THE PROBLEMS OF THE WEEK;;
Diophantus’ Riddle
Diophantus is often called the father of algebra.Little is known about his life except that he lived between 100 to 400 AD.However his age at death is known because it is said that one ofhis followers described his life in this riddle:
Diophantu’s youth lasted 1/6 of his life.He grew a beard after 1/12 more of his life.After 1/7 more of his life, Diophantus married.Five years later, he had a son who lived ½ as long as his father.Diophantus died just four years after his son’s death.All this sums up his life.
How old was Diophantus when he died?
The Paradox of the Unexpected Exam
A teacher announces that a test will be given on one of the five week days of the next week, but tells the class, “You will not know which day it is until you are informed at 8:00am of you 1:00pm test that day.”
Why won’t the test happen?
Hotel Infinity
One of the qualifications for a hotel clerk at Hotel Infinity is a working knowledge of infinity.Paul applied, was interviewed, and started working the following evening.Paul wondered why the hotel required that its entire staff know about infinity.He figured that since it was a hotel with an infinite number of rooms, it would be no problem finding rooms for its guests.After his first night on the job, he was glad he had the knowledge.
When Paul relieved the day clerk, he was informed that there were an infinite number of guests occupying an infinite number of rooms.After a few minutes on the post, a new guest walked in with a reservation.Paul needed to decide which room to give the guest.He thought for a moment, and then moved each occupant to a room with the next highest number, the guest in room 1 moved to room 2, the guest in room 2 moved to room 3, and so on.Therefore, Paul was able to vacate room #1.
Paul was satisfied with his decision, but as his shift was about to end, an infinite busload of new guests arrived.How will Paul give them their rooms?
Three men
Three men, blindfolded, are standing on a line facing one direction.Then three hats are taken from a bin of three white hats and two black hats.The men are given that information.A hat is then placed on top of each man.The blindfolds are then removed and each man is asked to determine what color hat he is wearing without looking at his own particular hat.
The man at the back of the line who sees the two men and their hats in front of him says, “I do not know which hat color I am wearing.”The man in the middle who heard the first and sees the man in front says the same thing.The man at the front who sees neither his hat nor the two men behind him, but has heard the other two men says,
“I KNOW WHICH HAT COLOR I AM WEARING.”
Which color is he wearing and how did he determine it?
Spider and Fly
In a rectangular room, 30 feet long, 12 feet wide, and 12 feet high, a spider is at the middle of one of the square walls, one foot from the ceiling.
A fly is at the middle of the opposite wall, one foot above the floor.The fly is so frightened by the spider, it can’t move.
What is the shortest distance the spider must crawl to capture the fly?
(Hint: less than 45 ft.) | 