Masters of Logic Puzzles III. (stamps)

[rookie1ja]

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 Grand Master's pocket and the two on his own forehead. 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 color stamps does B have?

This old topic is locked since it was answered many times. You can check solution in the Spoiler below.

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Masters of Logic Puzzles III. (stamps) - solution

B says: "Suppose I have red-red. A would have said on her second turn: 'I see that B has red-red. If I also have red-red, then all four reds would be used, and C would have realized that she had green-green. But C didn't, so I don't have red-red. Suppose I have green-green. In that case, C would have realized that if she had red-red, I would have seen four reds and I would have answered that I had green-green on my first turn. On the other hand, if she also has green-green [we assume that A can see C; this line is only for completeness], then B would have seen four greens and she would have answered that she had two reds. So C would have realized that, if I have green-green and B has red-red, and if neither of us answered on our first turn, then she must have green-red.

"'But she didn't. So I can't have green-green either, and if I can't have green-green or red-red, then I must have green-red.'

So B continues:

"But she (A) didn't say that she had green-red, so the supposition that I have red-red must be wrong. And as my logic applies to green-green as well, then I must have green-red."

So B had green-red, and we don't know the distribution of the others certainly.

(Actually, it is possible to take the last step first, and deduce that the person who answered YES must have a solution which would work if the greens and reds were switched -- red-green.)

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?

[Guest]

There is no specification of the two stamps distributed to each person being the same color.

[Guest]

That doesn't have to stipulated. If you draw out all the possibilities, this is the only stamp distribution in which one of the three would know without all three knowing. It takes a bit but it's worth it.

[Guest]

or you can think that the answer would not be able to be determined between red-red and green-green therefore must be red-green

[Guest]

she can as long as the other 2 ladies had 2 of the same colors on there heads and if they had the same colors. So if Lady a and c both had double red then b could say for sure that she had 2 green because all 4 red would be exposed. This is the only way because of the person holding 2 in his hand. If the 2 other ladies have red-Green that leaves 2 left of each color and so the hand can have green green or red red or red green but it's impossable to tell. You would need to know whats in the hand to answer.

we need to know the stamps on the other 2 ladies heads.

[Guest]

the only possibility is red and green on each

[Guest]

we don't need to know the stamps on the other ladies heads. the key here is that it took 'B' a second turn to realize the answer. if both other ladies had the same color, she would've known the answer immediately. since she was able to deduce the colors of the stamps on her head, this is the only situation where she could've done so.

A goes first (with either red-red or green-green) - sees a situation she cannot solve.

B goes next, sees A (with RR or GG) and MUST then see C (with the opposite of A). B cannot know for sure her own stamps.

C goes, sees A (RR or GG) and B (unknown). Since C does not answer, we can infer that B does not have the same color as A. B realizes this, and now knows that since neither A nor C stated their own colors, B must have one of each. B then answers the next time around.

[Guest]

Only for those who haven't figured it out completely yet:

If two or three persons have one of each color (RG), then nobody can say one's own color in any number of tries.

If two people have both same-colored stamps on their head (RR RR or GG GG), the third will have the answer instantly.

Only if one has same-colored and another the opposite but same-colored stamps (RR and GG) on their head can the third person (with different colored or RG) have the answer on her second try.

[Guest]

Only for those who haven't figured it out completely yet:

If two or three persons have one of each color (RG), then nobody can say one's own color in any number of tries.

If two people have both same-colored stamps on their head (RR RR or GG GG), the third will have the answer instantly.

Only if one has same-colored and another the opposite but same-colored stamps (RR and GG) on their head can the third person (with different colored or RG) have the answer on her second try.

What you said is exaactly how we know that that isn't the case. She DID know the answer and that is how you figure out how she knew.

[Guest]

...umm what? didnt quite understand that one

[Guest]

...umm what? didnt quite understand that one

A...B...C

if two have RR...

RR RR GG == C instantly has answer (sees all 4 R)

RR GG RR == B instantly has answer (sees all 4 R)

GG RR RR == A instantly has answer (sees all 4 R)

similarly if two have GG...

if two have RG...

RG RG RG == nobody can have any answer

RG RG RR == nobody can have any answer

RG RG GG == nobody can have any answer

RR RG GG

1st turn, nobody has the answer.

2nd turn, the person who sees one RR and one GG thinks:

If I had RR, the person having GG instantly must have had the answer.

If I had GG, the person having RR instantly must have had the answer.

But they did not...

So I have neither RR nor GG.

Therefore I have RG!

[Guest]

This puzzle is one move longer. Person A would be able to tell the second time, if B and C were RR GG or GG RR.

