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Joric and social egalitarianism

Source: Romanian TST 5 2007, Problem 2

June 7, 2007
limitprobabilitynumber theory proposednumber theory

Problem Statement

The world-renowned Marxist theorist Joric is obsessed with both mathematics and social egalitarianism. Therefore, for any decimal representation of a positive integer nn, he tries to partition its digits into two groups, such that the difference between the sums of the digits in each group be as small as possible. Joric calls this difference the defect of the number nn. Determine the average value of the defect (over all positive integers), that is, if we denote by δ(n)\delta(n) the defect of nn, compute lim⁡n→∞∑k=1nδ(k)n.\lim_{n \rightarrow \infty}\frac{\sum_{k = 1}^{n}\delta(k)}{n}. Iurie Boreico
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