Course:MATH110/Archive/2010-2011/003/Groups/Group 10/Homework 4

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.

""In the problem we know the following information:

That tosh owns a cat named Jun, Bianca owns a frog named Suzan, Jaela owns a parrot named Tosh, Jun owns a snake named Bianca and Suzan owns a turtle named Jaela.

We can deduce this information because:

We know that Tosh owns a cat. Therefore, we know Tosh’s animal. We know that her cat is named Jun, because it states that the cat is named Jun.

Furthermore, it states Bianca owns a frog. Therefore, we know Bianca’s animal is a frog, and it says that Suzan is the name of the frog.

The next three people are harder.

Jaela has a parrot and we are given the clue that it keeps on calling her darling.

Jun has a snake, who you shouldn’t mess with.

The name that they call the turtle is named after who has Tosh as their pet.

Suzan’s mother’s pet is Bianca.

Therefore, we need to find out which pet does Suzan’s mother have and Suzan’s mother in order to fill in the missing clue. There are four candidates to choose for Suzan’s mother, Tosh, Bianca, Jaela and Jun. Because Tosh is Jaela’s parrot, which we can deduce from the clues, we know then that Suzan’s turtle is rather Jaela or Bianca, but because the name that they call the turtle is named after who has Tosh as their pet then Suzan has a turtle named Jaela because Jaela has a parrot named Tosh leaving Jun to have a snake name Bianca.

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?

2 - Left Handed 3 - Right Handed 2 - Over 2m Height 3 - Under 2m Height Bohao + Dylan = Same Hand Tim + Chan = Different Hand Stuart + Chan = Same Height Dylan + Tim = Different Height

This problem can be approached by making assumptions with respect to the two individuals with the same height or same hand, and then testing if they can be true. For example:

Assume Bohan and Dylan are both Left Handed. Then, Tim, Chan and Stuart must be right-handed. This is a contradiction as Tim and Chan must have a different hand. Therefore, Bohan and Dylan are both right handed.

Next, assume Stuart and Chan are both over 2m height. Then, Tim, Dylan and Bohan must all be under 2m height. This is also a contradiction as Dylan and Tim must have a different height. Therefore, Stuart and Chan are both under 2m height.

The categorization of players can then be shown to be as follows:

Left Handed - One of Tim or Chan Right Handed- Bohan, Dylan and one of Tim or Chan Over 2m Height- One of Dylan and Tim Under 2m Height- Stuart and Chan

It can therefore be shown that the only possible player to be over 2m height AND left handed is Tim. (based on the fact that the uncertainty of Dylan possibly being over 2m height and Chan possibly being left handed is irrelevant since neither are capable of having both features).

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?

Let C= Carla, P= Petra, J=Janet, S=Sandra, L=Li and F= Fernanda The first match is CP but at the same time it is possible for JS, JF/LS, LF/ FS to have a match, let's assume JS and LF are playing against each other here. The second match consists of CJ and a possibility of the following pairings PL, PF/ LS,/ and FS. We assume that PL and FS play simultaneous to CJ. The third match is J against L, while the possible matches are PS, PF/ CS we assume that PF and CS play against each other. The fourth match is P against S and the possible matches at the same time are CL and JF. By the fifth match only Carla is left who has not played against Fernanda.

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 order to have come to this answer the problem must have been analysed. Based on the problem given we can immediately rule out the first Saturday,Sunday,Monday,Wednesday and the following Saturday and Sunday. This is because Homer is waken in all of these days. This leaves us with the Tuesday,Thursday and Friday however the problem also mentions that none of the noisemakers was quiet for three consecutive days and no pair made noise on more than one day. Looking at this we can slowly rule out each noisemaker based on which days they have already waken Homer. The construction workers would have waken Homer up on Thursday since none were quiet for three straight days while the Dog may have waken Homer on either Thursday,Friday or Saturday. This leaves us with the Salesman who must have waken Homer up on Friday since, like the other noisemakers it cannot be silent for 3 consecutive days. This leaves Tuesday free of any obstructions.