Course:MATH110/Archive/2010-2011/003/Homework/4

Here are the problems to work on for this week. These are harder than those of last week, I suggest making sure you try them before Tuesday night, especially if you split the work among yourselves, some might be a bit easier and some might need more than one brain to figure them out, so watch out, you've been warned.

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.

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?

Problem 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).

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?

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?