Does Not Divide Another

How many numbers between 1 and 100 can you pick at most, so that none of them divides another?

You can choose at most 50 numbers: 51, 52, 53, …, 100.

In order to see that you cannot choose more than 50, express each number in the form 2ⁿ×m, where m is an odd number. Since no 2 numbers can have the same m in their expressions, and there are only 50 odd numbers between 1 and 100, the statement of the problem follows.

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