You are blindfolded

Question:

You are blindfolded and are presented with a collection of coins on a table. You are told that exactly 26 coins show heads. How can you divide all the coins into two sets, with the same number of coins showing heads in each set? You cannot distinguish, by sight or by touch, which coins are showing heads or tails.

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C

A

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N

I

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E

R

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I

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W

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Solution: Select 26 coins at random to be one pile (or in general, select a number equal to the number of coins specified showing heads), and simply turn the coins in that pile over. Call all remaining coins the second pile. The two piles now have the same number of coins showing heads. Many people doubt that the solution is this simple. One can-didate explained it this way:

Let’s assume there are 50 coins in total. We know only 26 coins of the 50 show heads. Now, the first pile will have 26 coins; the second pile will have 24 coins. Let’s assume that, by pure chance, the 26 coins I selected are all showing heads. When I reverse the pile, there will be zero coins showing heads in either pile. Take another case. Assume that the first pile includes 26 coins of which 10 coins show heads and 16 coins show tails. By reversing the first pile, I end up with 10 coins showing tails and 16 coins showing heads. In this case, the other pile of 24 coins has 16 coins showing heads plus 8 coins showing tails. Both piles have 16 coins showing heads.

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