[jay_shark]

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my friend showed me this today, he doesn't know the answer and it has been bugging me, anyone wanna give a shot at it? please dont just look up answer, and if you know it don't post it. oh and my friend said it is a math riddle, not some trick like "turn on the light".

There are 50 coins, 18 heads up, 32 tails up in a dark room. You want to make two piles that have an equal number of heads. (You don't care what size these piles are, and the piles don't necessarily have to be the same size as each other. So, for instance, if you had a way to verify that two coils were tails, you could put them in two separate piles of 1 coin each, and you'd be done.) You cannot feel the coins or anything like that. The only thing you can do is move them around and flip them.

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When I first read this problem , I immediately thought of a related old problem : Show that if you cut a deck of cards in half , then the number of red cards in one pile is equal to the number of black cards in the other . Using this insight , we can grasp a solution .

Instead of dividing the coins in 2 equal piles , we divide the coins so that one pile has 18 random coins and the other has 32 .

Let a be the number of heads in pile 1(18 cards)
Let b be the number of tails in pile 1 .

a+b=18
18-a + 32-b =32

So the number of tails in pile 1 is equal to the number of heads in pile 2 . Now all you need to do is flip all the coins from pile 1 .