Robbers and bandits

[Guest]

This type of puzzle is called by some logicians a negative information through logical reasoning. In other words I give you all the information you need, but because of a negative event WITHIN the puzzle it can be solved

There are five people traveling through a dessert. Bandits capture them and bury them in sand such that two are facing in one direction and the other three are facing the first group behind a wall. Each can only see the people in front of him behind the wall.

they are each wearing different colored hat. The bandits say that whomever can determine what colotr hat he is wearing without saying anything else walks free

They are told that there are 3 types of hats 1 heart shaped one. and two blacks, and two whites. They are not told who is wearing what type but they are told that the heart is on the left of the wall. Each knows how many people are in front and behind of him (2/3)

ONLY ONE PERSON MUST SAY THE HAT THEY ARE WHERING.

A B C D E

? ? ? ? ? ?

A B C D E

? ? ? ? ? ?

? ? ? ? ?

D answers correctly

Because E was silent (and therefore unable to determine the color of his own hat) D knows that he must be different then the person in front of him (as they are different). Since they are on the right he knows that he does not have the heart. Therefore D must be white.

This riddle work just the same without the left side of the wall. It is just there to confuse you.

[Guest]

it seems that you have not solved this puzzle to its entirety. please correct me if i'm wrong, but firstly, there is no way of knowing offhand the order in which the hats will be placed, and so, your second diagram is only one possible arrangement.

that said, and assuming all the actors are logically inclined - on the left, the heart-hat wearing man will be able to quickly ascertain which hat it is he wears, whether he is in position A or B. if it is the man in pos. A, he will see that the man in front of him is not wearing a heart-shaped hat, and given that he knows it to be on his side of the wall, will immediately know it is he who wears it. if it is the man in position B, then A's silence will alert him that it is in fact he who wears it. the man left on this side of the wall will have to hope for a lucky arrangement on the other if he is to have any chance at survival.

on the right side of the wall, the game will begin with E. there are two possible arrangements of the men (C and D) between he and the wall. they will either be of the same color or opposite colors.

possibility 1 = if E sees that they (C&D) wear the same color, rejoice, for it is then possible that all may be saved... E knows that whatever color C&D share, his must be the opposite. D hears him call out his color, and reasons that this is only possible if he (D) shares the same color hat of the man in front of him © and so calls out his own color. C then realizes that the second color called out must also be his own, calls out his color, and the remaining man on the left side of the wall (assuming he was capable of hearing) has no question what color his own hat must be.

possibility 2 = E sees that C&D wear oppositely colored hats, and that he cannot therefore definitively deduct his own... however, E's silence alerts D that he and C must wear oppositely colored hats - and therefore, D yells out his color. hearing only one color called out behind him, C knows that if E had been able to figure out his color, then D would have figured out his color afterward (and there would have been two calls) - and thus, hearing only one color, C knows that the man who called out must be D, and that he © must wear the opposite color... he too calls out his color. alas, in this instance, both E and the man remaining on the left side of the wall have no way of discovering their colors, and are thereby relegated to guessing (or at least one of them is... a prisoner's dilemma of sorts? i could write another page on that)

[unreality]

dVs, ur reasoning is better and clearer than comperr's, I think. i didnt even understand the problem until you gave the answer lol. so that means at least 3 of 5 ppl go free, if they're as smart as you. the other 2 have to guess.

[Guest]

it seems that you have not solved this puzzle to its entirety. please correct me if i'm wrong, but firstly, there is no way of knowing offhand the order in which the hats will be placed, and so, your second diagram is only one possible arrangement.

This riddle includes an element often known as multiple arraignments: there are many possibilities for how the hats are arraigned but only one allows for an unambiguous answer. This riddle on its own is very hard and therefore I give diagram number 2.

that said, and assuming all the actors are logically inclined - on the left, the heart-hat wearing man will be able to quickly ascertain which hat it is he wears, whether he is in position A or B. if it is the man in pos. A, he will see that the man in front of him is not wearing a heart-shaped hat, and given that he knows it to be on his side of the wall, will immediately know it is he who wears it. if it is the man in position B, then A's silence will alert him that it is in fact he who wears it. the man left on this side of the wall will have to hope for a lucky arrangement on the other if he is to have any chance at survival.

This is sort of true. I did not make it clear what the victims know and do not know. The original version of this riddle had no heart. I was supposed to say the the heart wherer should not have a chance to speak. there are two answers to this riddle.

on the right side of the wall, the game will begin with E. there are two possible arrangements of the men (C and D) between he and the wall. they will either be of the same color or opposite colors.

True

possibility 1 = if E sees that they (C&D) wear the same color, rejoice, for it is then possible that all may be saved... E knows that whatever color C&D share, his must be the opposite. D hears him call out his color, and reasons that this is only possible if he (D) shares the same color hat of the man in front of him © and so calls out his own color. C then realizes that the second color called out must also be his own, calls out his color, and the remaining man on the left side of the wall (assuming he was capable of hearing) has no question what color his own hat must be.

Only one had to call out his color: did I not make that clear?

possibility 2 = E sees that C&D wear oppositely colored hats, and that he cannot therefore definitively deduct his own... however, E's silence alerts D that he and C must wear oppositely colored hats - and therefore, D yells out his color. hearing only one color called out behind him, C knows that if E had been able to figure out his color, then D would have figured out his color afterward (and there would have been two calls) - and thus, hearing only one color, C knows that the man who called out must be D, and that he © must wear the opposite color... he too calls out his color. alas, in this instance, both E and the man remaining on the left side of the wall have no way of discovering their colors, and are thereby relegated to guessing (or at least one of them is... a prisoner's dilemma of sorts? i could write another page on that)

This would actually not be a prisoners dilemma as there are only two possible states (free and bound) verses three (free, impaired, bound)

Your confusion stems from the fact that I did not make it clear that only 1 must be able to ascertain there hat color.

[Guest]

i do not see that i was confused, but i appreciate your clarifications nevertheless.

you should also modify the text above your second diagram...

"includes who is wearing what if you can't solve it on your own..." is misleading. since there are multiple potential configurations and yet only one which you intend to be used, you should give this particular one within the problem itself (and not after the fact as a hint) if you wish it to be the only one considered.

[Guest]

ok. thanks for the advice.

[bhramarraj]

There is no possibility when only one person will be able to answer the color of his hat.

Say A & B are on the right side of the wall and both of them know that one is wearing the heart shaped hat, and other one is wearing black or white hat. So if A sees heart shaped hat on B then he will not be able to determine color of his own hat, so he keeps silence. Thus, acknowledging silence of A, it becomes known to B that he is not wearing black or white hat, hence he is wearing heart shaped hat. So in this condition B can call his hat identity.

Again, say A sees B wearing black or white hat, then he will be able to tell That his hat is heart shaped.

Say C, D, & E are on the other side of wall. Say E sees two white or two black hats in front of him, then he will be able to call out his own hat's color.

And if E sees one black & one white colored hats in front of him, then he will not be able to able to call out his hat's color, but at the same time acknowledging the silence of E, it becomes known to D that he himself and C are wearing hats of different colors.

So D is able to call out his hat's color which must be black if white is seen on the head of C, and white if black is on the head of C.

So we see that in either conditions at least two persons will be able to identify their hats.