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Archive for December, 2010

Twelve Balls

Posted by Al Gelman under Tom (28 Responds)

You are given twelve balls which appear to be identical. However, one of these balls is either heavier, or lighter than the others. Using an equal arm balance, and a maximum of three weightings, determine: which of the balls is different, and whether it is heavier or lighter.

Naughts & Crosses Probabilities

Posted by Karl Sharman under Tom (59 Responds)

Most people are aware that Naughts and Crosses (Tic-Tac-Toe) is a game-theoretic draw (in other words, both players can force a draw, with decent play).
Assume, however, that neither player has any clue what he/she is doing, and plays randomly.
What are the odds for each player winning, and the odds of a draw?

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Monkey business

Posted by Chris under Mathemagic (28 Responds)

Ten people land on a deserted island. There they find lots of coconuts and a monkey. During their first day they gather coconuts and put them all in a community pile. After working all day they decide to sleep and divide them into ten equal piles the next morning.
That night one castaway wakes up hungry [...]

Next Numbers(s)

Posted by Pieter under Logic (5 Responds)

What are the next numbers in the following sequence :
61  52  63  94  …    ….

A lucky escape

Posted by Chris under Fun Physics (10 Responds)

Two boys walking in the woods decided to take a shortcut through a railroad tunnel. when they had walked two-third of the way through the tunnel, their worst fears were realized. A train was coming from the opposite direction, nearing the tunnel entrance. The boys panicked and each ran for a different end of the [...]

Sharing the gold

Posted by Chris under Logic (60 Responds)

Five pirates have obtained 100 gold coins and have to divide up the loot. The pirates are all extremely intelligent, treacherous and selfish (especially the captain).
The captain, who wishes to appear to be nice and democratic, says, “I’ll propose a distribution of the loot and the rest of you will vote on my proposal.  If  [...]

Bug off

Posted by Chris under Tom (16 Responds)

There is a 100 cm long scale with 100 bugs randomly placed on it. Assume that the bugs have an extremely small length, but are wide.  Each starts walking towards either end of the ruler.  The direction they start walking is completely random. Because they are wide, if  two of them meet, they have to turn around and walk in the [...]

Wizard Island

Posted by Chris under Logic (28 Responds)

A hundred wizards (please don’t all visit ToM) lived on an isolated island in the middle on nowhere (does that sound familiar to anyone?). One day, a ship sank nearby; one sailor survived and managed to reach the island. The wizards were very hospitable and took care of the sailor. When he was able to leave, [...]

Infidelity island

Posted by Chris under Logic (3 Responds)

There is an island that is isolated away from our world.  There’s a custom in this island which requires a woman to kill her husband the morning after she discovers that he’s having an affair with another woman.  It also happens that every woman knows whether every other man is having an affair, or not, except for her own [...]

The candidates

Posted by Chris under Logic (36 Responds)

There was a king that needed a new advisor. He wanted the smartest person for the job. The entire kingdom was searched and it was narrrowed down to 3 people.
The final test was about to begin. The king met with each and told them that he would either put a red dot or a blue [...]

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