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I believe the minimum number of drops is 4.
Divide the 100 by 3, drop at 33 and 66 (one floor over, include it later. 33 floors each drop)
Divide the survival “third” by 3, drop at first 3rd and second 3rd (11 floors on each drop)
Divide the survival third by 3, drop at first 3rd and second 3rd (3 floors each drop)
Drop egg on the second and 3rd floor of the identified floors. This gives the answer.

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