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Comment by mannykannot | Hacker News Reader

Then there are the questions that, at first sight, do not seem to have all the information, yet they do. Consider the one that opens this article:

http://www.solipsys.co.uk/new/NapkinRingVersusSphericalCap.h...

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> Then there are the questions that, at first sight, do not seem to have all the information, yet they do.

I love the following problem, in a similar vein:

There are two chosen natural numbers x and y, both between 1 and 100. Two smart people, Alice and Bob, are told this fact, and Alice is secretly told x*y, and Bob is secretly told x+y, and they are also told who knows what. Then the following conversation happens:

Alice: I don't know the two numbers.

Bob: I knew you wouldn't know them.

Alice: Now I do know the two numbers.

Bob: And now I do know them as well.

The question is, what are the two numbers?

4 and 13

Before anyone else gets lost trying to solve this, the parent posted the puzzle incorrectly.

The correct limits on the numbers are that: - Each of them is greater than 1, but their sum is less than 100

Still not all the information according to this link: https://en.wikipedia.org/wiki/Sum_and_Product_Puzzle

y > x is the last constraint

That constraint is not necessary as the problem only asked for the two numbers, not the values of x and y respectively.

What's interesting about that problem is that (for me, at least) knowing that that is enough information to solve it makes solving it a lot easier. If I was just told to make as much headway as I could, I'd get stuck on some tricky geometry, but once you're told that the answer is a single number, not in terms of any variables, the method of solution became clear.

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