Please be aware that, even when you know the answer to this brainteaser, the more you think about it, the more it will continue to drive you crazy!
The important thing to remember is what is implied by the response of each of the prisoners who can see and the fact that there were three white hats and two red hats:
The first prisoner did not know what colour hat he was wearing.
The only thing we can say for definite based on this is that the other two prisoners were not both wearing a red hat. If they had been then the first prisoner would instantly have known he was wearing a white hat. Instead, he has to say, “I don’t know.”
The second prisoner knows that he and the blind prisoner are not both wearing red hats (because of what the first prisoner said). He is, therefore, hoping to see the blind man wearing a red hat – at which point he would instantly know that he himself was wearing a white hat. Unfortunately, because he sees that the blind prisoner is wearing a white hat, he cannot say if his own is red or white! So, this prisoner also has to say, “I don’t know.”
The blind prisoner, on the other hand, on hearing the responses of the other two prisoners, instantly knows that he must be wearing a white hat. He declares this to the guard and all three prisoners walk free.
If you are still troubled by this – sorry! – you can find a short, one minute video, from the BBC Radio 4 website archive, in which three school children explain the answer clearly. The link to this clip is given below: