Course:MATH110/Archive/2010-2011/003/Groups/Group 11/Homework 4

Question 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.

So in this problem we will state who owns what pet and this could be done easily by looking at the information given

Jun owns snake Jaela owns a parrot Bianca owns a frog Tosh owns a cat Suzan owns the Turtle

Now we must give names to the pet to help clarify Jun's snake Jaela's parrot Bianca's frog is Suzan Tosh's cat name is jun Suzan' turtle

Given all that now we know that suzan's turtle can't be named Jun because it is the name of the cat, it can't be named suzan because it is the name of Bianca's frog, and Tosh.

Jun's snake is Bianca Jaela's parrot is Tosh Bianca's frog is suzan Tosh's cat is jun Suzan's is turtle is Jaela

Question 2

Using Polya's Method to organize the wording in this question, a solution can be found through the process of elimination. The goal: If the player at centre position is taller than 2m tall and left handed, who is he?

Taking the information given in the question and reworking it into the following we have: 5 players of a basketball team, Let B=Bohao, S=Stewart, D=Dylan, T=Tim and C=Chan.

2 are left handed and 3 are right handed. 2 are taller than 2m tall and and 3 are under 2m tall.

Polya's Method is helpful in translating the following excerpts of the question into simpler means.

"Bohao and Dylan are of the same handedness whereas Tim and Chan use different hands."

Translated: If T and C are different handedness and B and D are the same handedness, then B and D are right handed and either T or C is also right handed, keeping in mind out of these 5 players only 3 can be right handed. Already we can eliminate B and D as possibilities for the player at centre position because they are right handed and therefore do not satisfy the second quality of the centre position player being left handed. Our remaining possibilities are either T or C, whoever is not right handed.

Polya's Method is used again for the second part of the question.

"Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges."

Translated: If D and T are different height ranges and S and C are the same height range, then S and C are under 2m tall and either D or T is also under 2m tall, keeping in mind that only 3 out of the 5 players are shorter than 2m. Already we can eliminate S and C as possibilities for the player at centre position because they are under 2m tall and therefore do not satisfy the first quality of the centre position player being taller than 2m. Our remaining possibilities are either D or T, whoever is taller than 2m.

Summing up, we have Eliminated: B and D, S and C Remaining: T or C (from the first half of the question), D or T (from the second half of the question).

T occurs in both groups of remaining possibilities. D has already been eliminated as a possibility because he is right handed and C has been eliminated because he is shorter than 2m.

Conclusion: Tim plays centre position, he is left handed and taller than 2m.--BernadetteHii 17:53, 16 October 2010 (UTC)

Question 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).

Through a process of elimination based on the facts given above, the position of each player can be concluded as:

	Adam	Bobo	Charles	Ed	Hassan	Jason	Mathieu	Pascal	Sung
Right Outfielder	x	x	x	x	x	x	o	x	x
Center Outfielder	x	o	x	x	x	x	x	x	x
Left Outfielder	x	x	x	x	x	x	x	x	o
1st Baseman	x	x	x	x	x	x	x	o	x
2nd Baseman	x	x	x	x	x	o	x	x	x
3rd Baseman	o	x	x	x	x	x	x	x	x
Shortstop	x	x	x	o	x	x	x	x	x
Pitcher	x	x	x	x	o	x	x	x	x
Catcher	x	x	o	x	x	x	x	x	x

Some Clues I used to solve the problem are:

 - Adam can't be the catcher because he does not like the catcher
 - Ed can't be 2nd base
 - Mathieu can't be centre because he is the shortest player, and the centre fielder is taller than someone 
 - Hassan can't be the 3rd base because he lives in the same building as the third
 - Pascal and Charles can't be the pitcher 
 - Ed is not an oufielder
 - Pitcher, 3rd base, and catcher are married
 - right and centre and 2nd base (engaged) are bachelors
 - Ed, Pascal, Jason can't be right or centre 
 - Ed, Pascal, Jason can't be 3rd, Pitcher or Catcher 
 - Adam, Charles and Hassan are not outfielders 
        - therefore, out of the six infield and battery postiions, Adam, Charles, Hassan and Ed hold 4 
 - Pascal and Adam are not short stop
 - Hassan, Pascal, Bobo are not 2nd base or catcher
 - Sung is married can't be right, centre of 2nd base
 - Bobo is not short stop or 3rd base 
 - sung is part of the outfield because is taller than the battery and infielders 
 - Bobo is Centre field, therefore Mathieu is right, so Sung is Left 
 - Pascal is 2nd base because only a bachelor can be 2nd 
         - which leaves Pascal as the 1st base 
 - every other position can be determined from these facts

 - Right outfielder = Mathieu
 - Centre outfielder = Bobo
 - Left Outfielder = Sung
 - 1st Base = Pascal 
 - 2nd Base = Jason 
 - 3rd Base = Adam 
 - Shortstop = Ed
 - Pitcher = Hassan 
 - Catcher = charles

Question 4

The chart of the chess game is as follows;

The following chart shows Carla's game records;

For each day there are three possibilities. As shown above, there are three players Fernand could have played with for each day. If Carla was playing against Petra on the first day, the three combinations of players Fernand could have played with are Janet, Li and Sandra. When Carla beats Janet on the second day, the his three combination of players changed again to Li, Petra or Sandra. On the third day, Janet victoriously defeat Li, giving Fardanda a new 3 set of players he could have played with; Petra, Sandra or Carla. On the 4th day, Petra beat Sandra, hence the 3 possible players that would be playing with Fernanda that day would be Carla, Janet or Li . Once it has reaches the 5th day, all the players have at least played 5 times against each other and are in need of one more game to complete the tournament. If Sandra is playing with Li, Petra with Janet, then Fernanda must be playing with Carla on the fith day.

Question 5

With the given days he was disturbed already without applying the rule that no one of the noise makers could remain quiet for 3 consecutive days, the days Homer has to sleep has been narrowed down to Tuesday, Thursday and Friday. To narrow it down even more, between the wednesday and the second sunday, the dog has to have another day of waking Homer up with barking, following the rule of no silence for 3 consecutive days. Between the Monday and the saturday, the construction workers need at least 1 more day of disturbing Homer, during the week to satisfy the 3 consecutive days rule. This eliminates both thursday and friday with the previous 2 conditions as well as the next one. There are only 3 days available for there to be more than 2 waking him up on the same days, since there are only 3 pairs. Since monday was already eliminated by the doorbell and construction, and wednesday by the salesman and the dog. There remains only one more day where there are 2 of the disturbers available to wake homer. This day would either be thursday or friday. Hence Homer has tuesday and tuesday only to sleep in. Also to support this, the other necessary one that would need to make noise on tuesday would be the doorbell from the salesman, and since it is stated that he visits on Monday, Tuesday seems relatively free.