The Answer to the Hardest Logic Problem in Existence

A few weeks ago, I published a post under the title, “the hardest logic problem in existence”. I’ve gotten a lot of queries asking me about the solution, and it looks like I’ve kept everybody in the dark long enough – so here’s the answer, explained step by step.

If you missed the question, you can check it out here.

The answer is C.

Why?

Let’s read the question over carefully.

After a few moments’ silence, one of the boy raises his hand and correctly answers the question.

The key word, like I said in the hint, is “silence”. No one spoke for a few minutes.

Why is that important?

Let’s consider C’s position. He can see the boy in front of him – B – is wearing a white hat. He also knows that there are four boys in the room (although he doesn’t know that A is behind the wall – but it doesn’t really matter in the end).

So he assumes that there are two boys behind him (although there is only one – but, like I said, it doesn’t really matter as long as C realizes there is SOMEONE behind him).

C deduces thus:

If there is another boy behind him, he would have been able to see the hat colors of both B and C (himself).

If C had been wearing the same color as B, the boy standing behind C would have gotten the answer immediately.

However, the boy standing behind C (D in this case) did NOT say anything, so C deduced that he and B must have been wearing different hat colors.

Since B was wearing white, C must be wearing black.

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