The Coin Puzzle

Posted by Steven Bryant On February - 7 - 2006

The Puzzle

You are given 12 coins. 11 of the coins are identical to each other and have the exact same weight. The 12th coin is either heavier or lighter than any one of the other 11 coins, but you do not know which. You are also given a balance scale that can be used to compare one side of objects against the other side – tipping in the heavier direction.

Using the scale no more than 3 times, can you always identify which coin has the different weight? If you answer no, you have to prove why that is the case and if you answer yes, you should be able to demonstrate your answer.

The Answer

Many friends have found this puzzle to be extremely fun. Some have solved it within 2 hours while it has taken others several weeks or months. Without revealing the answer here, a big clue is that there is a real answer to this puzzle. I don’t want to put the answer here, in plain view, in order not to give away the answer too soon for those interested in solving it on their own. But, rest assured, there is an answer.

HINT 1: Several people have e-mailed me with possible solutions that begin by weighing one side of 6 coins against another side of 6 coins. They then discard either the heavier or lighter side before moving to their second weigh. I would like to offer the reminder that you do not know whether the coin is heavier or lighter, so you do not know which side to discard.

HINT 2: Try to also determine whether or not the coin you are seeking is heavier or lighter.

When you are ready, you’ll find the solutionĀ in the FAQ section.

What Does It Mean?

This puzzle demonstrates that some puzzles are hard to solve and require a different approach. With enough trial, error, and experimentation, you can find the answer. It helps to know there is a valid answer or you run the risk of giving up too soon. In reviewing Einstein’s work, identifying the problems and understanding the root causes are hard. It doesn’t mean that they aren’t there and can’t be solved. It just means they are hard.

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