Course:MATH110/Archive/2010-2011/003/Groups/Group 16/Homework 4

Homework 4 - due Wednesday October 20

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.

First it is important to state all the information we know:

Pet owners:

-Tosh (male)

-Bianca (female)

-Jaella (female)

-Jun (male)

-Suzan (female)

Note: we are able to conclude the owners genders by looking for gender indicating words. For example in the phrase "Bianca owns a frog that she loves", we can can conclude that Bianca is a female because it states that SHE loves her frog.

Pet owners and their pets: (Note: the pets names are in the parentheses)

Tosh -> cat (Jun)

Bianca -> frog (Suzan)

Jaella -> parrot

Jun -> snake

Suzan -> turtle

Note: The only pet not assigned to an owner is the turtle, therefore it is logical that the turtle is Suzan's pet

Note: Keep in mind that Suzan's mother's pets name is Bianca

We can make some further conclusions from the information provided in the question. Conclusions:

1)

-The name of the turtle will be a female owner of the pet Tosh. This is concluded from the phrase "The name by which they call the turtle is the name of the woman whose pet is Tosh"

-> because it is a woman, we recognize that the turtles name will be a females name

-> the turtle will have the name of the pet Tosh's owner

In effect of conclusion 1, we can recognize the name of Suzans turtle to be Janella. This can be done because all the friends names have been used as pets names except; Janella and Tosh. Therefore since the turtles name must be a females name we can conclude the turtles name is Janella.

Following we can conclude that Janella's pet parrot's name is Tosh since it states that "The name by which they call the turtle is the name of the woman whose pet is Tosh".

Therefore adding these new discoveries to our previous knowledge we can update our information.

Pet owners and their pets: (Note: the pets names are in the parentheses)

Tosh -> cat (Jun)

Bianca -> frog (Suzan)

Jaella -> parrot (Tosh)

Jun -> snake

Suzan -> turtle (Janella)

Therefore, since the snake is the only pet that has not been named and the name Bianca has not been assigned, we can conclude that Jun's snakes name is Bianca. Following, it is imperative to remember the Bianca is the snake,meaning the snake is the pet that belongs to Suzan's mother.

Hence, the snake named Bianca is Suzan's mother's pet.

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?

Based on the clues for handedness, we know that one of tim or chan must be the same handedness as Bahao and Dylan, who must be right handed. This means that Stewart must be a Lefty. Based on the clues for height, we know that Dylan or Tim must be the same height as Stewart and Chan, who must be under 2m tall. This means that Bahao must be over 2m tall

The only lefty we know is under 2m, and the only person we know over 2m is a righty. We know that dylan or tim must be over 2m, but Dylan is a righty. So the only way their is a lefty over 2m is if it is Tim

His name is Tim

Problem 3

This problem is quite difficult to map out so I will phrase it exactly how I did while finding solutions because that is what worked for me. In this exercise, the more we know about a particular person the better; however it could be possible that one person be suitable for more than one position and vice versa.

Adam: not a catcher, battery or infield, not shortstop

Bobo: not a catcher, not 3rd baseman, not shortstop, not 2nd baseman

Charles: not pitcher, could be outfielder, battery or infield

Ed: not 2nd baseman, not outfielder, not catcher, not 3rd baseman, bachelor, could be shortstop or 1st baseman

Hassan: not 3rd baseman, could be battery or infielder, not catcher, not 2nd baseman, could be either 1st baseman, shortstop, pitcher

Jason: not 3rd baseman, not catcher, bachelor. Jason is the 2nd baseman.

Matthieu: not centre field, shortest in height of the team

Pascal: not pitcher, could be outfielder, not shortstop, not catcher, not 2nd baseman, 3rd baseman, not right fielder, not centre fielder, bachelor. Pascal is the left outfielder.

Sung: married, not right fielder, not centre fielder, not left fielder, not 2nd baseman.

Important notes:

There are 5 bachelor, 4 married men, the catcher, the 3rd baseman and the pitcher are married.

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?

"SOLUTION"

Thanks to the information we are given, we know the players of one of the 3 matches played on Day 1 : CARLA vs PETRA. Consequently, we can randomly pair up JANET vs SANDRA and FERNANDA vs LI. This way, every player plays only one match a day, always against someone they haven't played against before. To summarize:

DAY 1:

CARLA vs PETRA JANET vs SANDRA FERNANDA vs LI

Again, thanks to the information we are given, we know the players of one of the 3 matches played on Day 2: CARLA vs JANET. We can pair up again the other 4 players, making sure that each player plays one and only one match a day with one other player (without repeating matches played in the previous days).

DAY 2:

CARLA vs JANET SANDRA vs FERNANDA LI vs PETRA

For Day 3, we know one of the 3 matches played simultaneously: JANET vs LI. We can pair up the other 4 players, making sure each of them plays against a new player they haven't faced before.

DAY 3:

JANET vs LI FERNANDA vs PETRA CARLA vs SANDRA

For Day 4, we know one of the 3 matches played simultaneously: PETRA vs SANDRA. Again, we pair up the other 4 players, making sure they are playing against someone they haven't played against before.

DAY 4:

PETRA vs SANDRA JANET vs FERNANDA LI vs CARLA

For Day 5, we carefully look back at all the previous matches over the past 4 days. Fernanda already played against Li on Day 1, with Sandra on Day 2, with Petra on Day 3, with Janet on Day 4. The only player she hasn't faced yet is Carla. We check every previously played matches (looking for the pairs that weren't paired up before) for all the other players too and reach this conclusion:

DAY 5:

FERNANDA vs CARLA PETRA vs JANET SANDRA vs LI

Fernanda plays against Carla on Day 5.

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?

From the question, we are able to extract the information of which noisemakers appearing on which days as listed below:

Saturday: Salesman

Sunday: Dog

Monday: Salesman, Construction

Tuesday: ?

Wednesday: Salesman, Dog

Thursday: ?

Friday: ?

Saturday: Construction

Sunday: Dog

Two conditions are also told to help us solve the question:

No one of the three noisemakers was quiet for three consecutive days

No pair of them made noise on more than one day during Homer's vacation.

Well looking at the preliminary information, we can see that there are three days that are unknown where one of them is when no noisemakers exists and also the day that Homer can sleep in, in which this is the answer to the question.

In order to solve the problem, we can first go back to the conditions of the situation, we are reminded that “no pair of them made noise on more than one day during Homer's vacation” therefore looking at the existing outcomes we are able to see that the only possible outcomes left are: “Salesman” and “Dog, Construction”

Next we can make use of the other outcome which is “no one of the three noisemakers was quiet for three consecutive days”. Looking at Wednesday we see that, that is the last time we are told that the Salesman appears. Yet if we are to meet the condition then the Salesman would have to appear at least once more either Thursday or Friday or else this would make him quiet for three consecutive days, seeing how both Saturday and Sunday are already occupied.

The situation is the same for Dog and Construction. The days that Dog must appear in order to meet the condition is Thursday and Friday while for Construction it is Tuesday and Thursday. Already we have established that the possible outcomes left are Salesman and Dog/Constructions, from this we can be sure that the outcome Dog/Construction appears on Thursday as this is the only day they have in common. Therefore this makes the Salesman appear on Friday. The information can now be organized as shown below,

Saturday: Salesman

Sunday: Dog

Monday: Salesman, Construction

Tuesday: No Noisemaker

Wednesday: Salesman, Dog

Thursday: Dog, Construction

Friday: Salesman

Saturday: Construction

Sunday: Dog

From this, we are able to see that the only day that no noisemakers appeared was on Tuesday. Therefore, the only day that Homer was actually able to sleep in was on Tuesday.