The Coin Flip

Here's a quick riddle. Setup: you are blindfolded, wearing thick gloves. There are twenty coins on the table in front of you: ten are heads and ten are tails. You do not know which; you cannot see them because of the blindfold and you cannot feel them because of the gloves. The only thing you can do is flip coins upside down or move them around.

You are to divide the coins into two equal groups (thus ten coins each). The assignment is to get the same number of heads and the same number of tails in both groups. How can you do it? No peeking!

Hint: The solution is easy. But reasoning to that point... less so!

Solution

Simply divide the coins (into two groups of ten) at random. Now flip over all the coins in one of the groups. There, you got it.

Heh... if you're anything like me, you're still puzzled. So let's clear things up. When you randomly took ten coins for one group, let's say it contained eight tails and two heads. There were ten tails and ten heads to begin with. This means the ten coins that are left consist of the opposite: two tails and eight heads! They will always complement each other like that. So when you flip over the group of eight tails and two heads, it will become a group of two tails and eight heads — exactly the same as the other group.