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        riddles >> general problem-solving / chatting / whatever >> problem of guessing 2 consecutive integers
        
(Message started by: BenVitale on Apr 21^st, 2010, 11:11am)

Title: problem of guessing 2 consecutive integers
Post by BenVitale on Apr 21^st, 2010, 11:11am

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.
.....................
.....................

"What is exactly the function of the clock?

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.

Title: Re: problem of guessing 2 consecutive integers
Post by towr on Apr 21^st, 2010, 11:28am

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.