# Firebox Card: Number 123

From Perplex City Wiki

**Illogical**

From the firebox advert. The card on the top of the advert contains the following text:

Between all the distractions and parties at university, I did manage to fit in a few experimental psychology lectures. One of the most interesting things I learned was how at heart, people aren't as logical as they think. Try this problem: Each of these cards has a letter (A or K) on one side and a number (2 or 7) on the reverse. If I told you there was a rule stating that a card with A on one side will have a 2 on the reverse, which two cards would you turn over to find out if the rule was true?

The cards displayed on the card are

A K 2 7The answer is A and 7.

Some people guess the answer is A and 2. The logical statement of the problem can be phrased "an A on one side implies there will be a 2 on the other." People who get the answer wrong also presume the converse is true, that "a 2 on one side implies there will be an A on the other." This is not the case; therefore the 2 does not need to be checked. Another way to see this is that the statement can be phrased "no card has an A on one side and a 7 on the other side".