This is a modification of the infamous egg drop problem, which I have seen formulated as in the following manner:
- Given $e$ eggs and a building of $f$ floors, how can we find the lowest floor at which the egg drops in the minimum number of throws?
- Given $e$ eggs and $t$ allowed throws, what is the highest floor we can test?
I know people can solve this using dynamic programming; however, is it possible to extend this to a building with infinite floors, but with a finite lowest floor at which the egg breaks? In other words,
- Given $e$ eggs and an infinitely tall building, is it possible to find the lowest floor at which the egg drops in as few throws as possible, and if so, how?