Presentation Date: Tuesday, Dec. 11, 2012, 23:59:59
Submission Date: Wednesday, Dec. 12, 2012, 23:59:59
See the Requirement Guidelines for In-Class Exercise (ICE) assignments.
This is an in-class group assignment. Fill in the names and email PIDs of the group members in the space provided below so that each group member knows who is in the group. Submit one copy of this to your instructor before you leave class.
| Group member name | Role | VT Email PID |
Pick a solver and a scribe for your group; the remaining members will play the role of listeners. Identify the role taken by each group member in the table above.
Follow the Solver/Listener paradigm to analyze and attempt to solve the given problem. It is important that you manage the discussions in a disciplined manner so that the scribe can take adequate notes to prepare a transcript of your session.
When you believe you have a solution to the problem, work together to prepare an outline to help the solver present your results to the class.
After the class, and by the announced deadline, prepare a written presentation of your session, including the interactions between the solver and the listeners and a detailed explanation of how you arrived at your solution. You may include diagrams and mathematical work if you used those as part of your process.
Only one group member, the scribe/recorder, must submit that to the Web-CAT System via the collection point for ICE04. The scribe must select the partners on the Web-CAT at the time of the submission.
Remember that the evaluation of your solution will depend primarily on the completeness and clarity of your explanation.
Problem List
1:
The Murder of Simon Legrew
On Wednesday, May 5, 1976, the wicked Simon Legrew was murdered at his home in a Boston suburb. The police were able to place the time of death at between 11:10 and 11:30 PM. They arrested four suspects --- Jeeves, the butler; Fifi, the French maid; Julia, the cook; and Jessica, Mr Legrew's private secretary. Under questioning, the four suspects made the following statements:
Jeeves: I didn't do it.
Jessica did it. Mr Legrew was blackmailing Jessica. Fifi
and I were watching television together from 10:10 PM
until 12:30 AM.
Fifi: I'm innocent. Jeeves
and I were watching television together at the time of
the murder.
Jessica was being blackmailed. I saw
Jessica speaking to Mr Legrew at 9:30 PM on the
night
of the murder.
Julia: I'm innocent. Jessica
was being blackmailed. Jeeves murdered Mr Legrew. I saw
Jessica leave the house at 10:00 PM.
Jessica:
I did not kill Mr Legrew. I was not being blackmailed. I
was in Chicago during the entire night of the murder.
Fifi is the murderer.
Each of the four suspects made two true statements and told two lies.
Who killed Simon?
Problem 2: Unknown Professions
Four men were asked about their yearly incomes. Their names were Earl, Moe, Luis, and Randy and their professions are architect, carpenter, plumber, and mason (not necessarily in that order). Each made two statements, but the only statements whose correctness can be depended on are those in which the speaker specifically mentions his own profession. Other statements may or may not be true.
Earl: The plumber makes three times as much
as the carpenter. The architect makes more
money than
I do.
Moe: The carpenter makes more money
than the plumber. Luis is either the mason or the
architect.
Luis: I make more than the
architect. The carpenter makes less than each of the
others.
Randy: The plumber makes twice as
much as the carpenter. I make more than the mason.
Match each person with his profession.
Problem 3: The Entertainers
Three women (Abby, Janice, and Linda) and two men (Martin and Roberto) are a singer, a dancer, a comic, a television writer, and a theatrical agent, although not necessarily in that order.
Abby said: I'm not the comic. The writer and
the dancer are happily married. The singer and the agent
are engaged to be married.
Janice said: The
singer is my cousin. The writer and the dancer are
siblings. The comic and the agent share an apartment.
Linda said: I am not the writer. The singer and
the agent hate each other. The dancer and the
comic
frequently work together.
Martin said: The
singer owes me $10. The writer and the dancer are not
related, and have never met. The comic and the agent are
next-door neighbors in an apartment house.
Roberto said The singer saved my life once. The
agent lives alone in an old mansion. The dancer and the
comic have never met.
If the only certainty is that every statement in which an individual alludes to his or her own profession is true, who is who?
Problem 4: Yeti?
Probably the first real evidence of the existence of an Abominable Snowman is a photograph taken by the renowned mountaineer Sir Hilary Edmund and his party.
Before the photograph was developed, Sir Hilary as asked to describe the beast: "It was over 7 feet tall, with long white fur, and 6 toes on each foot", replied Edmund.
"He's a liar", objected famed Sherpa guide Nenzing Torkay, grinning. "The Snowman has no fur at all, is under 5 feet tall, and has hooves".
The other three members of the expedition also disagreed in their descriptions.
Monte Everisto said that the Snowman was 6 feet tall and had long white fur and hooves.
Matty Horne claimed the Snowman was over 7 feet tall, had brown fur, and had 5 toes on each foot.
And Snowsov "Killer" Manjaro estimated the beast's height at under 5 feet and attributed brown furand 6-toed feet to the creature.
The discrepancies in the descriptions were probably due to the fact that the beast was sighted during a severe snowstorm. When the picture was developed, it proved that each of the five mountain climbers was correct about exactly one aspect of the Snowman's appearance.
What does an Abominable Snowman look like?
Problem 5: Anniversary Gift
The number of sons, the number of daughters, and the number of years that the parents had been married were three different prime numbers.
Find these numbers.
Problem 6: The Chickens and the Eggs
Three boys, Pedro, Quincy, and Ralph, and their sisters, Sandy, Trixie, and Vera (not necessarily in that order), had chickens for pets.
