Course:MATH110/Archive/2010-2011/003/Groups/Group 12/Homework/hw4

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.

Solution

Given the premises, let's state what we know so far.

We can observe that almost all the members own a pet.

Tosh owns a Cat named Jun; Bianca owns a Frog named Suzan; Jaela owns a Parrot; and Jun owns a Snake.

Now the question is, which pet does Suzan own? Since all the other members own a pet, the only pet with an unaccounted owner is the Turtle, so it is reasonable to conclude that Suzan is the owner of the Turtle.

We can also conclude the following:
1) Bianca is a female because the statement describes that SHE loves the frog.
2) Jaela is a female because the statement describes that the Parrot keeps calling HER "darling, darling".
3) Tosh's owner is a female because the statement describes that the Turtle shares the same name of the WOMAN whose pet is Tosh.
4) Jun is a male because the statement states "don't mess with HIM", which is referring to Jun and not the Snake.

It is also of great importance to state what pets are what.
5) Cat -> Jun
6) Frog -> Suzan
7) Parrot -> ?
8) Snake -> ?
9) Turtle -> ?

Now a question arises, what are the names of these animals? Tosh has to be the Parrot because of (3). We already know the name of Bianca's pet and from (3) we can eliminate Suzan's pet as a possibility for being named Tosh because of the fact that the Turtle shares the same name of the woman whose pet is Tosh. So... the Parrot has to be named Tosh. Revising (7) we now get:

7) Parrot -> Tosh

From this conclusion, we can also state that the Turtle is named Jaela because of (3), since the Turtle shares the same name of the woman whose pet is Tosh. Revising (9) we now get:

9) Turtle -> Jaela

Since the Snake is the only pet that remains unnamed, we know that the Snake must be named Bianca. Revising (8) we now get:

8) Snake -> Bianca

Given these conclusions, we can safely conclude that Jun belongs to Suzan's mother.

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?

Solution

Bohao, Stewart, Dylan, Tim, and Chan

2 = left handed, 3 = right handed
2 = over 2m tall, 3 = under 2m tall

Bohao, Stewart = same handedness
Tim, Chan = different handedness

Since we know that Bohao and Stewart are the same handedness and Tim and Chan are of different handedness then it is clear that Bohao and Stewart are right handed because Tim or Chan would join their category.

Stewart, Chan = same height
Dylan, Tim = different height

Since we know that Stewart and Chan are the same height and Dylan and Tim are different heights then it is clear that Stewart and Chan are under 2m tall because Dylan or Tim would join their category.

So if Tim were to be right handed then:

Bohoa, Stewart, Tim = right handed
Chan, Dylan = left handed

Stewart, Chan, Tim = under 2m tall
Dylan, Bohoa = over 2m tall

Meaning that Dylan would be the player who is left handed and over 2m tall. The reason why we know that Dylan is over 2m tall is because the players who have not been categorized are Tim, Dylan and Bohao and knowing Dylan is the only left handed player that is not defined, he is defined as over 2m tall.

But if Chan were to be right handed:

Bohoa, Stewart, Chan = right handed
Tim, Dylan,

Stewart, Chan, Dylan = under 2m tall
Tim, Bohoa = over 2m tall

Meaning that Tim would be the player who is left handed and over 2m tall. The reason why we know that Tim is over 2m tall is becausee the player who have not been categorized are Tim, Dylan, and Bohao and knowing Tim is the only left handed player that is not defined, he is defined as over 2m tall.

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).

Solution

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal and Sung have formed a baseball team. The following facts are true:

1) Adam does not like the catcher

Adam is not the catcher

Step 1
2) Ed's sister is engaged to the second baseman

Ed is not the second baseman

Step 2
3) The centre fielder is taller than the right fielder
4) Hassan and the third baseman live in the same building

Hassan is not the third baseman

Step 4
5) Pascal and Charles each won $20 from the pitcher at a poker game

Pascal and Charles are notthe pitcher

Step 5
6) Ed and the outfielders play cards during their free time

Ed is not an outfielder

Step 6
7) The pitcher's wife is the third baseman's sister

The pitcher is married

Step 7
8) All the battery and infield except Charles, Hassan and Adam are shorter than Sung

Charles, Hassan, and Adam could be either a battery or a infielder
Charles, Hassan, and Adam are not outfielder

