| Topic Name: |
Brainteaser |
| Message Name: |
answer |
| Date Posted: |
09/28/2001 |
| In Reply To: |
A variation of this problem: the three prisoners are told (as previously) that there is a bag with 3 black and 2 red hats, that every one will be given a hat, and that they won't be able to see their own colour, but only the colour of their fellow immates. But now, the offer is that the first one to deduce his/her own colour (and justify it) will be set free, and every prisoner is now arbitrarily given a black hat, with them not knowing it, of course. How can they solve the problem, without talking to each other? (No prisoner is blind now). |
| Message: |
What every prisoner can see is that the other two are black, and that nobody rushes to claim the prize. Anyone can suspect he is the only red, thinking that any of the other two are seeing a red and a black hat. But anyone who saw a red and a black would conclude that he must not be red (then must be black and would claim the prize), because if there were two reds, the one with the black could have already rushed to claim his freedom. Then, anyone with a red hat would have seen the other two claiming the prize. Therefore, the three of them conclude, without even talking to each other, that they are black, and claim the prize simultaneously.
|
|
