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7 replies to this topic

### #1 howardl1963

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Posted 11 October 2010 - 02:31 AM

A third party writes a positive integer on two post-it notes and then places one each on the foreheads of two perfect logicians. The integers are consecutive. All of this is common knowledge. He then asks the logician with the lower of the two integers to begin the conversation (this is not known by the two logicians). The following conversation ensues.

Logician A "I don't know my number."

Logician B "I don't know my number"......this stement is repeated N times.

Finally, one of the logicians says "I know my number."

As it relates to N, what is the integer on the forehead of the logician who first identifies his number? Why?
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### #2 maurice

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Posted 11 October 2010 - 04:27 AM

Edited by maurice, 11 October 2010 - 04:28 AM.

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### #3 mmiguel1

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Posted 11 October 2010 - 04:31 AM

A third party writes a positive integer on two post-it notes and then places one each on the foreheads of two perfect logicians. The integers are consecutive. All of this is common knowledge. He then asks the logician with the lower of the two integers to begin the conversation (this is not known by the two logicians). The following conversation ensues.

Logician A "I don't know my number."

Logician B "I don't know my number"......this stement is repeated N times.

Finally, one of the logicians says "I know my number."

As it relates to N, what is the integer on the forehead of the logician who first identifies his number? Why?

Spoiler for started sort of, but no time to finish... better get back to homework

Edited by mmiguel1, 11 October 2010 - 04:39 AM.

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### #4 maurice

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Posted 11 October 2010 - 04:45 AM

Spoiler for how I got answer

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### #5 maurice

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Posted 11 October 2010 - 05:10 AM

Spoiler for what I left out

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### #6 k-man

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Posted 11 October 2010 - 05:08 PM

Spoiler for how I got answer

I followed the same logic, but...
Spoiler for I got a different answer

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### #7 maurice

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Posted 11 October 2010 - 05:15 PM

I followed the same logic, but...

Spoiler for I got a different answer

Spoiler for according to the definition of N I was wrong but

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### #8 Chuck C.

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Posted 12 October 2010 - 12:00 AM

Spoiler for One way of thinking about it

All this said, I suspect there is an underlying falacy in this thinking.

Edited by Chuck C., 12 October 2010 - 12:02 AM.

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