Last week was an unusual one. Each chicken laid as many eggs as its owner owned chickens. Quincy had three times as many chickens as his own sister, and had eight more chickens than Ralph's sister. Furthermore, by the end of the week, Quincy had collected 56 more eggs than Pedro; Ralph had collected 52 more than Sandy; and Pedro had collected as many eggs as Sandy and Trixie together.
How many chickens did each of the six people own? Who
was whose sister?
Problem 7: Around the World
A group of airplanes is based on a small island. The tank of each plane holds just enough fuel to take it halfway around the world. Any desired amount can be transferred from the tank of one plane to the tank of another plane while the planes are in flight. The only source of fuel is on the island, and for the purposes of the problem it is assumed that there is no time lost in refueling, either in the air or on the island.
What is the smallest number of planes that will
ensure the flight of one plane around the world on a
great circle, assuming that the planes have the same
constant ground speed and rate of fuel consumption and
that all planes return safely to their island base?
Problem 8: The Math Will
According to the terms of the last will and testament of J P Moneybags, his entire fortune (which turned out to be worth $2,518,000) was to be divided equally (in exact multiples of $1000) among all of his direct descendants who were present at the conclusion of his funeral. The excess, if any, was to be donated to the Moneybags Home for Retired Mathematicians.
Mendel Giant, the director of the home, attended the funeral to determine how well the institution would make out.
Ten minutes before the funeral was scheduled to begin, only three heirs were present.
"I guess that means we'll get $1000", said Giant.
Just then another heir entered. "Good", said Gaint. "That means $2000 for us".
One minute later a fifth heir entered. "$3000", Giant mumbled.
As the funeral was about to begin, three more heirs came in. "Terrific", uttered Giant. "Now we'll get $6000".
During the funeral, three more heirs entered, one at a time. With each one, Giant mentioned a new figure. At the entrance of the ninth heir, Mendel said "$7000"; the tenth heir, "$8000"; and the final heir "$10000".
How was Dr. Giant able to determine so quickly how
much money the home will receive?
Problem 9: Sheep Inheritance
The younger brother complained that the older had drawn first, and also taken the last $10 bill.
The older brother offered to even things up partially by letting the younger one have all the silver dollars.
The younger brother complained that he still had not received half, at which point the older brother wrote a check for to even things up exactly.
What was the amount of the check?
Problem 10: Mathematician's Children
"I hear some children playing in the back yard", said Jones, a graduate student in mathematics. "Are they all yours?""Heavens, no", exclaimed Professor Smith, the eminent number theorist. "My children are playing with friends from three other families in the neighborhood, although our family happens to be the largest. The Browns have a smaller number of children, the Greens have a still smaller number, and the Blacks have the smallest of all".
"How many children are there altogether", asked Jones.
"Let me put it this way", said Smith. "There are fewer than 18 children, and the product of the numbers of children in the four families happens to be my house number, which you saw when you arrived".
Jones took a notebook and pencil from his pocket and started scribbling. A moment later he looked up and said, "I need more information. Is there more than one child in the Black family?"
As soon as Smith replied, Jones smiled and correctly stated the number of children in each family.
Knowing the house number and whether the Blacks had more than one child, Jones found the problem trivial. It is a remarkable fact, however, that the number of children in each family can be determined solely on the basis of the other information given above!
Problem 11: The Pet River Crossing
There are three dogs and three cats that have to be transported across a river: a big dog, a medium dog, and a small dog, a big cat, a medium cat, and a small cat. The boat can carry two animals at a time, and all of the animals can row.
The medium dog cannot be left alone with either of the other dogs, nor can the medium dog be transported with another dog, because if the two are by themselves they will fight. The big dog will not fight with the small dog. Also, the medium cat cannot be left alone with either of the other cats, nor can the medium cat be transported with another cat for the same reason, and the big cat never fights with the small cat.
To make matters worse, if there are ever more dogs than cats together on the shore, the dogs will fight with the cats.
How can the animals get across the river without a
fight breaking out?
Problem 12: Dinner Seating
Four married couples, Mr & Mrs White, Mr & Mrs Green, Mr & Mrs Brown, and Mr & Mrs Black had dinner together. They sat at a round table in such a way that men and women alternated, but all the married couples were separated. Mrs White sat between Mr Green and Mr Black, with the latter one sitting to the right of Mrs White. Mr White sat next to Mrs Black.Who was sitting to the right of Mrs Green?
Problem 13: The Farmer Family Pet River Crossing
A farmer, his son and daughter and their pets need to cross a river. The pets are a fierce dog, two hamsters, and two rabbits. There is a small two-seater boat that they can use. The boat can hold two people, or one person and a dog, one person and two hamsters, or one person and two rabbits. All three people can row the boat, but none of the animals can.
If the farmer is not around, the dog will bite everybody and everything.
If the son is not around, the daughter will tease the hamsters.
If the daughter is not around, the son will tease the rabbits.
The hamsters and the rabbits get along fine with each other.
How can everyone cross the river without any biting
or teasing?
Problem 14: The Farmer, the Wolves, the Dog, the Goat and the Bag of Grain
A farmer was trying to cross a river in a boat which held him and two items, to be chosen from two wolves, one dog, one goat, and one bag of grain. When the farmer was not around, either wolf would eat the dog or the goat, the dog would eat the goat, and the goat would eat the grain (if any of those opportunities arose).
How can the farmer transport all five items across
the river to his home?