# Maths problem

**URL:** <https://boards.straightdope.com/t/maths-problem/485504>\
**Category:** Factual Questions\
**Created:** [February 12, 2009, 7:12am UTC](https://boards.straightdope.com/t/maths-problem/485504 "2009-02-12T07:12:51Z")\
**Posts on this page:** 2\
**Page:** 3

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**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\
**Post date:** [February 14, 2009, 2:27am UTC](https://boards.straightdope.com/t/maths-problem/485504/41 "2009-02-14T02:27:01Z")

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> [@Lumpy](#):
>
> So if the sum is greater than 101, **Ms** can be completely confident that the product of the two unknown numbers can be factored more than one way.

This is erroneous. Suppose the sum were 102. Then it could possibly be the case that {a, b} = {5, 97}, both primes, in which case their product could only be factored in one legitimate way. Thus, if **Ms** sees the sum 102, they cannot be confident that the product of the two unknown numbers can be factored more than one way, even though 102 is greater than 101.

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**Author:** ![Lumpy](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lumpy/32/446_2.png) [@Lumpy](https://boards.straightdope.com/u/Lumpy)\
**Post date:** [February 14, 2009, 2:37am UTC](https://boards.straightdope.com/t/maths-problem/485504/42 "2009-02-14T02:37:08Z")

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My presumption is that the sum HAS to be odd, simply on the grounds that otherwise **Ms** couldn’t have derived any useful information from it. Is that an error on my part?

Grr, this meta-logic of “what is has to be based on their certainty” is making my head spin.

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