I'm still not particularly happy with the (Mathematica) function I came up with...
Code:
ballfall[maxfloors_] :=
Do[For[i = 0; cmax = IntegerPart[maxfloors];
cmin = 1, cmax - cmin > 0,
i += 1, temp = Ceiling[(cmax + cmin)/2]; cmin = temp];
Return[i], {1}]
^Highlight that code if you can't read it because of the colors
Ideally that would be a rounding-down function, not a ceiling function, but IntegerPart leads to an infinite loop of evil DOOM! when cmin is one less than cmax
... Still, the only mistakes should be that the smallest number of floors for which
n trials are required might seem to require only
n - 1 trials.
Here's a plot for up through 100 and a bit...
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