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?

We have the following 19 possible combinations for (A,B,C) :

01 (GG,GG,RR)  C1
02 (GG,GR,GR)
03 (GG,GR,RR)  B2
04 (GG,RR,GG)  B1
05 (GG,RR,GR)
06 (GG,RR,RR)  A1
07 (GR,GG,GR)
08 (GR,GG,RR)  A2
09 (GR,GR,GG)  B2
10 (GR,GR,GR)
11 (GR,GR,RR)  B2
12 (GR,RR,GG)  A2
13 (GR,RR,GR)
14 (RR,GG,GG)  A1
15 (RR,GG,GR)
16 (RR,GG,RR)  B1
17 (RR,GR,GG)  B2
18 (RR,GR,GR)
19 (RR,RR,GG)  C1

A's first answer eliminates 6 and 14.
B's first answer eliminates 4 and 16.
C's first answer eliminates 1 and 19.
A's second answer eliminates 8 and 12.
B's second answer means that he saw 3, 9, 11, or 17.
Since each has only GR for B, that is the answer.

Posted by Bractals on 2004-08-02 11:49:20