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The Turnover Puzzle

Posted on June 11, 2012 in Articles

Turnover Puzzle

Here’s a challenging logic puzzle that seems simple at first, but some people have trouble getting the right solution. Take a look at the photo above and consider this statement: Any card with an Ace on one side has a red back on the other side.

How many cards must you turn over to determine if this statement is accurate? Can you come up with the right answer?

Spoiler Alert! The Answer: If these are all normal cards, then you must turn over the Ace and the blue-backed card. You must turn over the Ace to make sure it has a red back, and you must turn over the blue-backed card to make sure it is not an Ace. You do not need to turn over the red-backed card, as it can be any value. The puzzle said all Aces have to have red backs, but it didn’t say all red-backed cards had to be Aces.

If you allow for non-standard playing cards to be used, then you must also turn over the King, just to make sure there isn’t an Ace on the other side! If there was, that would make the proposition false. Although we don’t normally encounter Kings with Aces on the other side in everyday life, there is nothing that excludes that possibility from a purely logical standpoint.

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