Logic - I think

[BigMac]

Four people are placed in holes in the ground, in a straight line, three on one side of a wall, one on the other. Each is blindfolded and given a cap - two black and two white. When the blindfold is removed, any ONE of them (and just one of them) must state with conviction "the colour of my cap is..." (there are, of course, dire consequences for getting it wrong).

The blindfolds are removed and one person makes the asertion and gets it right.

Which person and how did s/he know for sure?

Any help gratefully received.

[biley]

The three on the one side of the wall must have two caps of one colour and one of the other colour. The person who sees TWO caps of the same colour knows his/hers is of the opposite colour and can therefore say so with conviction. The other two on that side will both see one of each colour on the other two and therefore have no way of knowing which colour of cap they have.

[BigMac]

Thanks, Biley. That's exactly what I thought but it seemed too easy.

[biley]

Yes, BigMac, I have to admit I had the thought that this was too easy myself - hope we are not both missing something (!!!) - but don't think we are.

[crofter]

Does that really answer the question? Surely the three are facing forward and in a straight line. Each can see those in front - but not behind!

If there is an immediate answer, then I agree that it must come from the one at the back of the three (who can see the other two and see that they have the same colour, say). But what if there is NOT an immediate answer?

In this second scenario, I believe the middle person of the three has a chance of calling out their right colour by waiting a while and then calling out the colour OPPOSITE to the one in front of him/her.

By pausing through the silence, s/he willl know that the back person is looking at different coloured hats ...

[BigMac]

Thanks, Crofter. Yours is the more refined answer, given the assumptions about direction of sight, which weren't explicit in the question. So I'm going to have to offer both answers...