| Topic Name: |
Brainteaser |
| Message Name: |
I think I got it...and can explain it |
| Date Posted: |
01/08/2002 |
| In Reply To: |
Perhaps someone can help solve this question.
3 prisoners and a jailer. A bag with 3 black and 2 red hats. The prisoners are blind folded and each selects a hat and puts it on his head. The jailer will let them go if anyone of them can identify the color of the hat on his head and explain why he knew the color. In other words they just can't guess. They can see each others hats but not their own. The jailer asks the first prisoner if he knows and he says no. Then
he asks the second prisoner and he says no. The third prisoner is blind but when he is asked he correctly identifies the color and explains how he knew it. |
| Message: |
The third guy knows he is wearing a black hat because:
P1 looks at P2 and P3 and can't answer the question, meaning the possible hat colors for P2 and P3 are:
1)P2-B, P3-B
2)P2-R, P2-B
3)P2-B, P3-R
When P2 is asked the question, these 3 sets of possiblities become 6 as we factor in possible hat colors for P1:
1) P1-R, P2-B, P3-B
2) P1-R, P2-R, P3-B
3) P1-R, P2-B, P3-R
4) P1-B, P2-B, P3-B
5) P1-B, P2-R, P3-B
6) P1-B, P2-B, P3-R
P2 knows that these are the only six combinations possible. If P2 looks at P1 and P3 and both are wearing red (possiblity #3), he knows he must be wearing black, and would be able to answer confidently, therefore eliminating possiblity #3.
So we are left with:
1) P1-R, P2-B, P3-B
2) P1-R, P2-R, P3-B
4) P1-B, P2-B, P3-B
5) P1-B, P2-R, P3-B
6) P1-B, P2-B, P3-R
Of these remaining 5, we can also eliminate possibility #6 because if P2 knows P3 is wearing red, and factors in the fact that P1 was not able to answer the question, P2 knows he must not be wearing red (or else P1 would have been able to answer correctly), and thus must be wearing black.
That leaves us with only 4 possible solutions for P3, when his turn comes to answer the question:
1) P1-R, P2-B, P3-B
2) P1-R, P2-R, P3-B
4) P1-B, P2-B, P3-B
5) P1-B, P2-R, P3-B
And since the remaining possiblities all leave P3 wearing black, he can confidently answer without seeing either P1 or P2.
I can't believe I took the time to type that out.
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