A Variation On The "when Is Cheryl's Birthday?" Problem

jim360 | 17:54 Wed 15th Apr 2015 | Science

43 Answers

I was just given this nasty-sounding variation on the birthday problem that's been bugging the internet for the last few days. It goes like this:

Person A chooses a pair of numbers between and including 2 and 99, and finds their sum (S) and Product (P). He then tells one person only the product f the two numbers, and nothing else, and the other person is only toldtheir sum.

Person P says: I do not know what the two numbers are.
Person S says: I already knew that.
Person P says: Oh, then I know what the two numbers are now.
Person S says: Then so do I, now.

What are the two numbers?

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Hypognosis

Okay, I understand "not both prime" but why are you discounting factors which *are* odd but *not* prime?

Might this property be what is making the product's factors be ambiguous (ie the odd one being further divisible, giving flexibility to its partner).

jim360

Question Author

Ah -- well, for those ones, they get discarded at the next stage. I may have jumped a little ahead in my last post.

Hypognosis

This way, madness lies…

http://en.m.wikipedia.org/wiki/Sieve_of_Eratosthenes

Oh, the page starts normally enough but it becomes increasingly incomprehensible, the further down you go. So long as other sofware writers understand the author's style, I suppose it doesn't matter.

Other than that, one or two clues, which may or may not help.

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