(Answered) Discrete math questionshow many numbers without decimal

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Discrete Math questions.

How many numbers without decimal points must you select w/o replacement from the range [1, 101] in order to guarantee:

that at least 1 odd number is chosen?
that at least 1 even number is chosen?
that a perfect square is chosen?
that there exists a pair in the selected set that sums to an even number?

How many exams in a 7-day week must you do to guarantee:

there will be at least 1 day with at least 2 exams?
there will be at least 1 day with at least 3 exams?
there will be at least 1 day with at least

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