BG-MO 1973 Problem 3

Let $a_1,a_2,\ldots,a_n$ are different integer numbers in the range $[100,200]$ for which: $a_1+a_2+\ldots+a_n\ge11100$ . 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