Mar 20, 2012

The Camel & Bananas

You want to transport 3,000 bananas across 1,000 kilometers. You have a camel that can carry 1,000 bananas at most. However, the camel must eat 1 banana for each kilometer that it walks. What is the largest number of bananas that can be transported?

Can you solve it?

For extra credit, try deriving a general formula if you have B bananas, need to travel D distance, and the camel has a carrying capacity of C.


Sep 22, 2010

Card Cash

Someone offers you the following deal:

There is a deck of 100 initially blank cards. The dealer is allowed to write ANY positive integer, one per card, leaving none blank. You are then asked to turn over as many cards as you wish. If the last card you turn over is the highest in the deck, you win; otherwise, you lose.

Winning grants you $50, and losing costs you only the $10 you paid to play.

Would you accept this challenge?

Sep 21, 2010

29 hostages and a terrorist

29 hostages are captured by a terrorist. They are told, "You may meet today and plan a strategy. But after today, you will be in isolated cells and will have no communication with one another."

"There is an isolated switch room here, which contains two light switches labelled A and B, each of which can be in either the 'on' or the 'off' position. I am not telling you their present positions. The switches are not connected to anything."

"After today from time to time whenever I feel so inclined, I will select one hostage at random and escort him to the switch room. This hostage will select one of the two switches and reverse its position. He must move one, and only one of the switches. He can't move both and he can't move none either. Then he'll be led back to his cell."

“I will then take the next hostage there, and he'll be instructed to do the same thing. I am going to choose hostages at random. I may choose the same guy three times in a row, or I may jump around and come back."

"But, given enough time, everyone will eventually visit the switch room as many times as everyone else. "No one else will enter the switch room until I lead them."

"At any time anyone of you may declare to me, 'We have all visited the switch room.' and be 100% sure. "If it is true, then you will all be set free. If it is false, and somebody has not yet visited the switch room, you will be fed to the alligators."

What is the strategy they come up with so that they can be free?



Jan 19, 2010

Heads I win, Tails I lose.

Akshit took out a coin of his pocket and said to me, 'Heads I win, Tails I lose. I bet half the money in my pocket.'
He tossed and lost. And the game continued for number of times, each time betting half the money in his pocket. We don't remember how many times the coin was tossed or how long the game went, but he lost exactly the same no. of times as he won the bet.
What do you think, did he, on the whole, gain or lose?

Jan 17, 2010

Number of Triangles.

Take a good look at the figure below:

Count the no. of triangles in this figure.

Nov 21, 2009

The Cereal Box Surprise

Suppose a box of cereal costs 5$, and each box has a toy in it. There are 5 different toys for you to collect; by collecting all of them you can assemble them together and create a giant robot. If the toys have equal probabilities of turning up - that is, each toy is 1/5 likely to appear in a randomly chosen cereal box - how much will you have to spend, on average, before you can assemble the giant robot of your dreams?