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Q: 100 person are standing in a straight line all facing the head of the line. So the last person can see all 99 persons ahead of him, the second last person can see all 98 persons ahead of him. Some black and white hats are randomly distributed to these 100 persons. All the hats may be white or all the hats may be black or any other combination may be possible. Starting from the person standing at last, you ask him/her to guess the colour of his/her own hat ( which obviously he/she can not see ). After you are done questioning everybody, you give a score to that team depending upon how many of them could guess correctly. So for example, out of 100, if 5 could guess colour of their hats correctly then the score would be 5. Those 100 persons are given liberty to decide on a strategy before hats are put on their heads. What strategy should they decide in order to maximize their score in the worst case?
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Junior Software Engineer In Test

Interviewed at Yandex

4.1★
Aug 19, 2015

Q: 100 person are standing in a straight line all facing the head of the line. So the last person can see all 99 persons ahead of him, the second last person can see all 98 persons ahead of him. Some black and white hats are randomly distributed to these 100 persons. All the hats may be white or all the hats may be black or any other combination may be possible. Starting from the person standing at last, you ask him/her to guess the colour of his/her own hat ( which obviously he/she can not see ). After you are done questioning everybody, you give a score to that team depending upon how many of them could guess correctly. So for example, out of 100, if 5 could guess colour of their hats correctly then the score would be 5. Those 100 persons are given liberty to decide on a strategy before hats are put on their heads. What strategy should they decide in order to maximize their score in the worst case?

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