Course:MATH110/Archive/2010-2011/003/Groups/Group 02/Homework 4
Homework 4: Problem Solving
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.
From this question we can derive the following information: There are a total of five humans each owning one pet, that they have named afer each other. Meaning that Suzan's pet cannont be named Suzan. Tosh owns a cat, Bianca owns a frog, Jaela owns a parrot and Jun owns a snake. Since Suzan is the only person who is not given a pet in the clues we can find out that she is the owner of the turtle, through the process of elimination.
Thus:
Tosh owns a cat named Jun Bianca owns a frog named Suzan Jaela owns a parrot (name unknown- Bianca or Tosh) Jun owns a snake (name unknown- Bianca or Tosh) And Suzan owns a turtle (found out by process of elimination illustrated above)- name unknown
Below we figure out Suzan's turtle's name:
-We know that the name cannot be Bianca for it specifically states in the clues that Suzan's mother's pet is Bianca.
-Not Jun. (Mentioned in clues)
-Not Tosh because we cannont name the turtle after's it's namesake's pet. (Mentioned in clues.)
Therefore, the only possibility left is Jaela.
Since, the name by which they call the turtle (Jaela) is the name of the woman whose pet is Tosh (parrot, as we know Jaela owns a parrot from another clue) we can conclude that Jaela is the owner of a parrot.
Another clue states that Susan's mother pet is Bianca, therefore, she must be Jun (process of elimination).
The only pet name attatched to an animal is Bianca, and the only animal not been given a name is the snake. Therefore, it is safe to say that Bianca is a snake.
Conclusion:
Tosh owns a cat named after Jun
Bianca owns a frog named after Suzan
Jaela owns a parrot named after Tosh
Jun owns a snake named after Bianca
Suzan owns a turtle named after Jaela.
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?
We know that two people are left handed and three are right handed as well as that Bohao and Dylan are of the same handedness while Tim and Chan use different hands. Supposing Bohao and Dylan were left handed, there would already be two left handed people plus Tim or Chan has to be left handed because they use different hands, making a total of three left handed people on the team. This is wrong because the problem states that there are only two left handed people on the team. There are three right handed people on the team, so Bohao and Dylan must be right handed. This is true because Tim and Chan have different handedness, so one of them must also be right handed, making a total of three right handed people on the team.
We also know that Stewart and Chan are of the same height range, while Dylan and Tim are in different height ranges. Supposing that Stewart and Chan are over 2m tall, Dylan or Tim must also be over 2m tall because these two are in different height ranges. This cannot be true because the problem states that only two are over 2m tall. Therefore, Stewart and Chan must be under 2m, allowing Dylan or Tim to also be under 2m, making a total of three people under 2m.
We now know that Bohao and Dylan are both right handed, which eliminates their chances of being the centre player. We also know that Stewart and Chan are under 2m tall, which elminates their chances of being the centre player. Finally, we can conclude that Tim is the centre player that is over 2m tall and left handed.
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).''
This question took me a reallllllly long time. There are a few things to keep in mind:
1. Don't assume anything (all the facts are there)
2. If someone has a wife, that means their marrid (sung is married)
3. Don't assume that Ed and the outfielders were present at the poker game
4. It might help if you tart off with a table like this:
I followed these steps to get to the solution. Here we go:
Hassan and the third basemen live in the same building
Therefore Hassan is not the third basemen
Pascal and Charles won $20 some the pitcher at the poker game
Pascal and Charles are not the pitcher
Ed and outfielder play cards on their free time
So Ed is not an outfielder
The pitchers wife is the third baseman’s sister
So the pitcher is married
All battery and infield except Charles Hassan and Adam are shorter then Sung
Charles Hassan and Adam are part of the battery and infield. Not making them outfielders
Pascal Adam and Shortstop lose $100 at the race track
Therefore Pascal and Adam are not shortstop
The second basemen 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
Meaning that Sung is married (he still has a wife and can’t be considered a bachelor)
The catcher and the third basemen each have two legitimate children
Making the catcher and the third basemen married
From all this information, it is concluded that: Ed, Pascal, Jason, right fielder and the outfield center are bachelor
Ed, Pascal, Jason, the right field and the center field are bachelors
That means Ed, Pascal and Jason are not the right fielder and center fielder
From the information we can say that: the outfield right, the infield second and the outfield center are bachelors.
