interesting math riddle

[bunny]

<font color="white">Make a pile of 18 random coins - there are x heads in it.
This means pile one has x heads and 18-x tails.
Pile two has 18-x heads and 32 -(18-x) tails.
If you now flip pile one it has x tails and 18-x heads.
Both piles now have the same number of heads. </font>

[jay_shark]

[ QUOTE ]
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.

[/ QUOTE ]

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 .

[thylacine]

OP, let us know when the penny drops.

[GoRedBirds]

I saw this same riddle (different numbers) somewhere a couple days ago. Someone else said they saw it too. Any idea where we saw it? I'm drawing a blank.

[madnak]

I think you confused him, thylacine. Your answer is wrong:

<font color="white">You have to flip the 18, not the 32.

If you flip the 32 you'll always end up with more heads in that pile. The 18 pile will have x heads and 18-x tails, the 32 pile has 18-x heads and 32-(18-x) tails. Flip the 32 and you now have 18-x tails and 32-(18-x) heads. So x heads in the 18 pile and 32-(18-x) heads in the 32 pile. That's x and 14+x, the 32 pile will always have 14 more heads than the 18 pile.</font>

[thylacine]

[ QUOTE ]
I think you confused him, thylacine. Your answer is wrong:

<font color="white">You have to flip the 18, not the 32.

If you flip the 32 you'll always end up with more heads in that pile. The 18 pile will have x heads and 18-x tails, the 32 pile has 18-x heads and 32-(18-x) tails. Flip the 32 and you now have 18-x tails and 32-(18-x) heads. So x heads in the 18 pile and 32-(18-x) heads in the 32 pile. That's x and 14+x, the 32 pile will always have 14 more heads than the 18 pile.</font>

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Ok, I typed quickly thinking it started with 32 heads, 18 tails. Anyway, there are about ten explanations by now.