(Draknek has been working this out for far too long)
Changing the number of floors is fairly trivial (once you get how to do it at all, that is -
I didn't).
With only two balls, the formula is:
y = ceil(1/2*(sqrt(1+8x)-1))
Where y is the number of attempts you need to make and x is the number of floors. (Ceil means round up.)
Showing my working backwards, that formula is produced from this one:
1/2*y*(y+1) >= x
Which is, in turn, produced by this one:
(Sum of a between a=1 and a=y) >= x
Which is the original formula for 2 balls.
For one ball, the formula is:
y >=x
But that is equivelant to:
(Sum of 1 between a=1 and a=y) >= x
Going back to 2 balls:
(Sum of a between a=1 and a=y) >= x
Is the same as:
(Sum of (Sum of 1 between a=1 and a=b) between b=1 and b=y) >= x
Extending this, for three balls, it would be:
(Sum of (Sum of (Sum of 1 between a=1 and a=b) between b=1 and b=c) between c=1 and c=y) >= x
However, at 2:20 in the morning, I'm not willing to work that out and get a y=blah equation for three balls.
(Apologies if this makes little sense, is in a stupid order, or both. Draknek is tired now.)