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

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.

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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.

Yay, picture!

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?

Breaking Down the question - 5 players; Bohao, Tim, Dylan, Chan and Stewart - 2 left handed 3 right handed - 2 are >2m -3 are <2m

Bohao and Dylan-same hand ( Right) Tim and Chan- different hands (one either right or left) Dylan and Tim- Different hands. (Right/Left) Stewart and Chan- same height Bohao and dylan have same hands whereas Tim and Chan don't. Therefore, bohao and Dylan and EITHER Tim or Chan are right handed. Stewart and Chan have the same height and Dylan and Tim don't, Implying Stewart and Chan and Either Tim and Dylan are under 2m tall.

We can break the information down to each player--

Bahao- Right handed, over 2m. Chan- EITHER left/right, Under 2m. Stewart- Left handed EITHER greater than/under 2m. Dylan- Right Handed, EITHER greater than/under 2m. Tim- Either Right/left, EITHER Greater Than/under 2m.

Our objective is to find the player in the center who is left handed and >2m.

This objective eliminates Bahao, Dylan ( for being right handed), Chan (for being under 2m) which keeps Stewart and Tim.. Stewart gets eliminated because stewart and Chan have less than 2m height.

Therefore, Tim is the player who is in the center with left hand and more than 2m of height.

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?

Carla played against Fernanda on the fifth day. This is clearly shown by the following list:

Taking into account the matches given, assume the other matches were also played. Then this gives the information above. Therefore the answer is Carla.

(Note: 'Fernando' is meant to be 'Fernanda' in the table. Typo, sorry.)

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.