# shlomi-fish-homepage / t2 / MathVentures / two-angels-and-two-gates.html.wml

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There’s a famous riddle that goes like this:

You are standing in front of two gates (a left one and a right one) - one leads to paradise and the other leads to hell. You don’t know which gate leads where. Beside the gates, there are two angels: one of them always tells the truth and the other always lies, but you also don’t know which one is which.

You have one question to ask one of the angels, in order to find out which gate you should follow. What would that question be?

Now, I came up with a harder variation of this riddle, which you should consider only after you found the solution to the original:

You are standing in front of two gates (a left one and a right one) - one leads to paradise and the other leads to hell. Beside the gates, there are two angels, each one of them can either tell the truth all the time, or constantly lie. Every angel knows where each door leads to, and the other angel’s orientation, but you don’t, nor can assume anything. (They can both be liars or both truth-tellers, or one of each).

You can ask one of the angels a single question, in order to find out which gate you should follow. What would that question be?

The solution can be found some space below.

Solution:

The solution to the first puzzle is to ask one of the angels “If I asked the other angel, if the left gate leads to paradise, would he answer yes?”. One can see, that in this case, one will always get a false answer, according to which one can determine which is the right gate.

Now for the tougher variation. The answer to this is to ask one of the angels: