QUIZ: Too Easy?

[Steve Navra]

Too Easy?

So the local brains trust seem to find my puzzles to easy???

Try this one then:

The moderator 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 their 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 B's stamps, and how did B work it out?

A real toughie, must admit I bombed on this one.
(Aristotle's logic, philosophy I.)

Regards,

Steve

 

[Lotana]

Steve,

There are 2 questions within the problem: what are the colours and how did B work it out. The first one is really easy.

The colours of B's stamps are green and red.

My thinking is like this. The wording of the problem is symmetric in regards to red and green colours, i.e. if we swap "red" and "green" in the wording of the problem the answer shouldn't change. The only answer that wouldn't change is "red & green". (If the answer was "2 reds" there is no reason why "2 greens" wouldn't suffice".)

I'll post the answer you've expected in a couple of minutes.

Say cheese

Lotana

 

[Chris G]

I think B has Red/Green stamps. Now to explain my theory....(not very well....)

If the stamps that can be seen are all the same colour then the person would answer yes. I'll use pair to mean red/red or green/green and opposite to mean red/green.

A answers no: B and C can not be the same pair. A, B, C could be Opposites.

B answers no: A and C can not be the same pair. Also B knows that he/she is not the same pair as C. (from previous answer) (This is the bit I think I've stuffed up...... B now know's if A or B are a pair. For my theory B notices that C is a pair.)

C answers no: A and B can not be the same pair. Also C knows he/she can not be the same pair as B or A.(from previous answers)

Therefore if B is a pair then A MUST be opposites. (A would have to be the different pair to B. As C can not be the same pair as either B or A, if B is a pair then A can not be......makes sense?..lol)

A answers No: Therefore B MUST be opposite. B is Red/Green

Makes sense to me. Probably wrong. Probably makes no sense to anyone else....oh well...

Cheers
Chris

 

[Lotana]

The answer is "R & G" and that's how B worked it out.

We don't know what B sees, so let's consider all possible scenarios (9 in total).

A C
1.RR RR
2.RR RG
3.RR GG
4.RG RR
5.RG RG
6.RG GG
7.GG RR
8.GG RG
9.GG GG

Options 1 and 9 should be dismissed because B would know straightaway that he has 2 Gs or 2 Rs respectively.

If real life is like either Option 3 or 7, B would know that he has RG because if he had RR or GG than one of the other 2 people would see 4 stamps of the same colour and would know what they have.

If real life is like Option 2, then B knows that he can't have RR (there would be 5 Rs). He thinks: If I had GG then C would know that he has RG using the same reasoning as in the previous paragraph. So - I have RG. Options 4, 6, and 8 are similar to Option 2.

So - we are left with option 5 where B sees two RGs. Here he thinks: if I had both stamps of the same colour, say RR, A would see RR and RG and when asked for the second time he would think in the way described in the previous paragraph and would tell that he has RG. But he did not, so I can't have 2 stamps of the same colour, therefore I've got RG.

Thank you Steve - my brain is ticking again.

Say cheese

Lotana

 

[asy]

Sheesh!

I posted on this thread last night, but it got lost in cyberspace

I have seen this puzzle before, and therefore wasn't going to post an answer.

Seems everyone beat me to it anyway!!

Keep 'em coming!!

asy

 

[Ace in the Hole]

I'm not the brightest guy around here, but I have a different answer and I hope I don't look stupid if I made a basic error.

A B C
RR RG GG (as long as A is opposite to C)


A makes his call and sees RG, GG so he can be RR or RG.
B is ready to make his call, he sees RR and GG. He doesn't know what he's got in the hole but it can't be GG otherwise A would have called him. He's got either RR or RG.
C makes his call and has no idea, could be RG or GG so he must see B holding RG.
This gives a big tell to B letting him know that he doesn't hold the pair of R's.
On the second round A checks again not knowing whether he is holding RG or RR.
B thanks C for the tell and raises, taking the pot.

Adrian

 

[Luke]

Well done everyone

I'll add my weight to the Red/Green combination, and agree, then disagree with Lotana.
1. Yes, because the puzzle has a definite answer which we can figure out, then it must be a mix of the two colours. The fact that there is a solution indicates to us that the double of one colour cannot be it, because the symmetry of the puzzle could permit the other colour.

But then Lotana I disagree with your reasoning and will side with Adrian. I also think the actual stamps had to be
A=RR, B=RG, C=GG (or the mirror image A=GG, B=GR, C=RR, but I'll only work one side to avoid duplication.)
A No : B infers he is not GG (B<>GG)
B No : A<> GG : C<>RR
C No : B<>RR
A No : - ?no information given.
B YES (is not GG, is not RR, must be RG)

Lotana said:
If real life is like either Option 3 or 7, B would know that he has RG because if he had RR or GG than one of the other 2 people would see 4 stamps of the same colour and would know what they have.

If real life is like Option 2, then B knows that he can't have RR (there would be 5 Rs). He thinks: If I had GG then C would know that he has RG using the same reasoning as in the previous paragraph. So - I have RG. Options 4, 6, and 8 are similar to Option 2.

I don't think your reasoning is right on the second paragraph.
I don't think C can know he has RG, and certainly not by the first time he is asked the question. By virtue of the fact that we know the sequence of answers was No, No, No, No, Yes then the arrangement must be as above. (I'm not going to fill a whole screen with the way I tested out the other options )

hmmmm Some good thinking here... now how do we use this in real life?

Regards all
Luke

 

[Lotana]

Hi Luke,

You say:
>> hmmmm Some good thinking here...
>> now how do we use this in real life?

We already have! Each post tells us a tiny bit about its author helping to make the right contacts.

Say cheese

Lotana

 

[Steve Navra]

Solution

WELL DONE everyone!

Seems to me you all solved the problem; the difficulty was more in expressing the answer correctly.

As best as I can express it then:

B says: "Suppose I have red-red. A would have said on his / 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 he / 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 he / 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 he / 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 he / she would have answered that he / 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 he / she must have green-red.
"'But C 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 (A) didn't say that he / 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 with any certainty.

“Hmmmmm how do we use this in real life??” - Luke

"I THINK, THEREFORE I AM" - Descartes

I imagine that wealth creation and success requires a due diligent thought process???

So, practicing the "art" of thinking is thus part of our wealth creation path!

And this seem very ‘real life’ to me!!

Regards,

Steve

 

[Luke]

Retraction

Hi again everyone...

Lotana, the credit is yours... There are indeed seven possible answers for the arrangement, all with B=RG. I was incorrect in thinking it was only one. I humbly bow to your logic.

Lotana said:
>> hmmmm Some good thinking here...
>> now how do we use this in real life?
We already have! Each post tells us a tiny bit about its author helping to make the right contacts.

Of course, thank you... but I was just having some fun.

Congratulations