and on the final Sunday.

No one of the three noisemakers was quiet for three consecutive days; but yet, no pair of them made noise on more than one day during Homer's vacation. On which day of his holiday was Homer actually able to sleep late?'''

Course:MATH110/Archive/2010-2011/003/Groups/Group 09

2010-10-13T13:16:16Z

MariaFayloga:

Group members:
* Kazi Ahmed
* Edith Fan | xsaret@gmail.com
* Maria Fayloga | maria.fayloga@gmail.com
* Ali Hussein
* Ellen Tsang | ellentsang.nl@hotmail.com

<pre>I wrote something in the Discussion, please check it out. -- Ellen Tsang</pre>

=Homework 3, third part - Problem-Solving Skills=

==Q1==
'''A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.'''

The average speed for both the journey from the terminal to the airport and the journey from the airport back to the terminal is 30 mi/hr.
So why does one take 1 hour 20 min and the other take 80 min?

The time taken for the bus to travel from the terminal to the airport is:
1 hour = 60 min
1 hour 20 min = 60 + 20 = 80 min

This is the same as the time taken for the bus to travel from the airport back to the terminal, 80 min.

Hence, it can be concluded that the time taken to and back from the airport is the same, 80 min.

==Q2==
'''A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.'''

From this question we can note 3 things:
* The lady did not have her driver's license
* She failed to stop at a stop sign
* She went 3 blocks down a one-way street the wrong way
However, the policeman noted all this but did not stop her.

All of the above is assumed to be violations if the lady were driving, and the policeman should have stopped her.

However, the question never stated that she was driving.

Hence, the logical conclusion is that the lady was probably walking, running or some other similar method of travelling.

==Q3==
'''One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.'''

For example, the boxes are labelled:

BOX 1: APPLES

BOX 2: ORANGES

BOX 3: APPLES & ORANGES

We know all the boxes have incorrect labels, therefore the possibilites for what each box contains are:

BOX 1: ORANGES or APPLES & ORANGES

BOX 2: APPLES or APPLES & ORANGES

BOX 3: APPLES or ORANGES

If we take an apple out of BOX 3 (incorrectly labelled APPLES & ORANGES), it would have to be APPLES because it cannot be ORANGES (which obviously only contains oranges). So:

BOX 3 is APPLES.

If BOX 3 is actually APPLES, then BOX 2 cannot be APPLES. Hence:

BOX 2 is APPLES & ORANGES.

Then by elimination, since BOX 2 is APPLES & ORANGES:

BOX 1 is ORANGES (the only choice left).

==Q4==
'''I am the brother of the blind fiddler, but brothers I have none. How can this be?'''

The person reading this question may assume that the blind fiddler is male.

However, the blind fiddler's gender is not stated in the question.

Hence, the blind fiddler is probably female, so the 'I' in the question would have a sister, not a brother.

==Q5==
'''Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?'''

From the following diagrams, it can be seen that 1 rotation will bring the second coin (blue) halfway around the fixed coin (brown), and 2 rotations will bring the second coin (blue) to it's original position:

[[File:mathquarter1.jpg|400px]]
[[File:mathquarter2.jpg|400px]]
[[File:mathquarter3.jpg|400px]]
[[File:mathquarter4.jpg|400px]]
[[File:mathquarter5.jpg|400px]]

==Q6==
'''Three kinds of apples are all mixed up in a basket. How many apples must you draw (without looking) from the basket to be sure of getting at least two of one kind?'''

Answer= 4 apples. if we draw four apples, we would at least have one apple that is different than the rest ( assuming that we drew different apples each time).

==Q7==
'''Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting
(i) a pair of the same color, and (ii) a pair with different colors?'''

i) you can try by taking 3 socks. Within the 3 socks, two should be the same and one should be different.

ii) You can try by taking 3 socks. Within the three socks, there would be two that is different.

==Q8==
'''Reuben says, “Two days ago I was 20 years old. Later next year I will be 23 years old.” Explain how this is possible.'''

If his birthday is on the 31st of December. On the 30th of December he will be 2. On January 1st he says "Two days ago I was 20 years old. Later next year I will be 23 years old.” Later that year on december 31st he'll turn 22, so later next year he'll be 23.

==Q9==
'''A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?'''

If 10 rungs are showing with a interval of 1 ft, there should be 5 rungs showing with a tide of 5 ft.

==Q10==

'''Suppose one-half of all people are chocolate eaters and one-half of all people are women.
(i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.'''

