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?

B has one of each

from B's point of view

1 ) If A and C both have 2 reds or both have 2 greens he would no that he had the opposing colour immidiatly and since he answers no the first time this cannot be the case

2 ) If A has 2 reds and C has 2 greens the
 if B had 2 reds C would know that he had 2 greens
 if B had 2 greens A would know that he had 2 reds
scince they both say no the first time B would know that he has one of each

3 ) If A has 2 reds and C has one of each
 B would know that
 he could not have 2 reds
 if he had 2 greens C would no that he had one of each from 2)
 there for B knows that he has one of each

4 ) If C has 2 reds and A has one of each
 B would know that
 he could not have 2 reds
 if he had 2 greens A would no that he had one of each from 2)
 there for B knows that he has one of each

5) If A and C both have one of each
 B would know that if he had either 2 reds or 2 greens
  A would know that he had one of each from 3)

All other situations are logicaly eqivilent to one of these i.e red swaped for green.

In shorthand B knows that the only way the A would not know what colour his cards are by his second try is if he has one of each

Posted by matthew on 2004-08-05 04:30:50