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How many times is the digit 7 written from 1 to 1000?

countingdigits

You write out every whole number from 1 to 1000.

How many times do you write the digit 7? (The number 777 counts three times, since it contains three 7s.)

Then a follow-up: how many of the numbers from 1 to 1000 contain at least one 7?

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Think of the numbers 000 to 999 as three-digit strings. In each position, how often does a 7 appear?

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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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