(i)Yes. it does. say 1/2 of people eat chocolate * 1/2 of the people are women. therefore, 1/4 of all women are chocolate eaters.

(ii) Yes it does follow because assuming half of the people are men and half are women, it does follow the same conjecture of part 1.

==Q11==
'''A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?'''

Either the son or the daughter. This is because the mother and brother cant be twins since the brother is older.

==Q12==
'''A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation.'''

This happened because the trains to Brooklyn are minutes ahead of trains to Bronx and they arrive earlier though they take the same time; 10 minutes. since he takes the train that arrives first, he ends up rarely visiting his girl friend in Bronx, hence they broke up.

==Q13==
'''If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?'''

10 seconds. This is because the ratio 5 seconds to 5 spaced chimes is equal to 1. 5:5=1 then ten strikes with ten spaced chimes takes ten seconds

==Q14==
'''One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?'''

(i) There are six different ways of tagging two of the babies correctly and two incorrectly.

(ii) It is impossible to get three of the babies tagged correctly and one incorrectly since there are only four in number and if three are tagged correctly, then the remaining will obviously be tagged correctly also.

==Q15==
'''Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?'''

I would neither accept nor refuse, since there are 52 cards in a deck and consists of 26 red cards and 26 black cards. this is because the probability of getting red or blacks cards in the first half and second half is the same, 1/2.

==Q16==
'''Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?'''
Let:
D= number of daughters
S= number of sons

The daughter with the same number of brother and sisters also counts as another sister. Therefore, there is one less son than there are daughters:
S=D-1

"Each son has twice as many sisters as he has brothers" can be represented as:
D=2(S-1)

==Q17==
'''17. The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain.'''

I don't really know what's goin on here...but 105 kg-60 kg= 45 kg and 105 kg- 50 kg =55 kg and both those numbers give a reading that's 5 kg smaller than the number given when just one person steps on the scale.

So the scale gives readings that are higher?

==Q18==
'''18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?'''

If 1/3 is taken out each time, that means 2/3 is left in the jar each time. If you multiply the remaining 40 by 2/3's reciprocal, you should get the previous amount, since 2/3*3/2=1.

==Q19==
'''One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family?'''

To solve this question, I will put it into an algebraic formula.

Let:

M = total amount of milk consumed by Angela's family

C = total amount of coffee consumed by Angela's family

X = number of people in Angela's family

Angela drank 1/4 of the total amount of milk and 1/6 of the total amount of coffee, hence the first part of the formula would be:

M/4 + C/6

The rest of the formula is:

(M/4 + C/6)X = M + C

Because the amount of milk and coffee consumed by each individual person, (M/4 + C/6), has to be multiplied by the number of people, X.

And M + C is the total amount of milk and coffee consumed by the family.

Solving this equation, we get:

3M(X - 4) = 2C(6 - X)

Since M and C are both positive values, as you cannot consume negative amounts of anything, (X - 4) and (6 - X) also have to be positive.

The only possible solution for X is 5.

Therefore, the least number of people in Angela's family is 5.

==Q20==
'''20. Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart?'''

The clocks initially are 10 minutes apart.
There are 60 min/h, so for every 60 min that passes, the slower clock would be 10 min behind: 60/10.

==Q21==

Sven = middle of all runners so the total amount of runners should be odd -> middle of 7 is 4; but there is no middle of say, 8.

Dan is slower than Sven (in tenth place) so -> Sven > 10

Lars is in 16th place so Sven > Dan > 16

- assumed that Lars is not last as it was not stated explicitly in the question then the total runners > 16.

Therefore, the total number of runners has to be 17 because if the total number of runners exceed that, say, 19 then Sven would be number 20. However, that is not possible as the question states that he is slower than Sven at 10th place; Sven and Dan can not coexist in the same place number.

==Q22==

If we designate raining as R and sunny periods of time as S then we can make a simple table.

First, if it rains in the morning ---> afternoon is sunny

- rainy afternoon ---> sunny morning

Total R = 13

11 Sunny mornings

12 Sunny afternoons

Morn - R S S S S R R S S S S S R R S S R R

Noon - S S R R S S S R R S R S S S R S S S

^Sunny Mornings = 11

Sunny Noon = 12

Rainy = 13

--> Total days of vacation = 18

==Q23==

Products of age = 36

Oldest child = x

Second child = y

Third child = z

- then x * y * z = 36

Sum of all ages = a date

- then x + y + z = d ;; but d <= 31 (the largest amount of days in a month is 31)

A way to go about this question is to list every possibility that x, y and z will multiply to 36.

