Since I have not seen the correct answer – so here it is. Remember you only have 2 egg, so finding the solution for the number of eggs required is incorrect.

Start at floor 2 and drop the egg

– if egg 1 breaks, try again at 1
egg 2 breaks – answer is 0
egg 2 survives – answer is 1

– egg 1 does not break from floor 2 – go to floor 4
– if egg 1 breaks at floor 4 – answer is 3 if not go to floor 6

repeat until floor 96
– if egg 1 survives 96 go to 99
– if egg 1 survives 99 go to 100
– if egg 1 does not survive 99 go to 98
if egg 2 does not survive 98, answer is 97

Note 96, 97, 98, 99, and 100 are all covered in the final strategy.