[Guest]

Well, I think you stated this question wrong. Tech, they could have any from the way it is said, they could have purple-pink for all we know. You said a "set of 8". Set means 2. meaning 16. so even if moderator had red-red there still a bunch more out there.

[Guest]

I don't completely agree with the solution. It is true that B has one of each color, and C has to have some sort of pair. We just have no idea what A has.

The first three noes establish no two logicians have pairs of the same color. The fourth no, A's second, proves that A wasn't seeing two opposite-colored pairs. (She wouldn't have been able to have either type of pair, making her stamps obvious.) If C had a pair, B had to have one of each color, and it no longer mattered what A had.

Possible solutions:

-A- -B- -C-

RR RG GG

GG RG RR

RG RG GG

RG RG RR

So, A's ability to solve some configurations on her second turn stripped away some of the ambiguity that B faced in other configurations, thereby making it ambiguous as to which configuration was actually solved.

I would suggest shortening the puzzle so that it goes:

A: "No."

B: "No."

C: "No."

A: "Yes."

Sorry if anything is unclear, but it was taking much longer to express my view than it took to form it in the first place.

[Guest]

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.

[Guest]

Well, I think you stated this question wrong. Tech, they could have any from the way it is said, they could have purple-pink for all we know. You said a "set of 8". Set means 2. meaning 16. so even if moderator had red-red there still a bunch more out there.

FYE for everyone. The statement in bold is incorrect. Set, while a very versatile word ("Set has 464 separate definitions in the Oxford English Dictionary, the most of any English word; its full definition comprises 10,000 words making it the longest definition in the OED." -From the Wikipedia disambiguation page) does not in any way limit itself to refering to twos. The word that singinsly was thinking of, I believe, was 'pair'. The 'official' Oxford English dictionary definition that most closely relates is: "a number of things or people grouped together as similar or forming a unit."

The key words here being 'a number'. Not 'two', 'a number', meaning any number. Nuff said.

[Guest]

took me a few mins, but I did figure it out.

B has GR

it is important to look at the responses

A said NO meaning A must have seen a RG(B.) and a RR©

B said no-B see's a GG(A) and a RR©

C said no see can see the RG(B.) and GG(A)

A says no again

B says yes after ruling out the answers of the others and what they must see and can't figure it out. Each of them must have seen a RG on B otherwise they would have answered yes because B saw two greens and two reds.

I hope that explanation makes sense.

[Guest]

This one is sub-par compared to the other riddles.

[Guest]

the one that said yes knew because they had no stamp there were not enough to go around if the grand master took two away.

[Guest]

"Some of you people on here are such idiots????"

Mate, many folks are just learning to think logically here, and if they are taking the time to ask questions and learn, I would hardly call them idiots. On the other hand, someone who makes such arrogant statements about others . . . he in my opinion, would certainly deserve the label!

But in fairness . . . I agree no ambiguity here. B knows she is an RG.

To explain more politely why some went wrong, the puzzle states B was the first to say that she knew the colour of stamps. If the puzzle had been NO, NO, NO, YES, it would have meant that A had an RG. Similarly, if the puzzle had stated NO, NO, NO, NO, NO, YES, then C would have known she had an RG combo. But the puzzle said B knew in the second round, so that is the way we know she knew that she had an RG pair.

So what happens next?

A and C simultaneously ask if they can get extra credit, because they know not only what they have on their own heads, but also what is hidden in the Grand Master's pocket! B replies, that's silly ladies, everyone knows what is in the Grand Master's pocket. This one should be pretty easy, but how do they all know now?

OK I have an extension, variation on this one:

(Hopefully I've thought this one out properly, but if I have not I'd be happy to hear -- politely James!!!! -- why I my solution is incorrect)

In the next round, the answers are:

A: No

B: No

C: No

A: No

B: No

C: No

A: YES

B: No

C: YES

B: Bad Luck, looks like I lose this time! Can we play again?

Grand Master: Sure, why not, let me mix these up and paste them on again . . . OK ladies, you know the drill, your shot A . . .

A: No

B: No

C: No

A: No

B: No

C: No

A: No

B: No

C: No

A: YES

B: YES

C: YES

[Guest]

I understand the puzzle asks if B replies "Yes" during the second turn, what are her stamps and what is the situation, but why couldn't person A answer "Yes" during the second turn and state that she has the two opposite colors of person C?

[Guest]

B could have one of each by discareding situations

[Guest]

how many logicists are there?

[Guest]

I think that B only said yes so that they wouldn't have to keep playing this stupid game with stamps on their heads. loll.

[Guest]

This is a useless praise post:

Good puzzle! Took me a bit.

And, if there is any further doubt, I agree that it was completely unambiguous- just tricky.