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Palindromic dates in the 2020s

calendardigitspalindromescounting

Write a date as eight digits in the order day, month, year: for example 6 September 2026 is 06092026.

How many dates from 1 January 2020 to 31 December 2029 are palindromes, reading the same forwards and backwards? List them.

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The year 202X reversed gives the day and month. Reverse "202X" and see whether the result is a legal day-and-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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