## Thursday, December 21, 2017

### Elusive Conversation (brainteaser)

A mind-bender showed up on Twitter yesterday from a logic blogger. It's very similar to a puzzle that went viral a couple years back, which you may well remember (...but will likely still require some thoughtful-time to solve again). I’ve slightly adapted yesterday's Twitter version as follows:
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Alice and Bob are each given a different fraction of the form 1/n where n is a positive integer. Each of them knows their number (fraction) but does not know the other’s number (but does know they are different). Assume each participant thinks in a perfectly logical/rational manner (and understands the other individual is doing so as well), the following conversation takes place:

Me:  I gave each of you separately a different fraction of the form 1/n that you have had a chance to look at. Which of you has the larger number (fraction)?

Alice:  I don’t know.

Bob:  I don’t know either.

Alice:  I still don’t know.

Bob:  Yes, now I know who has the larger number.

Alice:  In that case, so do I, AND I know both numbers!

What numbers (fractions) were they each handed?

[yes, there is one exact, correct solution... have fun]

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I find this puzzle especially appealing because of a sort of 3-tiered evolving process it likely follows for most solvers:

1)  Upon first reading, it doesn’t seem like it will be solvable.

2)  Upon further contemplation it appears partially solvable, but seems like multiple solutions are possible.

3)  The final step needed to reach the one correct solution requires a bit of recursive thought that, once made, is both illuminating and very satisfying.

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....with that said.....
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