Course:MATH110/Archive/2010-2011/003/Groups/Group 15/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. Jaela owns a parrot. Jun owns a snake. 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.

Polya’s law is about ways to tackle a problem successfully so it should apply here as well. Step one: Read the question carefully. The question, when broken down, implicitly asks us two questions in place of one, because they both need to be answered before we can answer the original question. They are:

1. Who is Suzan’s mother?
2. What pet does Suzan’s mother own? (which is also the “ultimate” question)

From reading the question we are already given a useful clue. That is, Suzan’s mother, must not be Suzan. We can forget about Suzan and narrow the list of five candidates down to four (though this doesn't prove particularly useful for the problem at hand as you will be able to see). We then work down the list of other clues, basically taking them, a better description wanting, at face value (and easy, too!). By simple logic we know that Suzan’s pet is a turtle (because it is the only pet left without an owner). So we get the following data in the form of a sorted table (Polya’s Step 2: Plan and map out your strategy in a chart, table, graph, etc.).

We then try to find out the name of Suzan’s turtle. It is the name of the person whose pet is called Tosh. Tosh can be Jaela’s parrot or Jun’s snake, but not Tosh’s cat nor Bianca’s frog. (It cannot be Suzan’s turtle either unless the question is playing tricks with our head... A rather dumb trick that would be too, wouldn’t it?) So, if we express this in our table:

So, is it Jaela or Jun? Do we have enough data to determine that yet? ( Step 1: Identify if enough data is given to solve the problem) Turns out we do. Jun cannot be Suzan’s turtle’s name, because we already know that Tosh’s cat is called Jun. Therefore, the turtle’s name must be Jaela.

That leaves two more unknowns on our table to be determined: the names of Jaela’s parrot and Jun’s snake. They can only be either Tosh / Bianca (because that’s the only two names left – simple!) To find the next clue, we re-visit the original clues – it is important to revisit the question since as you are reading anything, as more information emerges the original material seems to present new meanings as you read it again because now you can read into deeper layers of meaning with additional perspective. So, since the turtle’s name is also the name of the woman who’s pet is Tosh, and Jaela being the turtle’s name, we conclude that the name of Jaela’s parrot is Tosh. That leaves Jun’s pet, whose name must be Bianca.

I believe you can now confidently answer the original question, which is “what pet belongs to Suzan’s mother”. We know from the beginning that Suzan’s mother’s pet is Bianca. When we look for Bianca in the table we’ve drawn up to tackle the problem, we can answer with a lot of confidence that Suzan’s mother is Jun, and perhaps more importantly (to answer the question directly), Suzan’s mother’s pet is a snake ("don't mess with him")...apparently a boy snake with a girly name!

Question 2

Bohao, Tim, Dylan, Chan and Stewart

5 players

3 of them are right handed 2 of them are left handed

3 of them are under 2m 2 of them are over 2m

We are looking for the centre player who is left handed and also over 2m.

-Tim or Chan must be right handed, because Dylan and Bohao are both right handed and Stewart is left handed. -Bohao is over 2m tall so this means that either Dylan or Tim must be the same height as Chan and Stewart who are both under 2m. -You can already see a common trend developing, the fact that we are trying to find both the variables for Tim's height as well as his handedness. -This then narrows down to Dylan and TIm to be over 2m -Dylan is right handed though

This leads us to the conclusion that Tim is the centre player because he is the only valid option, Dylan who is over 2m is right handed and therefor does not fit the description.

Question 3

Adam, Bobo, Charles, Ed, Hassan, Jason, Mathieu, Pascal, and Sung have formed a basketball team. The facts are in BOLD and their interpretations after them:

Adam does not like the cather, -The catcher isnt adam Ed's sister is engaged to the second baseman, -ED isnt the second baseman The center fielder is taller than the right fielder, -Look at last point Hassan and the third baseman live in the same building, -Hassan aint the third baseman Pascal and Charles each won $20 from the pitcher at a poker game, -Pascal and Charles are not the pitcher Ed and the outfielders play cards during their free time, -ED is not an outfielder The pitcher's wife is the third baseman's sister, -The pitcher is married All the battery and infield except Charles, Hassan and Adam are shorter than Sung, -Charles, Hassan and Adam are not the outfielder but could be the battery or infield Pascal, Adam and the shortstop lost $100 each at the race track, -Pascal and Adam are not the shortstop The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards, -So Pascal, Hassan and Bobo are not the second basemen and the catcher Sung is in the process of getting a divorce, -Sung is married The catcher and the third baseman each have two legitimate children, -They are both married Ed, Pascal, Jason, the right fielder and the center 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 The shortstop, the third baseman and Bobo all attended the fight, -Bobo is neither the shortstop or the third baseman Mathieu is the shortest player of the team, -So he is obviously not the center fielder

If you plot all of the above on a table you find out that:

Catcher = Charles First Baseman = Ed Center Fielder = Bobo Pitcher = Hassan Second Baseman = Jason Right Fielder = Mathieu Left Fielder = Pascal Shortstop = Sung 3rd Baseman = Adam

Question 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?

1). First of all we sort out the details given by the question: 6 players-> P, C, J, S, L and F.

Tournament= 5 days

->each player plays each of others ONCE.

->3 matches are played in 5 days

Therefore, we know that 2 people play against each other in each day.

1st day: C vs P ( C wins) J,S,L,F

2nd day: C vs J ( C wins) P,S,L,F

3rd day: J vs L (J wins) P,C,S,F

4th day: P vs S (P wins) C,J,L,F

5th day: F vs ???

Then, we use the info given, try to pair the unknown ones up:

1st day: CP, ( JS, LF )

2nd day: CJ, ( PL, SF)

3rd day: JL, ( PF, CS)

4th day: PS, ( CL, JF)

5th day: F havn't played with C according to the info above.

Therefore, Fernanda is playing against Carla on the 5th day.

Question 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? First, We notice that: Saturday --> Salesman Sunday --> Dog Monday --> Salesman/Construction Tuesday --> ? Unknown? Wednesday - Salesman/Dog Thursday --> ? Unknown? Friday --> ?unknown? Saturday --> Construction Sunday --> Dog

By following the rule : “No one of the three noisemakers was quiet for three consecutive days” and “no pair of them made noise on more than one day” Tuesday, Thursday and friday are all unknown. As we can see we could put it like below.

Saturday --> Salesman Sunday --> Dog Monday --> Salesman + Construction Tuesday --> Sleep in. Wednesday - Salesman + Dog Thursday --> Construction Friday --> Salesman Saturday --> Construction Sunday --> Dog