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Subject: Riddler for June 10 - The Perfectionist Professors rss

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Matthew M
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Didn't see a thread from MABBY for this one, and I was excited because I think I actually nailed this one!


http://fivethirtyeight.com/features/solve-the-mystery-of-the...

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A university has 10 mathematicians, each one so proud that, if she learns that she made a mistake in a paper, no matter how long ago the mistake was made, she resigns the next Friday. To avoid resignations, when one of them detects a mistake in the work of another, she tells everyone else but doesn’t inform the mistake-maker. All of them have made mistakes, so each one thinks only she is perfect. One Wednesday, a super-mathematician, whom all respect and believe, comes to visit. She looks at all the papers and says: “Someone here has made a mistake.”

What happens then? Why?
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What happens

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Nothing happens until the tenth Friday, on which all 10 professors resign.


Why

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If only one person had made a mistake then the person not aware of anyone else making a mistake would resign on the first Friday.

If two people had made mistakes then each would assume the other person was the only one to make a mistake. When that person does not resign on the first Friday it can only be because they know about someone who also made a mistake. As they each only know of the other's mistake, they must be the mystery second so each resign on the second Friday.

This pattern holds for 3 mistake prone professors each resigning on the third Friday, 4 on the fourth Friday, etc. For 10 professors, they all resign on the 10th Friday.
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Joe McKinley
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When I heard the learn’d astronomer; When the proofs, the figures, were ranged in columns before me; When I was shown the charts and the diagrams, to add, divide, and measure them; When I, sitting, heard the astronomer, where he lectured with
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much applause in the lecture-room, How soon, unaccountable, I became tired and sick; Till rising and gliding out, I wander’d off by myself, In the mystical moist night-air, and from time to time, Look’d up in perfect silence at the stars. W.W.
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Matt
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Octavian wrote:
Didn't see a thread from MABBY for this one, and I was excited because I think I actually nailed this one!


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Yep! Nicely explained, too!

After I read the problem I realized I had heard a similar puzzle a long time ago about red hats and black hats (and not being able to see your own hat) and it brought back a flood of memories about those types of puzzles, some of which are downright evil...devil
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