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Wondered what would happen if you went up several floors at a time. Serendipity had it that I started at the tenth floor, ascending another ten if the egg didn't break and testing at each of the previous nine floors if it did. Turns out to be 19 tests - which appears to be a minimum. After playing around in Excel and resurrecting 40 year old calculus:
In general for a building with F floors, split into N stages of x floors the number of tests T required are: T = N + x - 1
N = F/x so T = F/x + x -1 with derivative dT/dx = 1 - F/x^2; giving a minimum at x = sqrt(F)
For 100 floors the minimum is at 10 and 19 tests are required.