Course:MATH110/Archive/2010-2011/003/Groups/Group 08/PROBLEM SOLVING QUESTIONS 1-5 HW4
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.
Solving Problem 1: Found in links below
Page 1: http://wiki.ubc.ca/File:Math_1.JPG
Page 2: http://wiki.ubc.ca/File:Math1_continued.JPG
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?
Solving Problem 2: Found in link below
Page 1: http://wiki.ubc.ca/File:Math_110_Group_HW_Oct_20.png
Problem 3
1.Adam does not like the catcher,
2.Ed's sister is engaged to the second baseman,
3.The centre fielder is taller than the right fielder,
4.Hassan and the third baseman live in the same building,
5.Pascal and Charles each won $20 from the pitcher at a poker game,
6.Ed and the outfielders play cards during their free time,
7.The pitcher's wife is the third baseman's sister,
8.All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
9.Pascal, Adam and the shortstop lost $100 each at the race track,
10.The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
11.Sung is in the process of getting a divorce,
12.The catcher and the third baseman each have two legitimate children,
13.Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
14.The shortstop, the third baseman and Bobo all attended the fight,
15.Mathieu is the shortest player of the team,
Find out the positions of all of the players on the baseball team.
Solving Problem 3:
""In the beginning, we assume all of them have the possibility to be any positions.""
1st =Adam Ed Hassan Pascal Charles Sung Bobo Jason Mathieu
2nd = Adam Ed Hassan Pascal Charles Sung Bobo Jason Mathieu
3rd = Adam Ed Hassan Pascal Charles Sung Bobo Jason Mathieu
Short Stop = Adam Ed Hassan Pascal Charles Sung Bobo Jason Mathieu
Left = Adam Ed Hassan Pascal Charles Sung Bobo Jason Mathieu
Centre = Adam Ed Hassan Pascal Charles Sung Bobo Jason Mathieu
Right = Adam Ed Hassan Pascal Charles Sung Bobo Jason Mathieu
Catcher = Adam Ed Hassan Pascal Charles Sung Bobo Jason Mathieu
Pitcher = Adam Ed Hassan Pascal Charles Sung Bobo Jason Mathieu
""Then, we cancel out the possibilities by the given statements.""
1.Adam does not like the catcher,
2.Ed's sister is engaged to the second baseman,
3.The centre fielder is taller than the right fielder,
4.Hassan and the third baseman live in the same building,
5.Pascal and Charles each won $20 from the pitcher at a poker game,
6.Ed and the outfielders play cards during their free time,
7.The pitcher's wife is the third baseman's sister,
8.All the battery and infield except Charles, Hassan and Adam are shorter than Sung,
9.Pascal, Adam and the shortstop lost $100 each at the race track,
10.The second baseman beat Pascal, Hassan, Bobo and the catcher at billiards,
11.Sung is in the process of getting a divorce,
12.The catcher and the third baseman each have two legitimate children,
13.Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married
14.The shortstop, the third baseman and Bobo all attended the fight,
15.Mathieu is the shortest player of the team,
""In club 13, we know that Ed, Pascal Jason, the right fielder and the centre fielder are bachelors, the others are all married. so, now we can cancel out more possibilities.""
""In clue 3, the centre fielder is taller than the right fielder - clue 16 Adam is shorter than Bobo. Bobo is therefore the centre fielder and Adam the right fielder.""
Catcher = Charles - MARRIED
Pitcher = Hassan - MARRIED
Short Stop = Ed - BACHELOR
1st = Pascal - BACHELOR
2nd = Jason- BACHELOR
3rd = Adam- MARRIED
Left = sung- MARRIED
Centre = Bobo- BACHELOR
Right = Mathieu - BACHELOR
so, we can conclude that
Catcher = Charles
Pitcher = Hassan
Short Stop = Ed
1st = Pascal
2nd = Jason
3rd = Adam
Left = sung
Centre = Bobo
Right = Mathieu
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?
Solving Problem 4: Found in links below
Page 1: http://wiki.ubc.ca/File:Math_110_Group_HW_Oct_200001.png
Page 2: http://wiki.ubc.ca/File:Math_110_Group_HW_Oct_200002.png
Page 3: http://wiki.ubc.ca/File:Math_110_Group_HW_Oct_200003.png
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?
Solving Problem 5:
The given information tells us that his first saturday he was awakened by a salesmen, sunday was dog barking, monday was the salesman and construction workers. On wednesday it was the salesman and dog barking, saturday was the construction workers and on the final sunday it was the dog barking. First make a chart so the information is easier to see and understand.
Saturday-Salesman
Sunday-dog barking
Monday-salesman and construction workers
Tuesday-
Wednesday-salesman and dog barking
Thursday-
Friday-
Saturday-construction workers
Sunday-dog barking
So far we know that Friday, Thursday and Tuesday are the only days that he could have possibly slept in on. The last set of information tells us that 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. We then look at the 3 sets of 3 consecutive days and make sure that there are the three noisemakers within the first set of 3 consecutive days, the second set and the third set. We also look at how no pair of them made noise on more than one day during the vacation.
Saturday-Salesman
Sunday-dog barking
Monday-salesman and construction workers
Tuesday-
Wednesday-salesman and dog barking
Thursday-
Friday-
Saturday-construction workers
Sunday-dog barking
By using deductive reasoning we see that on friday Homer was awakened by the salesman because within the 3 consecutive days the salesmen was the only one that hadn't woken him yet. On thursday the construction workers woke him because within the 3 consecutive days they were th ones who had yet to awake him. we know this because on the first 3 consecutive days (sat, sun and mon) the salesman, dog barking and construction workers woke him. Therefore, tuesday is the only day in which Homer could sleep in on his vacation.
Saturday-Salesman
Sunday-dog barking
Monday-salesman and construction workers
Tuesday-
Wednesday-salesman and dog barking
Thursday-construction workers
Friday-salesman
Saturday-construction workers
Sunday-dog barking