Coin Picking

Coin picking puzzle

Question:

There is a large* pile of coins in a room. Almost all of them are turned heads up, except just 20 which are turned tails up. You know this, but are wearing a blindfold and gloves (which cannot be removed) so you have no way of telling which are heads and which are tails.

The challenge: split the coins into two groups, such that both groups have the same number of coins which are tails up. How would you achieve this?

*it can be assumed that there are infinitely many coins.

Hint: the piles do not have to be the same size, which makes sense as the original pile is endless!

Answer: (click to show)

Take any 20 coins from the pile and turn them all over to the opposite face. Now you have completed the challenge!

This works because:
Of the 20 coins you chose, x are tails, where x is between 0 and 20. In the large pile there were originally 20 tails, but now there are 20-x tails. You've taken 20-x heads from the large pile, and turned them over to be tails.

So now there are 20-x tails up coins in each pile!