Counting and probability puzzles (contest style)

Questions at easy, medium and hard levels. Pick a level and get a fresh set every time, with instant feedback.

Learn it Count with the multiplication principle, use inclusion–exclusion for "or" (add, then subtract the overlap), and fix one person for round tables.

Example: How many numbers from 1 to 100 are multiples of 4 or 6?

Multiples of 4: 25. Of 6: 16.
Of both (LCM 12): 8.
$25 + 16 - 8 = 33$.

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