[[File:Tttable.png]]

The original question states that Paul didn't get it even though it the ages add up to a date. The table above shows that all of the sums (or dates) are unique so the only possibilities are ages 2, 2, 9 and ages 1, 6, 6. However, if we assume that the oldest child and the second are not the same age (or twins) then we can say that x > y => z. So it leaves that Paula's children are ages 2, 2 and 9 respectively.

==Q24==

Time taken for candle A to burn out = 6 hours

Time taken for candle B to burn out = 3 hours

And to solve the question, we can say that Candle A = 2*Candle B

If we assume time starts at 0 and 'burning of the candle' is constant then:

Candle A = 6 hours then it means it will burn 1/6 per hour

Candle B = same as above; it will burn 1/3 per hour

Then Candle A = (6-x)/6

Candle B = (3-x)/6

x = time in hours

- as stated above: Candle A = 2(Candle B)

Then if we calculate the two states of Candle B before it burns out and not at its full length:

<math>2((x-3)/3) = (6-x)/6</math>

<math>6(6-2x) = 3(6-x)</math>

<math>36-12x = 18-3x</math>

<math>18 = 9x</math>

<math>x = 2 hours</math>

So the time it takes for one of the candle to be half of the other candle is 2 hours.

==Q25==

Candle A has length L and is lit at 6 h.

Candle B has length (L + 1) and is lit at 4.5 h.

At 8.5 h, Candle A = Candle B

Candle A burns out at 10 h while Candle B burns out at 10.5 h. Then the total burning time of Candle A = 10-6 = 4h; Candle B = 10.5-4.5 = 6h.

Burning time till 8.5h for Candle A = 8.5 - 6 = 2.5h

Burning time till 8.5h for Candle B = 8.5 - 4.5 = 4h

let x = candle a length ;; aka. L

let y = candle b length

--> y = x+1

let b1 = burning constant for x

let b2 = burning constant for y

-> Candle A = Candle B at 8.5 h

<math>x-4*B1 = x+1-2.5B2</math>

--> x cancels out to

<math>4*B1 = 1-2.5B2</math>

---> What at B1 and B2 then?

<math>y=6B2</math> ;; at end time

<math>x=4B1</math> ;; at end time

<math> x = y</math>

<math>6B2 = 4B1 + 1</math> ;; the one comes from x+1

<math>B2 = (4B1+1)/6</math>

<math>B1 = (6B1-1)/4</math>
Using the above equations and substituting back into the original

---> <math>4*B2 = 1-2.5B1</math>

<math>4*B2 = 1-2.5((6B2-1)/4)</math>

<math>4*B2 = 1-((15B2-2.5)/4)</math>

<math>4(4B2-1) = 15B2-2.5</math>

<math>16B2-4 = 15B2-2.5</math>

<math>B2 = -2.5+4</math>

<math>B2=1.5</math> <-- plug in back to y=6B2

<math>4*((4B1+1)/6) = 1-2.5B1</math>

<math>B1=2</math> <-- plug in back to x = 4B1

<math> y = 6B2</math>

<math> y = 6(1.5) = 9</math>

<math> x = 4B1</math>

<math> x = 4(2) = 8</math>

Length of Candle B (longer candle) is 9 units and the length of the Candle A (shorter candle) is 8 units.

Course:MATH110/Archive/2010-2011/003/Groups/Group 09

2010-10-13T13:15:04Z

MariaFayloga:

Group members:
* Kazi Ahmed
* Edith Fan | xsaret@gmail.com
* Maria Fayloga | maria.fayloga@gmail.com
* Ali Hussein
* Ellen Tsang | ellentsang.nl@hotmail.com

<pre>I wrote something in the Discussion, please check it out. -- Ellen Tsang</pre>

=Homework 3, third part - Problem-Solving Skills=

==Q1==
'''A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.'''

The average speed for both the journey from the terminal to the airport and the journey from the airport back to the terminal is 30 mi/hr.
So why does one take 1 hour 20 min and the other take 80 min?

The time taken for the bus to travel from the terminal to the airport is:
1 hour = 60 min
1 hour 20 min = 60 + 20 = 80 min

This is the same as the time taken for the bus to travel from the airport back to the terminal, 80 min.

Hence, it can be concluded that the time taken to and back from the airport is the same, 80 min.

==Q2==
'''A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.'''

From this question we can note 3 things:
* The lady did not have her driver's license
* She failed to stop at a stop sign
* She went 3 blocks down a one-way street the wrong way
However, the policeman noted all this but did not stop her.

