Tuesday, February 13, 2007

You have 50 pound coins on the table in front of you. You are blindfolded and cannot discern whether a coin is heads up or tails up by feeling it. You are told that x coins are heads up, where 0 < x < 50. You are asked to separate the coins into two piles in such a way that the number of heads up coins in both piles is the same at the end. You may flip any coin over as many times as you like. How will you do it?

1 Comments:

Blogger steven said...

Take x coins and flip them. These form one pile, the remainder form the other.

Here's how this works :-
Let y be the number of heads in the pile with x coins. Therefore there are (x-y) tails in the pile with x coins. When you flip this pile, there will be (x-y) heads and y tails.
In the other pile, there are already (x-y) heads (as x is the total number of heads in both piles to start with, and y coins have been taken away).
So flipping the pile with x coins gives you an equal number of heads in both piles. QED.

February 19, 2007 at 12:04 PM  

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