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The answer should be 13.
- Alex April 02, 2008Let's assume x is the optimal number of times to try.
1st drop: f1 <= x+1 (because if fails you can use the other egg from the 2nd floor to x)
2nd drop: f2-f1 <= x (again worst case is fail and drop the other egg from f1+1 to f2-1)
3rd drop: f3-f2 <= x-1
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xth drop: fx-fx-1 <= x+2 - x = 2
Add all the inequality up, left side = fx, right side = x(x+1)/2 + x
so fx <= x(x+1)/2 + x
and the xth drop should be >= 100, thus
x(x+1)/2+x >= 100
Solving the equation, you can get x>= 13
Any solution less than 13 can be proved wrong.