All of the above is assumed to be violations if the lady were driving, and the policeman should have stopped her.

However, the question never stated that she was driving.

Hence, the logical conclusion is that the lady was probably walking, running or some other similar method of travelling.

==Q3==
'''One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.'''

For example, the boxes are labelled:

BOX 1: APPLES

BOX 2: ORANGES

BOX 3: APPLES & ORANGES

We know all the boxes have incorrect labels, therefore the possibilites for what each box contains are:

BOX 1: ORANGES or APPLES & ORANGES

BOX 2: APPLES or APPLES & ORANGES

BOX 3: APPLES or ORANGES

If we take an apple out of BOX 3 (incorrectly labelled APPLES & ORANGES), it would have to be APPLES because it cannot be ORANGES (which obviously only contains oranges). So:

BOX 3 is APPLES.

If BOX 3 is actually APPLES, then BOX 2 cannot be APPLES. Hence:

BOX 2 is APPLES & ORANGES.

Then by elimination, since BOX 2 is APPLES & ORANGES:

BOX 1 is ORANGES (the only choice left).

==Q4==
'''I am the brother of the blind fiddler, but brothers I have none. How can this be?'''

The person reading this question may assume that the blind fiddler is male.

However, the blind fiddler's gender is not stated in the question.

Hence, the blind fiddler is probably female, so the 'I' in the question would have a sister, not a brother.

==Q5==
'''Two quarters rest next to each other on a table. One coin is held fixed while the second coin is rolled around the edge of the first coin with no slipping. When the moving coin returns to its original position, how many times has it revolved?'''

From the following diagrams, it can be seen that 1 rotation will bring the second coin (blue) halfway around the fixed coin (brown), and 2 rotations will bring the second coin (blue) to it's original position:

[[File:mathquarter1.jpg|400px]]
[[File:mathquarter2.jpg|400px]]
[[File:mathquarter3.jpg|400px]]
[[File:mathquarter4.jpg|400px]]
[[File:mathquarter5.jpg|400px]]

==Q6==
'''Three kinds of apples are all mixed up in a basket. How many apples must you draw (without looking) from the basket to be sure of getting at least two of one kind?'''

Answer= 4 apples. if we draw four apples, we would at least have one apple that is different than the rest ( assuming that we drew different apples each time).

==Q7==
'''Suppose you have 40 blue socks and 40 brown socks in a drawer. How many socks must you take from the drawer (without looking) to be sure of getting
(i) a pair of the same color, and (ii) a pair with different colors?'''

i) you can try by taking 3 socks. Within the 3 socks, two should be the same and one should be different.

ii) You can try by taking 3 socks. Within the three socks, there would be two that is different.

==Q8==
'''Reuben says, “Two days ago I was 20 years old. Later next year I will be 23 years old.” Explain how this is possible.'''

If his birthday is on the 31st of December. On the 30th of December he will be 2. On January 1st he says "Two days ago I was 20 years old. Later next year I will be 23 years old.” Later that year on december 31st he'll turn 22, so later next year he'll be 23.

==Q9==
'''A rope ladder hanging over the side of a boat has rungs one foot apart. Ten rungs are showing. If the tide rises five feet, how many rungs will be showing?'''

If 10 rungs are showing with a interval of 1 ft, there should be 5 rungs showing with a tide of 5 ft.

==Q10==

'''Suppose one-half of all people are chocolate eaters and one-half of all people are women.
(i) Does it follow that one-fourth of all people are women chocolate eaters? (ii) Does it follow that one-half of all men are chocolate eaters? Explain.'''

(i)Yes. it does. say 1/2 of people eat chocolate * 1/2 of the people are women. therefore, 1/4 of all women are chocolate eaters.

(ii) Yes it does follow because assuming half of the people are men and half are women, it does follow the same conjecture of part 1.

==Q11==
'''A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?'''

Either the son or the daughter. This is because the mother and brother cant be twins since the brother is older.

==Q12==
'''A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation.'''

This happened because the trains to Brooklyn are minutes ahead of trains to Bronx and they arrive earlier though they take the same time; 10 minutes. since he takes the train that arrives first, he ends up rarely visiting his girl friend in Bronx, hence they broke up.

==Q13==
'''If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?'''

10 seconds. This is because the ratio 5 seconds to 5 spaced chimes is equal to 1. 5:5=1 then ten strikes with ten spaced chimes takes ten seconds

==Q14==
'''One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?'''

(i) There are six different ways of tagging two of the babies correctly and two incorrectly.

