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one number has two equal digits in base 10

Source: Bulgaria 1973 P3

June 20, 2021
number theoryPhp

Problem Statement

Let a1,a2,…,ana_1,a_2,\ldots,a_n are different integer numbers in the range [100,200][100,200] for which: a1+a2+…+an≥11100a_1+a_2+\ldots+a_n\ge11100. Prove that it can be found at least number from the given in the representation of decimal system on which there are at least two equal digits.
L. Davidov
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