Chork's Puzzle 40
Difficulty Rating: 6
The emperor gathered the 100 wisest men in his empire and set them a task. If they manage to complete the task impressively, they will be generously rewarded.
The task is as such. The 100 men will be placed in a straight line and either a black hat or a white hat will be placed on their heads. Once they are lined up, they are not allowed to
(1) communicate amongst themselves
(2) turn back and look behind them
(3) remove the hat on their heads
The wise men will be able to see all the hats in front of him, but not the colour of his own hat or the colours of the hats behind him. They will, however, be able to hear the answers of the people behind them.
The king will then start with the man right at the back and ask: "What is the colour of your hat?" The wise man is only allowed to answer "black" or "white" and nothing more. After which, the man is not allowed to say anything more.
The king will the move on to the next man in line and ask the same question, all the way until he reaches the last man. Each man can only speak up when the king asks him the question and can say nothing more than "black" or "white". At the end of the whole task, the king will then tally the number of correct answers.
Before the wise men were lined up, they were allowed to get together and strategise, but they were told that the king would randomly line the men up.
The emperor gathered the 100 wisest men in his empire and set them a task. If they manage to complete the task impressively, they will be generously rewarded.
The task is as such. The 100 men will be placed in a straight line and either a black hat or a white hat will be placed on their heads. Once they are lined up, they are not allowed to
(1) communicate amongst themselves
(2) turn back and look behind them
(3) remove the hat on their heads
The wise men will be able to see all the hats in front of him, but not the colour of his own hat or the colours of the hats behind him. They will, however, be able to hear the answers of the people behind them.
The king will then start with the man right at the back and ask: "What is the colour of your hat?" The wise man is only allowed to answer "black" or "white" and nothing more. After which, the man is not allowed to say anything more.
The king will the move on to the next man in line and ask the same question, all the way until he reaches the last man. Each man can only speak up when the king asks him the question and can say nothing more than "black" or "white". At the end of the whole task, the king will then tally the number of correct answers.
Before the wise men were lined up, they were allowed to get together and strategise, but they were told that the king would randomly line the men up.
What is the maximum number of correct answers that is GUARANTEED if the men strategise correctly?
If you know the answer, post it in the comments section of this post.
posted by chorkie @ 7:30 PM
2 Comments:
At Sunday, October 22, 2006 10:24:00 PM,
fiveless said…
I say 99! Haha, this would be amusing if the wise men could like whisper if it was a white in front of him and shout if it was a black =D Then the dude from the first guy onwards would definitely get it right, assuming everyone is paying attention. Hahahaha. I dunno :P
At Sunday, October 22, 2006 11:01:00 PM,
chorkie said…
haha. tts a nice idea, and the answer is correct but ive another solution that works if they are supposed to shout out all their answers. (: it will be posted in a while.
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