perplexus.info :: Logic : Logic and Stamps

Logic and Stamps (Posted on 2004-07-31)

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?

Submitted by Brian Smith

Rating: 2.5000 (8 votes)

Solution: (Hide)

There are only 19 possible combinations of stamps on logicians' heads. They are listed below, along with the statement they are eliminated by. Each statement eliminates any unique combinations:
A B C Statement rr rr gg 3 rr rg rg rr rg gg rr gg rr 2 rr gg rg 3 rr gg gg 1 rg rr rg 4 rg rr gg 4 rg rg rr rg rg rg rg rg gg rg gg rr 4 rg gg rg 4 gg rr rr 1 gg rr rg 3 gg rr gg 2 gg rg rr gg rg rg gg gg rr 3
In the remaining seven combinations, B has one stamp of each color.
DJ provides a more logically worked out here.
Federico Kereki makes use of a symmetry argument here.

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-09-04 08:49:40
What are the colors of B's stamps?	Bruno	2004-12-09 03:08:17
solution	Kristin	2004-09-08 23:38:52
Solution	Arpan	2004-08-17 13:01:13
re: Solution	dhruv	2004-08-17 06:45:10
stamps	Michele Rossi	2004-08-15 20:58:55
solution	amy	2004-08-15 16:08:54
logically	Robert Botwood	2004-08-10 22:56:44
solution	S	2004-08-10 19:22:51
my solution	Pete Za	2004-08-08 17:37:36
solutionnnnnnn	Kelly	2004-08-06 22:43:06
No Subject	matthew	2004-08-05 04:30:50
solution	matthew	2004-08-04 13:04:48
Elimination	Bractals	2004-08-02 11:49:20
No thinking needed	Federico Kereki	2004-08-02 07:37:12
solution	a.t.	2004-08-02 01:45:06
My solution	angela schultz	2004-07-31 18:43:07
Solution	DJ	2004-07-31 13:00:35

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