The infield third, the pitcher and the catcher are married.
Ed is not the infield third the pitcher or the catcher.
Jason is no the infield third the pitcher or the catcher.
Sung is not out field right out field center and infield second
The third basemen, the shortstop and Bobo attended the fight
Concluding that Bobo is not the shortstop or the third baseman.
Mathieu is the shortest player of the team
Meaning that Mathieu cannot be center field because it is stated that the center fielder is taller than the right fielder
(We crossed Mathieu out of this position earlier on, just double checking)
Following all these steps we can conclude that Bobo is the outfield center. So Bobo is not any of the other positions
From this elimination, we can find that Mathieu is outfield right. This eliminates him from the rest of the positions
We can conclude that Bobo is a bachelor because he is outfield center
We can conclude that Mathieu is a bachelor because he is outfield right
Only a bachelor can be infield second so that leaves us with Jason.
Jason is the infield second and is eliminated from the other positions
We can conclude that Adam, Charles, Hassan, Sung are married
Sung is the outfield left because he is not the battery or the infield since they are shorter than him.
Eliminating the rest of the people being outfield left.
When this elimination is made: Pascal is the infield first. This eliminates everyone else from that position.
When this elimination is made: Ed is the infield shortstop this means that no one else is shortstop.
This eliminates everyone from short stop.
When this elimination is made: Hassan is the pitcher. This means no one else can be the pitcher.
When this happens we can conclude that Adam is the infield third. So everyone is eliminated from the position
So…. Charles is the catcher.
ADAM= infield third
CHARLES= battery catcher
HASSAN= battery pitcher
PASCAL= infield first
ED= infield shortstop
JASON= infield second
SUNG= outfield left
BOBO= outfield center
MATHEIU= outfield right
THIS IS A LOT OF INFORMATION.... but at the end you feel soooooo good :)
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?
Petra=P Carla=C Janet=J Sandra=S Li=L Fernanda=F On the fourth day, P plays with S, J can only play with F since J played with L and C before. Get (P,S),(J,F),(L,C). On the first day, C plays with P, J can only play with S since J played with L and F before. Get (P,C),(J,S),(L,F). On the third day, J plays with L, P can only play with F since P played with S and C before. Get(P,F),(J,L),(S,C). On the second day, C plays with J, P can only play with L since P played with S and F before. Get (P,L),(J,C),(S,F). Then the schedule for the fifth day must be (F,C),(S,L),(J,P) Thus,Fernanda plays with Carla.
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? ' 1. Character Symbols C= Construction Workers D = Neighbor's dog S = Salesman
2. Diagram Confirming the Days Homer was Awoken :
Sat: S
Sun: D
Mon: S+C
Tues: ?
Wed: S+D
Thurs: ?
Fri: ?
Sat: C
Sun: D
3. Key Information to keep in mind. a) Not one of the 3 noisemakers were quiet for 3 consecutive days
b)No pair of the noisemakers made noise on more than 1 day during Homer's holiday, which means that
there could be a pair of the dog+construction workers on a certain day.
c)The construction worker has to annoy Homer on Thursday.
d) From the information listed above, the salesman has to come by on Friday, since the last stated day he came was on Wednesday. He could not come by on Thursday.
e) The last time the dog makes a sound is on Sunday so the dog has to bark on a day prior to Thursday. But due to conflicting information, the dog has to bark on Thursday. It should work as the construction workers and dog did not combine their forces for any time in the given information.
4. Chart:
Sat: S
Sun: D
Mon: S+C
Tues: Rest
Wed: S+D
Thurs: C+D
Fri: S
Sat: C
Sun: D
5. Conclusion The vacation day where Homer gets to sleep has to be Tuesday.