The Grand Master takes a set of 8 stamps, 4 red and 4 green, known to the logicians, and loosely affixes two to the forehead of each logician so that each logician can see all the other stamps except those 2 in the Grand Master's pocket and the two on her own forehead. He asks them in turn if they know the colors of their own stamps:
Again, he asks them in turn if they know the colors of their own stamps.
What color stamps does B have?
I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!
Friday, January 15, 2010
Labels: logic puzzle
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B has 1 red, 1 green.ReplyDelete
To work, the other two must have either:
Taking the first case:
-B sees A=GG, C=RR
-When A doesn't know what she has, it means B can't possibly have RR, or A would know.
-On B's first turn, she still isn't sure if she has GG or RG.
-When C doesn't know what she has, it means B can't possibly have GG, or C would know.
-So B then knows she must have one of each, RG.
The same logic works for A=RR, C=GG.
B says: "Suppose I have red-red. A would have said on her second turn: 'I see that B has red-red. If I also have red-red, then all four reds would be used, and C would have realized that she had green-green. But C didn't, so I don't have red-red. Suppose I have green-green. In that case, C would have realized that if she had red-red, I would have seen four reds and I would have answered that I had green-green on my first turn. On the other hand, if she also has green-green [we assume that A can see C; this line is only for completeness], then B would have seen four greens and she would have answered that she had two reds. So C would have realized that, if I have green-green and B has red-red, and if neither of us answered on our first turn, then she must have green-red.ReplyDelete
"'But she didn't. So I can't have green-green either, and if I can't have green-green or red-red, then I must have green-red.'
So B continues:
"But she (A) didn't say that she had green-red, so the supposition that I have red-red must be wrong. And as my logic applies to green-green as well, then I must have green-red."
So B had green-red, and we don't know the distribution of the others certainly.
(Actually, it is possible to take the last step first, and deduce that the person who answered YES must have a solution which would work if the greens and reds were switched -- red-green.)
Oops, forgot to add my 'bravo' for Andy, too. Your explanation was a more succinct than mine.ReplyDelete