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Five Fridays, five Saturdays and five Sundays

calendarcountingdeduction

A certain month contains five Fridays, five Saturdays and five Sundays.

What day of the week is the 1st of that month, and how many days does the month have? Explain why no other answer is possible.

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Four full weeks account for four of each weekday. The extra days beyond 28 all come at the very start of the month.

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The theory behind this question.

Balls and Bins and the Birthday ProblemBinomial Coefficients and Pascal's TriangleBurnside's Lemma and Polya CountingCatalan NumbersCounting: Permutations and Combinations

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