June 16, 2010

PUZZLE OF THE DAY

QUESTION:-

Three scientists went on an expedition in the Amazon forests where they were captured by cannibals. The cannibal chief likes having fun, so he devised a game that gives the scientists a chance to survive! He took them to a tent where he had 3 white hats and two black hats (no points for guessing where he got the hats from!). He then put one hat on the head of each of the scientists (since there were 5 hats, 2 hats remained unused). There is no light in the tent and there is no way the scientists can see or figure out which hat is which.

He told the scientists that they have to walk out of the tent in a queue, and then any one of them has to guess the colour of the hat on top of HIS head. They are to stand so that the third scientist can see the colour of the hats on the two scientists in front of him. The middle one can only see the colour of the hat on the scientist in front of him. The first scientist cannot see anyone's hat. The scientists were given 10 minutes inside the tent to discuss their strategy. Once they walk out, the only thing any one of them is allowed to say is "The colour of my hat is ..........". If the colour is correct they will all be set free. If the colour is wrong or anyone says or does anything else, all of them will be cooked and eaten!

The scientists went out, they stood there for some time, and then one of them said "The colour of my hat is ........!". What colour was his hat?

SOLUTION:

The colour was white!

If the last scientist saw two black hats ahead of him, he would know that his hat had to be white. If he kept quiet for a fixed time, it would indicate to the scientists ahead of him that at least one of the other two had a white hat.
Now the second scientist would know that there was at least one white hat between him and the first scientist. If the first one has a black hat, then he himself should have a white hat. But he kept quite. So, the first scientist knew that he had a white hat.
Using the strategy explained above, at least one of the scientists will always be able to correctly predict the colour of the hat on his head (whatever be the distribution of hats!)

 
 
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