(ii) It is impossible to get three of the babies tagged correctly and one incorrectly since there are only four in number and if three are tagged correctly, then the remaining will obviously be tagged correctly also.

==Q15==
'''Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?'''

I would neither accept nor refuse, since there are 52 cards in a deck and consists of 26 red cards and 26 black cards. this is because the probability of getting red or blacks cards in the first half and second half is the same, 1/2.

==Q16==
""Suppose that each daughter in your family has the same number of brothers as she has sisters, and each son in your family has twice as many sisters as he has brothers. How many sons and daughters are in the family?""
Let:
D= number of daughters
S= number of sons

The daughter with the same number of brother and sisters also counts as another sister. Therefore, there is one less son than there are daughters:
S=D-1

"Each son has twice as many sisters as he has brothers" can be represented as:
D=2(S-1)

==Q17==
""17. The zero point on a bathroom scale is set incorrectly, but otherwise the scale is accurate. It shows 60 kg when Dan stands on the scale, 50 kg when Sarah stands on the scale, but 105 kg when Dan and Sarah both stand on the scale. Does the scale read too high or too low? Explain.""

I don't really know what's goin on here...but 105 kg-60 kg= 45 kg and 105 kg- 50 kg =55 kg and both those numbers give a reading that's 5 kg smaller than the number given when just one person steps on the scale.

So the scale gives readings that are higher?

==Q18==
""18. Alice takes one-third of the pennies from a large jar. Then Bret takes one-third of the remaining pennies from the jar. Finally, Carla takes one-third of the remaining pennies from the jar, leaving 40 pennies in the jar. How many pennies were in the jar at the start?""

If 1/3 is taken out each time, that means 2/3 is left in the jar each time. If you multiply the remaining 40 by 2/3's reciprocal, you should get the previous amount, since 2/3*3/2=1.

==Q19==
'''One morning each member of Angela's family drank an eight-ounce cup of coffee and milk, with the (nonzero) amounts of coffee and milk varying from cup to cup. Angela drank a quarter of the total amount of milk and a sixth of the total amount of coffee. What is the least number of people in the family?'''

To solve this question, I will put it into an algebraic formula.

Let:

M = total amount of milk consumed by Angela's family

C = total amount of coffee consumed by Angela's family

X = number of people in Angela's family

Angela drank 1/4 of the total amount of milk and 1/6 of the total amount of coffee, hence the first part of the formula would be:

M/4 + C/6

The rest of the formula is:

(M/4 + C/6)X = M + C

Because the amount of milk and coffee consumed by each individual person, (M/4 + C/6), has to be multiplied by the number of people, X.

And M + C is the total amount of milk and coffee consumed by the family.

Solving this equation, we get:

3M(X - 4) = 2C(6 - X)

Since M and C are both positive values, as you cannot consume negative amounts of anything, (X - 4) and (6 - X) also have to be positive.

The only possible solution for X is 5.

Therefore, the least number of people in Angela's family is 5.

==Q20==
""20. Of two clocks next to each other, one runs 5 min per hour fast and the other runs 5 min per hour slow. At midnight the clocks show the same time. At what time are they are one hour apart?""

The clocks initially are 10 minutes apart.
There are 60 min/h, so for every 60 min that passes, the slower clock would be 10 min behind: 60/10.

==Q21==

Sven = middle of all runners so the total amount of runners should be odd -> middle of 7 is 4; but there is no middle of say, 8.

Dan is slower than Sven (in tenth place) so -> Sven > 10

Lars is in 16th place so Sven > Dan > 16

- assumed that Lars is not last as it was not stated explicitly in the question then the total runners > 16.

Therefore, the total number of runners has to be 17 because if the total number of runners exceed that, say, 19 then Sven would be number 20. However, that is not possible as the question states that he is slower than Sven at 10th place; Sven and Dan can not coexist in the same place number.

==Q22==

If we designate raining as R and sunny periods of time as S then we can make a simple table.

First, if it rains in the morning ---> afternoon is sunny

- rainy afternoon ---> sunny morning

Total R = 13

11 Sunny mornings

12 Sunny afternoons

Morn - R S S S S R R S S S S S R R S S R R

Noon - S S R R S S S R R S R S S S R S S S

^Sunny Mornings = 11

Sunny Noon = 12

Rainy = 13

--> Total days of vacation = 18

==Q23==

Products of age = 36

Oldest child = x

Second child = y

Third child = z

- then x * y * z = 36

Sum of all ages = a date

- then x + y + z = d ;; but d <= 31 (the largest amount of days in a month is 31)

A way to go about this question is to list every possibility that x, y and z will multiply to 36.

