Multiples of everything
There is a row of 100 glasses with their mouths facing downwards. They are numbered 1, 2, 3, ..., 99, 100, starting from the left. For the first time, turn over the glasses with numbers that are multiples of 1. For the second time, turn over the glasses with numbers that are multiples of 2. For the third time, turn over the glasses with numbers that are multiples of 3...
Repeat the process in this way. After 100 times, how many glasses are still facing downwards?
The answer is 90.
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