[rookie1ja]

Head Bands - Back to the Logic Puzzles
Three Palefaces were taken captive by a hostile Indian tribe. According to tribe’s custom they had to pass an intelligence test, or die. The chieftain showed 5 headbands – 2 red and 3 white. The 3 men were blindfolded and positioned one after another, face to back. The chief put a headband on each of their heads, hid two remaining headbands, and removed their blindfolds. So the third man could see the headbands on the two men in front of him, the second man could see the headband on the first, and the first could not see any headbands at all.
According to the rules any one of the three men could speak first and try to guess his headband color. And if he guessed correctly – they passed the test and could go free, if not – they failed. It so happened that all 3 Palefaces were prominent logicians from a nearby academy. So after a few minutes of silence, the first man in the line said: "My headband is ...".
What color was his head band? Why?

Spoiler for Solution:

Head Bands - solution
The first one (he did not see any head bands) thought this way:
The last one is silent, which means, he does not know, ergo at least one of head bands he sees is white. The one in the middle is silent too even though he knows what I already mentioned. If I had a red head band, the second one would have known that he had a white head band. However, nobody says anything, so my head band is not red – my head band is white.

Spoiler for old wording:

Three white men were taken captive by a hostile Indian tribe. The chieftain was willing to let them go so he took them to a tepee, where there was no light. He put one head band on each of their heads (he had 3 white and 2 red - so 2 head bands were not used - captives were informed about these numbers). Then they went out in a queue so that each man saw the head-band of those standing in front of him (the first one did not see any head band, the second one saw the first one's head band, and the third one saw the head bands of the other two ). If somebody said the color of his head-band, they all would be free. After a few minutes of silence one of them said: "My head-band is ...".
What color was his head band? And how would you reason it?

Edited:
You have to assume that all the prisoners are fairly intelligent and have confidence in the intelligence of their fellow prisoners.
An incorrect guess deems them to imprisonment.
Only one guess can be made by the group.
All the captives want to be free and live.

[cheizmann13]

Couldn't the last person in the queue also be able to guess this correctly? Assuming the 3 men knew the amount of white and red bands (3 and 2) the last man could see that the first two men both have red bands. The 3rd man knowing there are only 2 red bands could then realize that he must have a white band and state that thus setting them free.

[Nitevizn]

I sort of disagree with this, or I am missing something. The second one only sees in front of him. So, if the first one's band has a red, then the second one could not be sure the third has a white and would remain silent. The third would only see one white and would be unsure and would remain silent. That scenario would be the same if the first had a white and the second a red. Both second and third would remain silent in that case as well. Am I missing something?

[rookie1ja]

Try to think as if you were the first one - as I mentioned above. Of course, we have to assume that all 3 are quite intelligent to pass the test that way.

[jbstorch]

cheizmann13 and Nitevizn:

The key to both of your questions is that there was no immediate response from anyone.

Cheizmann13, your answer doesn't work because the guy in back would see two red head bands and respond without delay.

Nitevizn, the second guy would see one red head band, and he would know that if he also had a red head band, the third guy would respond without delay. When this doesn't happen, the second guy would know his head band was white.

[MikeFalcor]

Actually, whether or not they knew the number of each color is irrelevant. "He took them to a tepee, where there was no light" - Therefore, without stating that the headbands were in the possession of the Chief PRIOR to taking them out to the tepee, this puzzle cannot be solved as they would not be able to see the colors (or anything else for that matter) of the headbands nor the quantities.

[senti_2k2]

I don't know whether i'm right or wrong.Pls clarify.

If the 1st guy sees 2 white bands, he might think whether he has a white or red.

So the 2nd guy has 2 options
1)either both of them are white
or
2)one of the 2 headbands is white.

So he can't answer even if the first guy(who doesn't see anything) is red or white.

If that's the case how come the first guy(who doesn't see anything) can confirm he is white.
It might be red too, becoz i see the solution to be justified for only option 2 for the 2nd guy.

Correct me if have missed something.

[larryhl]

the clues we have are as follows:

1st and 2nd can't both have red because 3rd person would have immediately known he had a white headband. Therefore 1st and 2nd either both have white or have one red and one white.

The only logical conclusion is that the first person has a white headband then. Why? Because if the first person had a red headband, the 2nd person would have immediately said that he himself had a white headband if the 3rd person didn't say anything. Since the 2nd person didn't say anything (due to there being a "quiet while" - long silence), the 1st person can conclude that the 2nd person isn't seeing a red headband, so the 1st person must have a white headband.

[malu_nike]

like senti_2k2 said....what if third sees 2 white headbands?

[larryhl]

i am going to post my explanation again, for the benefit of those confused. this time, there will be colors denoting the important parts...

the clues we have are as follows:

1st and 2nd can't both have red because 3rd person would have immediately known he had a white headband. Therefore 1st and 2nd either both have white or have one red and one white. (Note: if 1st and 2nd both have white then the 3rd sees 2 white headbands, which is what everyone seems confused about...)

The only logical conclusion is that the first person has a white headband then. Why? Because if the first person had a red headband, the 2nd person would have immediately said that he himself had a white headband if the 3rd person didn't say anything. Since the 2nd person didn't say anything (due to there being a "quiet while" - long silence), the 1st person can conclude that the 2nd person isn't seeing a red headband, so the 1st person must have a white headband.

Obviously, if the 3rd person sees 2 white headbands, the 2nd person wouldn't see a red headband on the 1st person. I guess I really needed to point that out? ><