[[File:Tttable.png]]

The original question states that Paul didn't get it even though it the ages add up to a date. The table above shows that all of the sums (or dates) are unique so the only possibilities are ages 2, 2, 9 and ages 1, 6, 6. However, if we assume that the oldest child and the second are not the same age (or twins) then we can say that x > y => z. So it leaves that Paula's children are ages 2, 2 and 9 respectively.

==Q24==

Time taken for candle A to burn out = 6 hours

Time taken for candle B to burn out = 3 hours

And to solve the question, we can say that Candle A = 2*Candle B

If we assume time starts at 0 and 'burning of the candle' is constant then:

Candle A = 6 hours then it means it will burn 1/6 per hour

Candle B = same as above; it will burn 1/3 per hour

Then Candle A = (6-x)/6

Candle B = (3-x)/6

x = time in hours

- as stated above: Candle A = 2(Candle B)

Then if we calculate the two states of Candle B before it burns out and not at its full length:

<math>2((x-3)/3) = (6-x)/6</math>

<math>6(6-2x) = 3(6-x)</math>

<math>36-12x = 18-3x</math>

<math>18 = 9x</math>

<math>x = 2 hours</math>

So the time it takes for one of the candle to be half of the other candle is 2 hours.

==Q25==

Candle A has length L and is lit at 6 h.

Candle B has length (L + 1) and is lit at 4.5 h.

At 8.5 h, Candle A = Candle B

Candle A burns out at 10 h while Candle B burns out at 10.5 h. Then the total burning time of Candle A = 10-6 = 4h; Candle B = 10.5-4.5 = 6h.

Burning time till 8.5h for Candle A = 8.5 - 6 = 2.5h

Burning time till 8.5h for Candle B = 8.5 - 4.5 = 4h

let x = candle a length ;; aka. L

let y = candle b length

--> y = x+1

let b1 = burning constant for x

let b2 = burning constant for y

-> Candle A = Candle B at 8.5 h

<math>x-4*B1 = x+1-2.5B2</math>

--> x cancels out to

<math>4*B1 = 1-2.5B2</math>

---> What at B1 and B2 then?

<math>y=6B2</math> ;; at end time

<math>x=4B1</math> ;; at end time

<math> x = y</math>

<math>6B2 = 4B1 + 1</math> ;; the one comes from x+1

<math>B2 = (4B1+1)/6</math>

<math>B1 = (6B1-1)/4</math>
Using the above equations and substituting back into the original

---> <math>4*B2 = 1-2.5B1</math>

<math>4*B2 = 1-2.5((6B2-1)/4)</math>

<math>4*B2 = 1-((15B2-2.5)/4)</math>

<math>4(4B2-1) = 15B2-2.5</math>

<math>16B2-4 = 15B2-2.5</math>

<math>B2 = -2.5+4</math>

<math>B2=1.5</math> <-- plug in back to y=6B2

<math>4*((4B1+1)/6) = 1-2.5B1</math>

<math>B1=2</math> <-- plug in back to x = 4B1

<math> y = 6B2</math>

<math> y = 6(1.5) = 9</math>

<math> x = 4B1</math>

<math> x = 4(2) = 8</math>

Length of Candle B (longer candle) is 9 units and the length of the Candle A (shorter candle) is 8 units.

Course:MATH110/Archive/2010-2011/003/Groups/Group 09

2010-10-13T07:18:10Z

MariaFayloga: /* Homework 3, third part - Problem-Solving Skills */

Group members:
* Kazi Ahmed
* Edith Fan | xsaret@gmail.com
* Maria Fayloga | maria.fayloga@gmail.com
* Ali Hussein
* Ellen Tsang | ellentsang.nl@hotmail.com

=Homework 3, third part - Problem-Solving Skills=

==Q1==
'''A bus traveled from the terminal to the airport at an average speed of 30 mi/hr and the trip took an hour and 20 min. The bus then traveled from the airport back to the terminal and again averaged 30 mi/hr. However, the return trip required 80 min. Explain.'''

The average speed for both the journey from the terminal to the airport and the journey from the airport back to the terminal is 30 mi/hr.
So why does one take 1 hour 20 min and the other take 80 min?

The time taken for the bus to travel from the terminal to the airport is:
1 hour = 60 min
1 hour 20 min = 60 + 20 = 80 min

This is the same as the time taken for the bus to travel from the airport back to the terminal, 80 min.