Step 8
9) Pascal, Adam and the shortstop lost $100 each at the race track

Pascal and Adam is not the shortstop

Step 9
10 The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards

Pascal, Hassan, Bobo is neither the catcher or the second basemen

Step 10
11) Sung is in the process of getting a divorce

Sung is married

Step 11
12) The catcher and the third baseman each have two legitimate children

The catcher and the third baseman are both married

Step 12
13) Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married

Ed, Pascal, Jason right fielder, center fielder are all not married.
Ed, Pascal, Jason are neither the right fielder or center fielder.
The pitcher the catcher are married
- Ed is not the third basemen, the pitcher, or the catcher
- Jason is not the third basemen, the pitcher, or the catcher
- Sung is not the right outfield, the out field center, or second basemen

Step 13
14) The shortstop, the third baseman and Bobo all attended the fight

Bobo is not the shortstop or the third basemen

Step 14
15) Mathieu is the shortest player of the team

Mathieu is not the center field since center fielder is taller then in the right fielder

Step 15
16) Bobo is now narrowed down to the Center Outfield.

Bobo is not married because he is Center Outfield

17) Now that we have identified BoBo as the Center Outfield this allows us to identify Mathieu as the Right Outfield

Mathieu is not married because he is Right Outfield

18) Jason is Second Baseman

Only a bachelor can be a second baseman

19) Adam, Charles, Hassan, and Sung are married
20) Sun is Left Outfield

Sung is not battery or infield since he is taller then both the batteries and infielders

21) Pascal is first baseman
22) Ed is shortstop
23) Hassan is the pitcher
24) Adam is third baseman
25) Charles is the catcher
Last Step

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?

Solution

From the description, we know that Carla had a match against Petra. We also know that there are three matches played at the same time during each of the five days. So, from these statements, we know that these matches could be a possibility:

Janet vs Sandra
Janet vs Fernanda
Sandra vs Li
Sandra vs Fernanda
Fernanda vs Li

On the second day, we know that Carla had a match against Janet. Leaving us with these possible match-ups:

Petra vs Janet
Petra vs Li
Petra vs Fernanda
Sandra vs Li
Sandra vs Fernanda
Fernanda vs Li

On the third day, we know that Janet had a match against Li. Leaving us with these possible match-ups:

Petra vs Li
Petra vs Fernanda
Carla vs Sandra
Carla vs Li
Carla vs Fernanda
Sandra vs Li
Sandra vs Fernanda
Fernanda vs Li

On the fourth day, we know that Petra had a match against Sandra. Leaving us with these possible match-ups:

Carla vs Li
Carla vs Fernanda
Janet vs Petra
Janet vs Fernanda
Li vs Fernanda

Using the possible match-ups above, we can conclude the following possible match-ups:

Day One

Janet vs Sandra (This possible match-up only exists on Day 1)
Fernanda vs Li (This possible match-up exists across all four days whereas other possible match-ups don't. Since this is universal, it has the be this match-up)

Day Two

Petra vs Li (This possible match-up exists up until Day 4, so this match-up has to occur either on this day or the next; whether on this day or the next does not matter)
Sandra vs Fernanda (This possible match-up exists up until Day 4, so this match-up has to occur either on this day or the next; whether on this day or the next does not matter)

Day Three

Petra vs Fernanda (Has to occur because this match-up does not exist on Day 4.)
Carla vs Sandra (Has to occur because this match-up does not exist on Day 4.)

Day Four

Fernanda vs Janet (Remaining match-ups from information given)
Carla vs Li (Remaining match-ups from information given)

From the listed match-ups above, we can safely conclude that Carla had the match against Fernanda because of the face that each member plays each other once.

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?

Solution

homer%20simpson.jpg

The given information of what wakes up Homer is:

Saturday: Annoying Salesman
Sunday: Barking Dog
Monday: Noisy Construction
Tuesday: ___
Wednesday: Annoying Salesman/ Barking DogM
Thursday: ____
Friday: ___
Saturday: Noisy Construction
Sunday: Noisy Construction

Since, “no one of the three noise makers was quiet for three consecutive days, this means that Homer must have woken up early on Friday (Friday, Saturday, Sunday = three consecutive days). So Homer was able to sleep in on his Holiday in either Tuesday or Thursday because Wednesday cannot be left by itself.