“I don't know the numbers”: a math puzzle

I like puzzles like this, where it's not just "what does each person know?" but also "when did they know it?"

Another similar puzzle, with more logic and fewer numbers, is this one which was nicely written up on xkcd: https://xkcd.com/blue_eyes.html

Is it that the other person was told either the sum or the product? Or that the number they were told is the sum or product?

edit: After rereading the problem they weren’t told the parameters of the problem or even that they are participating in a puzzle.

That the other person is following the same system as them to decide whether they "know the numbers". It would be super easy for one of them to say they don't know for some other reason, in which the others' reasoning would be false.

That was a fun puzzle. I have another one that is math puzzle:

> You are given two eggs, and access to a 100-storey tower. Both eggs are identical. The aim is to find out the highest floor from which an egg will not break when dropped out of a window from that floor. If an egg is dropped and does not break, it is undamaged and can be dropped again. However, once an egg is broken, that’s it for that egg.

> If an egg breaks when dropped from a floor, then it would also have broken from any floor above that. If an egg survives a fall, then it will survive any fall shorter than that.

> The question is: What strategy should you adopt to minimize the number egg drops it takes to find the solution? (And what is the worst case for the number of drops it will take?)

I wrote up a solution for this (along with a generalized analytical solution) on my blog: https://blog.kdheepak.com/the-egg-tower-puzzle

Billed as "the hardest logic puzzle in the world". Now I feel less dumb for not solving it myself when it appeared in Cracking the Code Interview.