Course:MATH110/Archive/2010-2011/003/Groups/Group 17/Problem Solving 2

Problem Set 2

Question 1

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. The question is asking, which pet belongs to Suzan's mother? - we can figure this out by connecting the names of the different pets to their owners as the pets are all named after these individuals First: the info from the question: Tosh has a cat named Jun Bianca has a frog named Susan Jaela has a parot named - ? Jun has a snake named ? Suzans owns a turtle named ? Suzans mother cannot be susan(susans mother cannot be her daughter...), or Bianca (Susan's mother's pet name is Bianca) Tosh has a cat named Jun Bianca has a frog named Susan Jaela has a parot named - (Bianca or Tosh) Jun has a snake named (Jaela, Bianca or Susan) Suzans owns a turtle named (Tosh or Jaela) The only way the question satisfies all points is if : Tosh has a cat named Jun Bianca has a frog named Susan Jaela has a parot named - Tosh Jun has a snake named Bianca Suzans owns a turtle named Jaela Therefore: Susans mother is Jun and she owns a snake

Question 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?

So, we need to find out who on the team is over 2m tall and left-handed.

Looking at the information about the players, we see that there are 3 right-handers and two left-handers. We know that Bohao and Dylan are the same handedness, while Tim and Chan are different. This tells us that either Tim or Chan have the same handedness as both Bohao and Dylan. This means that Bohao and Dylan must be right-handed, since they are in a group of 3 people that share the same hand.

Looking at height, we can use the same deduction. There are three people under 2m tall and two over 2m tall. If Stewart and Chan are of the same size, and Dylan and Tim are different, then we know that Stewart and Chan are in a group of three people, and therefore must be under 2m tall.

Finally, we need someone who is over 2m and left-handed. Bohao and Dylan are out, since they are right-handed. Chan and Stewart are out, since they are under 2m tall. From the list of 5 players, the only remaining player is Tim. Therefore, Tim is our centerman.

BenJeffery

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).

	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

The graph above depicts with "x's" and "o's" the correct placement of each player on the baseball field. "X" being were they aren't and "o" being where they are...obviously.

Here are some of the facts that I derived from the statements the question gave us to come up with an answer.

Hassan is not the third baseman because he lives with the third baseman.

Ed is not the 2nd baseman because his sister is engaged to the second baseman.

Adam is not the catcher because he does not like the catcher.

Mathieu is not the center fielder because the center fielder is taller than the right fielder. Mathieu is the shortest of them all.

Pitcher has wife, therefore it can’ t be Ed, Pascal Jason, the right fielder and the centre fielder

Pascal and Adam aren’ t shortstop because both of them and the shortstop lost 100$ at the race track

Pascal, Hassan, Bobo cant be the second baseman or catcher because the second baseman beat Pascal, Hassan, Bobo, and the catcher at billiards

All the battery and infield except Charles, Hassan and Adam are shorter than Sung, Therefore, Charles, Hassan, and Adam are either battery or infield

Pascal and Charles can’ t be the pitcher because they won money from him at a poker game

Ed can’ t be an outfielder because he plays cards with them

This list would go on and on, but you get the idea. MarcoGasparian

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?

During the 9 days of vacation, Homer will be able to sleep on Tuesday. In coming to this conclusion I analyzed the problem creating a chart of the 9 days Homer had vacation and simply listed the days he had been disturbed in his sleep. According to the problem Homer was awaken on the first Saturday,Sunday,Monday,Wednesday and the following Saturday and Sunday. This leaves us with Tuesday,Thursday, and Friday. A quick detail in the problem states, "no one of the three noisemakers was quiet for three consecutive days". Considering that the construction worker and the salesman do not have a consecutive three in the days of Thursday and Friday those days were ruled out leaving Tuesday to be the only day Homer got too sleep late. AviHarry