Brain Teaser #48

There are three chests, each of which contains 100 coins. One chest has 100 gold coins, one has 100 silver coins, and the third has an equal split of 50 gold coins and 50 silver coins.

Each chest is labeled, but all are labeled incorrectly. You are allowed to pick one coin from just one of the chests and after his you must correctly identify each of the three chests.

What should you do?

Solution

Take a coin from the chest labeled 50/50.

If you pick a gold coin, you know that chest must contain all gold coins (it can't be the 50/50 chest because all the chests are incorrectly labeled). So the chest labelled silver must be the 50/50 chest and the one labeled gold must be the silver chest.

On the other hand if you pick a silver coin, you know that chest must contain all silver coins, the one labeled silver must be the gold chest and the one labeled gold must be the 50/50 chest.