## Tuesday, July 03, 2012

### Bert Goes to a Party

You are at a logic master's party.  The host has decided to play a game.  He takes 8 stamps, 4 red and 4 green and announces the rules.  He will affix two stamps to each party goers head and then he will place the remaining two in his pocket.  You, Bert, and two others, Al and Casey, can see the other stamps, but don't know your own stamps and cannot see the stamps in the host's pocket.

The host then asks each of you in turn if you know the colors of your own stamps:
A: "No."
B: "No."
C: "No."
A: "No."
B: "Yes."

What color stamps do you have?

1. red and green
(Jim May)

2. Whoa I'm so confused...

3. Jim May is correct. Every time someone says "no" they are eliminating some possibilities. For example, when Al first says "No", he is really saying "I know that I don't have two green stamps because I don't see four red stamps on Bert and Casey's foreheads".

1. NOTATION: Suppose x is ij and y is kl, where i, j, k, and l are what x and y are wearing. i, j, and k can be R or G, which stand for red and green. Then xy is ijkl.
1. A can't determine it, so BC can't be GGGG or RRRR
2. B can't determine it, so AC can't be GGGG or RRRR.
3. C could now determine, if AB were GGRR or RRGG, that he is RG. So AB is not GGRR or RRGG.
4. Since C can't determine it, it also can't be RRRR or GGGG.
5. If B has either RR or GG, A can have neither RR nor GG, because of steps 3 and 4, so A could find out that he is RG if B is either RR or GG.
6. He doesn't work this out, so B must be neither, and B must be RG.

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