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Posted 23 July 2008 - 02:08 PM
It has been established that if the first 2 had red bands then the third person would know they have a white band and reply immediately.
As they did not we know that of the first two, one has a white the other has a red band. The second person can see what colour the first has and so replies with the other colour.
Posted 01 August 2008 - 10:03 AM
Edited by AliceJH, 01 August 2008 - 10:09 AM.
Posted 11 September 2008 - 06:48 PM
Simply stated, you must tell the puzzlee that the chief has promised that the three captives will not all wear red head bands. The fact that at least one captive will wear a red headband is self-evident in the number of available white headbands in relation to the number of captives. However, as the riddle is currently worded, it is entirely possible that the third man in line would look forward to see two red headbands on his fellow captives and have no certainty whatsoever that he himself is not wearing a red one as well, or for that matter has been adorned with one of the white ones. His silence, or reluctance to make a guess, offers no information to either other man as to the color of his headband, except of course for the obvious point that both front men are not simultaneously wearing white.
To avoid a more exhaustive explanation, the second man cannot know in any case (as currently posed in the riddle) the color of his own headband unless a very specific order of the bands is being used (1.White,2.Red,3.Of no consequence). No.2's silence (when added to the third man's silence) does afford a bit of information to the first man in the line, but only in the circumstance that if he (the second man) sees a white headband on the man in front of him, then he can clearly only know that his own headband is not also white, as just proven in the above placement. Otherwise, the third man would have claimed his own to be red right away. (If you have trouble understanding why this is so, or perhaps do not agree right away, keep in mind that all three headbands could conceivably be red in the current wording of the riddle)
The first man would never be the only captive with the answer to the solution, no matter how the bands were arranged. I won't bother describing the logic to this, but suffice it to say that there a number of situations in which the first man could know the color of his own headband, but not without the second man already being aware of his own and speaking up.
The person who posed the riddle has given us a good logic puzzle, but unfortunately left out a key detail. There are simply too many scenerios (placements of colors coupled with silence) in which no man would be able to answer the riddle definitively at such high stakes without knowing for certain beforehand that the chief was forbidden to give every man a red headband.
Posted 13 September 2008 - 05:10 AM
So, since there is a little ambiguity, there are 2 correct answers: the first man or the third man responded white, but the only man who could answer without guessing is the third man, so that may actually be the best answer!
Edited by RaDazzle1, 13 September 2008 - 05:13 AM.
Posted 24 September 2008 - 02:58 AM
Posted 24 September 2008 - 08:57 AM
Posted 16 October 2008 - 05:27 PM
Second man would guess correctly
The last man would say his hat is white if the other 2 had red. So, if he is silent that means the first two have different colored head bands. The second man would guess the opposite of the color the first man has. So if first man has red he would say white, if first had white he would say red.
Posted 16 October 2008 - 09:45 PM
If the 3rd person answers he says my band is white. (because he see the two red)
If the 2nd person answers he says my band is white. (because he knows one must be white and he see a red)
Finally if the 1st person answers he says my band is white. (because the 3rd and 2nd person did not answer)
OF INTEREST WHOEVER ANSWERS WILL SAY WHITE. Thanks !!!
Posted 06 November 2008 - 04:42 AM
Edited by ryaneverett, 06 November 2008 - 04:43 AM.
Posted 07 November 2008 - 12:35 AM
The second guy can see the first guy, however, his answer really depends on the 3rd guyes actions.
Guy # 1 has a white hate on, that leaves 2 other white hates
Guy # 3 see's another white hate on the 2nd guy therfore the 3rd guy is still confused on the color becuase he could either have a red or a white.
Now, since guy # 2 doesnt hear an answer from guy #3 that means guy # 3 cannot find the pattern which means his hate is the opposite of the first.
If guy #3 saw 2 red hats, he could tell a pattern and know his hat is white.
However, if guy #3 could not fnid a pattern, guy #2 will realize his hat is the opposite or same color depending on the 3rd guys answer.
Now, you may ask well what happens if the colors go white white red, or white red red,
Simple, if guy #3 cant tell a pattern ( 2 reds) and guy number 2 cant tell the pattern ( guy infrotn fo him needs to have red) then the first guys knows, he has a white hat on because thats the only color that would keep #2 and #3 speechless .
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