Hence, it can be concluded that the time taken to and back from the airport is the same, 80 min.

==Q2==
'''A lady did not have her driver's license with her when she failed to stop at a stop sign and then went three blocks down a one-way street the wrong way. A policeman saw her, but he did not stop her. Explain.'''

From this question we can note 3 things:
* The lady did not have her driver's license
* She failed to stop at a stop sign
* She went 3 blocks down a one-way street the wrong way
However, the policeman noted all this but did not stop her.

All of the above is assumed to be violations if the lady were driving, and the policeman should have stopped her.

However, the question never stated that she was driving.

Hence, the logical conclusion is that the lady was probably walking, running or some other similar method of travelling.

==Q3==
'''One of three boxes contains apples, another box contains oranges, and another box contains a mixture of apples and oranges. The boxes are labeled APPLES, ORANGES and APPLES AND ORANGES, but each label is incorrect. Can you select one fruit from only one box and determine the correct labels? Explain.'''

For example:

BOX 1: APPLES

BOX 2: ORANGES

BOX 3: APPLES & ORANGES

We know all the boxes have incorrect labels, therefore the labels for the boxes are:

BOX 1: ORANGES or APPLES & ORANGES

BOX 2: APPLES or APPLES & ORANGES

BOX 3: APPLES or ORANGES

==Q11==
'''A woman, her older brother, her son, and her daughter are chess players. The worst player’s twin, who is one of the four players, and the best player are of opposite sex. The worst player and the best player have the same age. If this is possible, who is the worst player?'''

Either the son or the daughter

==Q12==
'''A Manhattan fellow had a girlfriend in the Bronx and a girlfriend in Brooklyn. He decided which girlfriend to visit by arriving randomly at the train station and taking the first of the Bronx or Brooklyn trains that arrived. The trains to Brooklyn and the Bronx each arrived regularly every 10 minutes. Not long after he began his scheme the man's Bronx girlfriend left him because he rarely visited. Give a (logical) explanation.'''

This happened because the trains to Brooklyn are minutes ahead of trains to Bronx and they arrive earlier though they take the same time; 10 minutes. since he takes the train that arrives first, he ends up rarely visiting his girl friend in Bronx, hence they broke up.

==Q13==
'''If a clock takes 5 seconds to strike 5:00 (with 5 equally spaced chimes), how long does it take to strike 10:00 (with 10 equally spaced chimes)?'''

10 seconds

==Q14==
'''One day in the maternity ward, the name tags for four girl babies became mixed up. (i) In how many different ways could two of the babies be tagged correctly and two of the babies be tagged incorrectly? (ii) In how many different ways could three of the babies be tagged correctly and one baby be tagged incorrectly?'''

(i) There are six different ways of tagging two of the babies correctly and two incorrectly.

(ii) It is impossible to get three of the babies tagged correctly and one incorrectly since there are only four in number and if three are tagged correctly, then the remaining will obviously be tagged correctly also.

==Q15==
'''Alex says to you, “I'll bet you any amount of money that if I shuffle this deck of cards, there will always be as many red cards in the first half of the deck as there are black cards in the second half of the deck.” Should you accept his bet?'''

ANS: I would neither accept nor refuse, since there are 52 cards in a deck and consists of 26 red cards and 26 black cards. this is because the probability of getting red or blacks cards in the first half and second half is the same, 1/2.

==Q16==

Let:
D= number of daughters
S= number of sons

The daughter with the same number of brother and sisters also counts as another sister. Therefore, there is one less son than there are daughters:
S=D-1

"Each son has twice as many sisters as he has brothers" can be represented as:
D=2(S-1)

==Q17==

I don't really know what's goin on here...but 105 kg-60 kg= 45 kg and 105 kg- 50 kg =55 kg and both those numbers give a reading that's 5 kg smaller than the number given when just one person steps on the scale.

So the scale gives readings that are higher?

==Q18==

If 1/3 is taken out each time, that means 2/3 is left in the jar each time. If you multiply the remaining 40 by 2/3's reciprocal, you should get the previous amount, since 2/3*3/2=1.

==Q19==
I don't get this one...

==Q20==

The clocks initially are 10 minutes apart.
60 min/h
60 min/10 min

==Q21==

Sven = middle of all runners so the total amount of runners should be odd -> middle of 7 is 4; but there is no middle of say, 8.

Dan is slower than Sven (in tenth place) so -> Sven > 10

Lars is in 16th place so Sven > Dan > 16

- assumed that Lars is not last as it was not stated explicitly in the question then the total runners > 16.

