A moderator takes a set of 8 stamps, 4 red and 4 green, known to three logicians, and affixes two to the forehead of each logician so that each logician can see all the other stamps except those two in the moderator's pocket and the two on his or her own head. He asks them in turn if they know the colors of their own stamps:
1. A: "No"
2. B: "No"
3. C: "No"
4. A: "No"
5. B: "Yes"

What are the colors of B's stamps?

red and green

A would only know the color of his stamps if all four stamps on the heads of the other two were the same color.

B knows this, but that doesn't help him determine anything except that if Cs stamps are the same, both of his are not. Also, B would know the colors of his own stamps if all four of A's and C's were the same color.

C would similarly know the color of his own stamps if A's and B's four stamps were all the same color. He would also know if A's two stamps were one color and B's two stamps were another color, that his stamps were different colors. Thus, at least one of A or B has two stamps of different colors.

A, knowing this, would see if B had two stamps that were the same color; if they were, then his own stamps must be one red and one green.

A did not know the color of his stamps, so B now knows that his stamps must be different colors, one red and one green.

Posted by DJ on 2004-07-31 13:00:35