Digit Sums - Futility Closet

Digit Sums

Sort the numbers 0, 1, 2, …, 123456 into two sets. In one set put all the numbers who digits add to an even sum; in the other put those whose digits produce an odd sum. Which set is larger?

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The digit sum of each even number differs by 1 from that of the odd number that follows it, so they have opposite parity. Thus the score remains tied until we reach the last number, 123456, whose digits total 21. So the second set is larger than the first by a single member. (By Polish mathematician Paul Vaderlind.)

March 19, 2013March 29, 2013 | Puzzles