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# Masters of Logic Puzzles III. (stamps)

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Nice puzzle, though I don't think you needed to reveal B's second answer. The first four responses:

A: "No."

B: "No."

C: "No."

A: "No."

left only one possible answer for B

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Here's a quick variation. They played again, same rules except this time everybody answers twice even if somebody has already said "Yes".

A: "No"

B: "No"

C: "No"

A: [ history has not recorded what A's second answer was ]

B: [ nor B's ]

C: "Yes"

What were A and B's second answers?

A: "Yes"

B: "No"

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• 5 weeks later...

i think this does'n make any sense because they don't know the colour of the 2 stamps in the moderators poket "each logician can see all the other stamps except those 2 in the moderator's pocket and the two on her own head"

or if they all have red and green on their head this doesn't work either

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Though I have heard this one before, I think that your question gives away the answer, unless the answer was "the color can't be determined, but they are the same color".

The stamps have to be one of each color by the phrasing of the question, else they color could not be isolated.

Still a good riddle.

-Doug

Edited by DugALug
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• 1 month later...

Arbitrarily, I chose x:y, x=red, y=green. 3-1 for AC would mean RRRG or GRRR.

A 1: says no so everyone knows BC isn't 4-0 0-4 so only possibilities for BC are 3-1 2-2 1-3 1-1-1-1. (RGGG GGGR GGRR RRGG RRRG GRRR GRGR)

B 1: B also says no which means everyone knows AC isn't 4-0 0-4. B sees 3-1 2-2 1-3 1-1-1-1 possibilities for AC.

C 1: says no when she knows BC and AC both don't have 4-0 or 0-4. If she sees AB = 2-2 then she would know she has RG. For AB = RRGG GGRR C must be RG or else AC or BC would have been 4-0 0-4. Therefore C didn't see 2-2 because she said no. Since AB can't be 2-2 everyone knows possible AB are 1-3 3-1 1-1-1-1.

A 2: says no so BC can't be GGGR RRRG RRGG GGRR or else A would be RG because if A is RR/GG while BC is any of those then AB would be 2-2. A knows AB can't be 2-2 from C 1 saying no. All thats left for BC is RGGG GRRR GRGR.

B 2: figures it out from A 2 saying no. BC can only be GRRR or RGGG or GRGR and all three have B as RG.

Don't know if this is more clear.

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• 7 months later...

Masters of Logic Puzzles III. (stamps) - Back to the Logic Puzzles

Try this. The grand master takes a set of 8 stamps, 4 red and 4 green, known to the logicians, and loosely affixes two to the forehead of each logician so that each logician can see all the other stamps except those 2 in the moderator's pocket and the two on her own head. He asks them in turn if they know the colors of their own stamps:

A: "No."

B: "No."

C: "No."

A: "No."

B: "Yes."

What are the colors of her stamps, and what is the situation?

Who posted this problem? The actual questions are "What color stamps does B have? What colors have A and C?", not "What are the colors of her stamps, and what is the situation?". The 'situation' is that the second question in the actual problem (please see http://brainden.com/logic-puzzles.htm ) CANNOT BE DETERMINED, not by man, not by computer, not by fish. Whoever posted the problem, please remove the second question.

(The answer to the first question is straight-forward, and hinges on 'C' replying "No". That "No" indicates that whatever else C observes on A and B, She cannot see 2 pairs, therefore at least one of A and B have both green and red stamps on their forehead. Both A and B realize this. A subsequently answers "No" which tells B she cannot have 2 like-colored stamps (otherwise A would have known her colors, which would have been G-R), so B knows She is G-R, 100%.)

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Some of you people on here are such idiots.

The whole point of the puzzle is you need to work out the situation where

A: "No."

B: "No."

C: "No."

A: "No."

B: "Yes."

and what B's stamps are.

Why do you get people like Wordblind who start saying "its ambiguous". It is not ambiguous. There is only one solution.

B has 2 different coloured stamps (red and green)

A has a pair of stamps which are the same colour. (red or green).

C has a pair of stamps which are the same colour, but not the same colour as A's pair. (red or green).

It does not matter what colour A or C's pair are, all that matters is the situation. The situation being that both A and C will have the same colour stamps in their pair, and B will have stamps of different colours in B's pair.

Several people have already explained why this is the case. There are no other possible answers if you are being sensible and not just being a fool.

There is NOT only ONE solution, sly. 'A' does NOT have to have a pair (2 of the same color), nor does 'C' HAVE to have a pair. B would know her answer second time around, same pattern of answers, in ANY of the following combos:

A - RG

B - RG

C- RG

A - RG

B - RG

C - GG (or RR)

A - GG (or RR)

B - RG

C - RG

A - RR

B - GR

C - GG (or reversing pair colors with A and C, of course)

Let me know if you need this explained.

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• 4 months later...

Very Very Simple.....................

In Fact 2 round is not required at all. Please read this below and tell me why we need second round?

Assuming that all have the fair chance: then here are the combinations:

1. No 2 member will have same colors i.e

A B C

RR RR GG

this type of combination's will not exist's

2. if above is true then below is also true

A B C

RR RG GG

this type of combination's will not exist's too.

in this case since B know's no 2 will be having same colors he will easily identify that he has RG

3. Finaly we have following combinations

A B C

----------------

Group 1:

RR RG RG

GG RG RG

----------------

Group 2:

RG RR RG

RG GG RG

----------------

Group 3:

RG RG RR

RG RG GG

----------------

Group 4:

RG RG RG

----------------

So in first chance if A say "yes" Group 2 or Group 3 exists.

if A say's "no" means means there exist either group 1 or group 4 combination

So now if Group 4 combination holds true then B will say "no" else if group 1 combination exists then he will say "yes"

Now if both A and B say "no" then C will say "yes" as this has to be group 4 combination:

So in all this is not an fair chance competition infact it's luck.

Edited by Ganesh Sawant
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