Solve the Coin Riddle: There Are 18 Silver-Side-Up Coins in the Treasure Pile–Can You Divide Them Into 2 Piles Each With the Same Number of Silver-Facing Coins?

July 11, 2019 Updated: July 11, 2019

Here’s a fun riddle that stumps most people who hear it for the first time—but once you get the answer, you’ll never forget it!

There are several variations (including a card trick), but here’s our version:

Imagine that you are exploring an old medieval castle in search of treasure. You delve into one of the towers, and to your amazement, you stumble across a huge pile of precious metal coins.

The room is dark, but it is lit by torches, so you know that somebody is home.

You are just about to lay your hands on the treasure and toss as many into your duffle bag as you can haul, but before you are able to, in a puff of green smoke, a powerful wizard suddenly appears before you.

“I forbid you to take my treasure!” says the wizard. The wizard tells you that he is unwilling to part with the coins unless you prove yourself worthy of it by solving a puzzle.

He explains:

Each of these coins bears the same emblem on both sides. But each side is made of a different metal; one side is gold; the other is silver.

Most of the coins are gold-side-up. But there are 18 coins hidden somewhere in the pile that are silver-side-up.

The wizard pauses for a moment before waving his staff, magically causing a gust of wind to blow out the torches, leaving you in total darkness. Then the wizard continues:

In the dark, your task is to divide the coins into 2 piles, and each pile must have the same number of coins facing silver-side-up.

If you succeed, you may take the treasure. If you fail, you will remain in this tower forever!

A shiver runs down your spine as the wizard vanishes in a puff of smoke.

You remember seeing several coins that were silver-side-up, but now that it’s pitch dark, you have no way to know for sure which ones those were. You are careful not to spill the coins as you touch the metal. The emblem feels the same on both sides.

You must think of a way to divide the coins into 2 piles. The piles don’t have to have the same number of coins, but both piles must have the same number of coins that are silver-side-up.

Can you save yourself from this predicament and walk home with the treasure? If you need to, take a few moments to come up with a strategy before you scroll down for the answer below:

Suddenly, a burst of inspiration hits you, and you come up with a surprisingly simple solution: being very careful not to accidentally flip the coins, you take 18 coins randomly from the pile and set them aside to make another pile totaling 18.

Then, you flip each of the 18 over so that the opposite side is facing up.

“Done!” you cry out triumphantly.

Suddenly, the torches light up again and the wizard reappears and smiles.

“Well done!” he says.

You realized that by drawing the same number of coins at random as there were silver-side-up coins, it wouldn’t matter which coins you drew. By flipping the pile of randomly drawn coins, both sides would equate with one another.

For example, supposing you drew 18 gold-side-up coins, by flipping them over, you would then have the opposite—the same number of silver-facing coins in both piles.

And in fact, this strategy works for any number of silver-side-up coins.

Supposing you drew 13 coins that were gold-side-up and 5 that were silver-side-up, by flipping the over, you would have the reverse: 5 gold-side-up coins and 13 silver-side-up coins. Again, the same in both piles, since you drew 5 silver-side-up coins, leaving 13 in the larger pile.

After loading up your bag with enough to pay off your student loan, you march off victoriously.

Photo Credit: Illustration – The Epoch Times