This is gonna bug me. Any help? #brainteasers #wtf (Taken with Instagram)
I think I got it: Only click “Read More” to find the solution
First, there are only seven possible scenarios:
Scenario 1 1W 2W 3W
Scenario 2 1R 2W 3W
Scenario 3 1W 2R 3W
Scenario 4 1W 2W 3R
Scenario 5 1R 2R 3W
Scenario 6 1R 2W 3R
Scenario 7 1W 2R 3R
Notice that there are three scenarios where Prisoner 3 wears a red hat and four where Prisoner 3 wears a white hat.
Second: if the prisoners all knew that there were two red hats and three white hats, then the only way a prisoner can know which hat he wears by sight alone is by seeing the other two prisoners wearing both of the red hats (thus meaning his own hat is white).
And so: Prisoner 1 only had his sight to go on. He did not see two red hats. He didn’t know which hat he had. This eliminates Scenario 7.
Prisoner 2’s sight didn’t help him figure out his own hat. This eliminates Scenario 6. But since Prisoner 2 also effectively knew that Scenario 7 was eliminated, he must have known that there was only one possible scenario in which Prisoner 3 wears a red hat. If Prisoner 3 had a red hat, Prisoner 2 would have known that it was Scenario 4 and thus known his hat was white. Prisoner 2 did not see Prisoner 3 wearing a red hat, so he didn’t know which hat he was wearing.
Therefore, Prisoner 3 knew that all possible Scenarios in which he wore a red hat were eliminated. Prisoner 3 knows he is wearing a white hat.