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Topic: problem of guessing 2 consecutive integers (Read 931 times) |
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Benny
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problem of guessing 2 consecutive integers
« on: Apr 21st, 2010, 11:11am » |
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Problem :
Two people, A and B, are assigned consecutive positive integers. They are each informed of their own integer and made aware that the two integers are consecutive. The task for them is to guess the other fellow's integer.
They sit in the same room but are forbidden to communicate in any way. There is a wall clock that strikes every hour. A and B are instructed to announce their solution as soon as they get one but only immediately after a clock strike.
Read more (Problem+Solution): http://www.cut-the-knot.org/blue/TwoConsecutiveNumbers.shtml
There are 2 items in the solution that are not clear to me:
Quote:
For the distribution 1/2 the owner of the lower number is able to make an announcement after the FIRST strike.
For the distribution 2/3 the owner of the lower number is able to make an announcement after the SECOND strike.
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"What is exactly the function of the clock?
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I'm not clear on this distribution. Could anyone clarify? What happens to the distribution after the third strike, the 4-th one,...k-th strike?
Why does he ask about the function of the clock?
I thought the exact function of the clock is clear.
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If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
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towr
wu::riddles Moderator
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Some people are average, some are just mean.
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Re: problem of guessing 2 consecutive integers
« Reply #1 on: Apr 21st, 2010, 11:28am » |
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To people familiar with this kind of riddle the function of the clock and the procedure would be clear, but most people have terrible difficulty with this problem. Just look up the red eyed monk thread.
Every strike of the clock eliminates possible worlds; where one has a 1 the other a 2, where one has a 2 the other a 3, etc. At some point the person with the lowest number cannot image that the other could have a lower number and not yet have realized it, and thus knows what the situation is.
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Wikipedia, Google, Mathworld, Integer sequence DB
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