Dark Coin Riddle

You find some ancient coins in a dungeon that are guarded by a wizard.

Each coin has one side in gold and the other side in silver.

The wizard promises to give you the coins, if you solve a simple puzzle:

Split the coins into 2 piles with the same number of coins facing silver side up.

The wizard then turns off all the lights, and you can't tell which coin is which.

Given the information below, can you solve it?

There are hundreds of coins in the pile.
At the beginning, there are exactly twenty coins facing silver side up.
You must divide all of the coins into two piles. Each pile can have any number of silver coins, so long as there are an equal number of silver coins in each pile.
Each pile can contain any number of coins greater than zero. The two piles don't have to be equal in size.
There is no way to tell which side of any particular coin is facing up.
Flipping coins is allowed. Resting coins on their sides is not.

Hint:

The solution is very simple and depends on the fact that if a pile has N coins facing silver side up, then the remaining coins are gold side up, and vice versa.

Source: https://mes.fm/puzzles/dark-coin-riddle

Dark Coin Riddle.jpeg

Solution

Although this riddle sounds difficult to solve, the solution is in fact very simple. This is because any pile with N coins facing silver side up means that the remaining coins are facing gold side up, and vice versa.

We know there are initially 20 coins facing up in the pile, but can't remember which.

Take any 20 coins and then flip them each. You have solved the riddle!

Why it works:

If your second pile has N coins facing silver side up, then:

The first pile has 20 - N coins facing silver side up.
Your second pile has 20 - N coins facing gold side up.
Flipping your second pile means it has 20 - N coins facing silver side up.

Thus, the first pile and second pile both have 20 - N coins facing silver side up.