Two Egg problem confusion

Question

Two Egg problem:

• You are given 2 eggs.
• You have access to a 100-storey building.
• Eggs can be very hard or very fragile means it may break if dropped from the first floor or may not even break if dropped from 100 th floor.Both eggs are identical.
• You need to figure out the highest floor of a 100-storey building an egg can be dropped without breaking.
• Now the question is how many drops you need to make. You are allowed to break 2 eggs in the process

I am sure the two egg problem ( mentioned above ) has been discussed sufficiently. However could someone help me understand why the following solution is not optimal.

Let's say I use a segment and scan algorithm with the segment size s. So,

d ( 100 / s   + (s-1) ) = 0    [ this should give the minima,  I need '(s-1)' scans per segment and there are '100/s' segments]
-
ds

=> -100 / s^2 + 1 = 0
=> s^2 = 100
=> s = 10

So according to this I need at most 19 drops. But the optimal solution can do this with 14 drops.

So where lies the problem?

Answer 1

You seem to be assuming equal-sized segments. For an optimal solution, if the first segment is of size N, then the second has to be of size N-1, and so on (because when you start testing the second segment, you've already dropped the egg once for the first segment).