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

countingdigitsedge-cases

Write out every whole number from 1 to 1000 inclusive.

How many times does the digit 1 appear in total? (The number 111 contributes three.)

Then: how many of the numbers from 1 to 1000 contain the digit 1 at least once?

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Count the numbers 000 to 999 position by position, then remember the number 1000 itself.

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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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