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Three wise men could not decide which of them is the wisest. Helped them passer-by. He got out of the bag five caps, three white and two black, and said that the wisest will be announced the first person to guess what color it cap. Then put the contenders against each other, tied it over his eyes, put on the cap and allowed to remove the bandages.

Long thought the wise men finally one of them exclaimed: "now I'm a white hat!"

How did he solve the problem? The traditional answer to this ancient problem is. The wise man thought: "I see the two white cap. For example, on my black cap. Then any of my opponents need to reason: "Before me was a black and white caps. If I also black, then the opponent in a white cap is not easy to solve the problem." But none of them are still not aware about the color of his cap. Therefore, to me white cap". If to take into account the options with the initial "let's say I white cap", the reasoning is significantly lengthened.

The answer turned out to be correct, but for us it is important that the wisest of the sages thought for a long time. And all because he was not familiar with modern methods of system analysis and heuristic methods of solving problems.

A systematic approach requires consideration of all the circumstances accompanying the solution of the problem.

The wise man thought only of his rivals, whereas participants in the game had four, including a passer-by. Behind him followed to speculate and, as we shall see, this option is the fastest led to the goal.

Heuristic methods do not guarantee a correct answer, but to save time required for solving the problem, with a sufficiently large probability of obtaining an outcome that is close to optimal.

Modern wise man would say: "the Judge must be impartial person. Then he'll try to put us on equal footing. But this is possible only in one way: to put us on the white cap. Suppose, however, that he isn't. But not as stupid to put two black hood, prompting the third obvious answer. Discard this option as unlikely. The option of using one of the black cap rate probability in one second. And the probability that it is me he is wearing, is equal to one-third. Therefore, with probability at least five-sixths I must be white cap".

Moreover, this analysis could be conducted and blindfolded. However, there was likely to make a mistake. But, isn't it the traditional answer? After all, the reasoning of the ancient sage fair, provided that his opponents a certain level of intellectual ability. And because not every man who is reputed to be or pretend to be a sage is such in fact, the probability of error is saved in this case.

A. Konovalov, Izhevsk, Professor
"Technology - Youth", No. 12, 1990


Your comments:

2013-12-17 14:41:55
not easy!
I am studying in the third grade she decided for the moment!
(if you do not understand, I believe that easy!)
2013-07-21 20:04:04
in the reflection of the eyes))
2013-02-12 17:12:20
Excellent and complete explanation. Previously only seen the first part, well, there's a complete logical analysis. Bravo
2012-09-06 14:42:41
the whole brain was piperonyl-hogwash
2012-06-13 08:37:32
I Nitsche not understand

2012-04-04 13:12:02
2012-02-19 09:42:19
Yes, easy puzzle
2011-02-05 11:33:51
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