Therefore, the total number of runners has to be 17 because if the total number of runners exceed that, say, 19 then Sven would be number 20. However, that is not possible as the question states that he is slower than Sven at 10th place; Sven and Dan can not coexist in the same place number.

==Q22==

If we designate raining as R and sunny periods of time as S then we can make a simple table.

First, if it rains in the morning ---> afternoon is sunny

- rainy afternoon ---> sunny morning

Total R = 13

11 Sunny mornings

12 Sunny afternoons

Morn - R S S S S R R S S S S S R R S S R R

Noon - S S R R S S S R R S R S S S R S S S

^Sunny Mornings = 11

Sunny Noon = 12

Rainy = 13

--> Total days of vacation = 18

==Q23==

Products of age = 36

Oldest child = x

Second child = y

Third child = z

- then x * y * z = 36

Sum of all ages = a date

- then x + y + z = d ;; but d <= 31 (the largest amount of days in a month is 31)

A way to go about this question is to list every possibility that x, y and z will multiply to 36.

[[File:Tttable.png]]

The original question states that Paul didn't get it even though it the ages add up to a date. The table above shows that all of the sums (or dates) are unique so the only possibilities are ages 2, 2, 9 and ages 1, 6, 6. However, if we assume that the oldest child and the second are not the same age (or twins) then we can say that x > y => z. So it leaves that Paula's children are ages 2, 2 and 9 respectively.

==Q24==

Time taken for candle A to burn out = 6 hours

Time taken for candle B to burn out = 3 hours

And to solve the question, we can say that Candle A = 2*Candle B

If we assume time starts at 0 and 'burning of the candle' is constant then:

Candle A = 6 hours then it means it will burn 1/6 per hour

Candle B = same as above; it will burn 1/3 per hour

Then Candle A = (6-x)/6

Candle B = (3-x)/6

x = time in hours

- as stated above: Candle A = 2(Candle B)

Then if we calculate the two states of Candle B before it burns out and not at its full length:

<math>2((x-3)/3) = (6-x)/6</math>

<math>6(6-2x) = 3(6-x)</math>

<math>36-12x = 18-3x</math>

<math>18 = 9x</math>

<math>x = 2 hours</math>

So the time it takes for one of the candle to be half of the other candle is 2 hours.

==Q25==

Candle A has length L and is lit at 6 h.

Candle B has length (L + 1) and is lit at 4.5 h.

At 8.5 h, Candle A = Candle B

Candle A burns out at 10 h while Candle B burns out at 10.5 h. Then the total burning time of Candle A = 10-6 = 4h; Candle B = 10.5-4.5 = 6h.

Burning time till 8.5h for Candle A = 8.5 - 6 = 2.5h

Burning time till 8.5h for Candle B = 8.5 - 4.5 = 4h

let x = candle a length ;; aka. L

let y = candle b length

--> y = x+1

let b1 = burning constant for x

let b2 = burning constant for y

-> Candle A = Candle B at 8.5 h

<math>x-4*B1 = x+1-2.5B2</math>

--> x cancels out to

<math>4*B1 = 1-2.5B2</math>

---> What at B1 and B2 then?

<math>y=6B2</math> ;; at end time

<math>x=4B1</math> ;; at end time

<math> x = y</math>

<math>6B2 = 4B1 + 1</math> ;; the one comes from x+1

<math>B2 = (4B1+1)/6</math>

<math>B1 = (6B1-1)/4</math>
Using the above equations and substituting back into the original

---> <math>4*B2 = 1-2.5B1</math>

<math>4*B2 = 1-2.5((6B2-1)/4)</math>

<math>4*B2 = 1-((15B2-2.5)/4)</math>

<math>4(4B2-1) = 15B2-2.5</math>

<math>16B2-4 = 15B2-2.5</math>

<math>B2 = -2.5+4</math>

<math>B2=1.5</math> <-- plug in back to y=6B2

<math>4*((4B1+1)/6) = 1-2.5B1</math>

<math>B1=2</math> <-- plug in back to x = 4B1

<math> y = 6B2</math>

<math> y = 6(1.5) = 9</math>

<math> x = 4B1</math>

<math> x = 4(2) = 8</math>

Length of Candle B (longer candle) is 9 units and the length of the Candle A (shorter candle) is 8 units.

User:MariaFayloga

2010-09-20T05:59:48Z

MariaFayloga: Created page with 'I'm an Arts student.'

I'm an Arts student.