# An interesting logic puzzle

I thought this is a real cool problem… IT is all about logical thinking…

A teacher took out 8 stamps from a box – four of them white and four of them black. He got three of his brightest students – X, Y and Z and made them stand facing each other. He showed them the stamps, blindfolded each of them and then put two stamps on each of their foreheads. He put the final two stamps back in the box and closed the box. Then he opened the blindfolds. So, each of X, Y and Z could see the stamps on the forehead of the other two (but not their own – or the ones in the box). But they could obviously hear each other.

The teacher asked X first what were the color of the stamps (White White or Black Black or White Black) on his forehead. He said he did not know. The teacher asked then Y the same question. Y said he did not know either. Similarly the teacher asked Z and he too replied he did not know.

The teacher went back to X and asked if he now knew what he had. X again replied in the negative. The teacher asked Y next. And he did answer.

What was his answer? How did he deduce it?

Marek CyzioonMessaged you with an answer.

Rajib RoyonMarek, your answer is correct. Now I have to figure out your logic. This is one of those cases where it is easier for me to explain my logic than understand somebody else logic. Fear not! I have a flight tomorrow!! ðŸ™‚ But your answer is correct

Marek CyzioonIt must be because I am Polish and my logic is reversed ðŸ˜‰

Marek CyzioonOne interesting twist to this puzzle is that after X says the second time he does not know what stamps he has, Y and Z immediately know what do they have on their heads. And poor X still has no idea.

Manivannan SadasivamonMarek, Y and Z will have the same combination of stamps but not WW,WW or BB, BB.

Rajib RoyonSolution:

I liked Arvindhâ€™s explanation best. So, I am going to try and paraphrase it hereâ€¦

Since Y answered the question (in second chance), letâ€™s see how he must have thought. His thought process would have gone something like this: â€œCan I have White White? If I did, letâ€™s see why X could not answer just now (second time).

He would have seen the White White on my forehead and would have realized that he cannot have White White also. If he did, then Z would have seen all the four Whites on us (X and Y) and said Black Black for himself when he got a chance. But he did not. So X cannot possibly have White White.

Could X have had Black Black? Well, if he did, what would Z have thought when he just got his chance? Z would have seen a White White on X and a Black Black on Y and would have guessed that he cannot have White White or Black Black because then Y or X (respectively) would have seen all the four Whites (or Blacks respectively) on X or Y (respectively) and immediately answered that he had Black White. But Z said he could not answer.

Going back to Xâ€™s thoughts, he realized (remember he saw Y having White White – which is the original assumption we are still working on) that he could not have Black Black either. So X could not have White White or Black Black. So, he would have concluded that he had Black White. But he said he did not know.

That means, Y realized, that he did not have White White.

By exactly the same logic (colors are symmetrical), Y realizes he does not have Black Black either.

He must have had Black White then.

(Many have concluded the colors of X and Z – Black Black and White White or vice versa. Actually X and Z can be many other combinations. But Y has to be Black White).

Rajib RoyonSolution:

I liked Arvindhâ€™s explanation best. So, I am going to try and paraphrase it hereâ€¦

Since Y answered the question (in second chance), letâ€™s see how he must have thought. His thought process would have gone something like this: â€œCan I have White White? If I did, letâ€™s see why X could not answer just now (second time).

He would have seen the White White on my forehead and would have realized that he cannot have White White also. If he did, then Z would have seen all the four Whites on us (X and Y) and said Black Black for himself when he got a chance. But he did not. So X cannot possibly have White White.

Could X have had Black Black? Well, if he did, what would Z have thought when he just got his chance? Z would have seen a White White on X and a Black Black on Y and would have guessed that he cannot have White White or Black Black because then Y or X (respectively) would have seen all the four Whites (or Blacks respectively) on X or Y (respectively) and immediately answered that he had Black White. But Z said he could not answer.

Going back to Xâ€™s thoughts, he realized (remember he saw Y having White White – which is the original assumption we are still working on) that he could not have Black Black either. So X could not have White White or Black Black. So, he would have concluded that he had Black White. But he said he did not know.

That means, Y realized, that he did not have White White.

By exactly the same logic (colors are symmetrical), Y realizes he does not have Black Black either.

He must have had Black White then.

(Many have concluded the colors of X and Z – Black Black and White White or vice versa. Actually X and Z can be many other combinations. But Y has to be Black White).

Avinash MisraonJust wondering , Are there others ways to figure such problems out other than going thru a set of possibilities and eliminating some ?