self Maths Puzzle

You have to do an experiment to determine the highest floor on a 100-floor building from which a manufactured snooker ball may be dropped without breaking.

You are given two identical snooker balls, which you can drop from various floors of the building, to carry out your experiment.

If a ball doesn't break after being dropped, it may be reused without suffering any loss of quality. But if both balls break before you have determined the highest floor, then you are an incompetent bungler and your boss is ultimately going to fire you.

What is the least number of times you must drop the snooker balls in order to determine the highest floor?

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self Other Question
We know very little about the life of the mathematician Diophantus (often known as the 'father of algebra') except that he came from Alexandria and he lived around the year 250 AD.

However, there remains a riddle that describes the spans of Diophantus's life:

"This tomb hold Diophantus. Ah, what a marvel! And the tomb tells scientifically the measure of his life. God vouchsafed that he should be a boy for the sixth part of his life; when a twelfth was added, his cheeks acquired a beard; He kindled for him the light of marriage after a seventh, and in the fifth year after his marriage He granted him a son. Alas! late-begotten and miserable child, when he had reached the measure of half his father's life, the chill grave took him. After consoling his grief by this science of numbers for four years, he reached the end of his life."

In simpler English it says: Diophantus's youth lasted 1/6 of his life. He had the first beard in the next 1/12 of his life. At the end of the following 1/7 of his life Diophantus got married. Five years from then his son was born. His son lived exactly 1/2 of Diophantus's life. Diophantus died 4 years after the death of his son.

How long did Diophantus live? The founders of Hairytown decreed years ago that:

1. No two people can have the same number of hairs
2. No one can have 999 hairs.
3. No one can have more than, or the same number of hairs as, the population of the town

The town has now reached its maximum population - what is it?