A quick naive not completely optimal but still relevant solution:
Since you have 2 eggs you can start on the 33rd floor. It breaks you can use the 2nd egg from 1st to 32nd floor.
If it doesn't break, use the first egg on the 66th floor. If it does break, the answer is between 33 and 65, if it doesn't the answer is between 66 and 100. That cuts the maximal testing time time from splitting at 1/2 (1st egg at flr 50), to 1/3rd.
To optimize further, since in the bad case we'd have to search up to 34/35 floors, you can mathmatically find a number where you split the drops at an interval (IIRC the "real" optimal answer is 14, then 13, then 12, etc), which means you're doing less explicit checking.
At 14 - i, you have 10 drops to find a range of 13 - i floors in which the optimal path is found. So instead of a worst case of 35, you have a worst case of around 17.
I find the best way to approach this sort of problem is to first find one optimization, and then use the same process to find if there are further optimizations.
