Baltic Way 1991 · Problem 11

Among any ten integers $\overline{a_{1} \ldots a_{n} 0}, \overline{a_{1} \ldots a_{n} 1}, \ldots, \overline{a_{1} \ldots a_{n} 9}$ there are exactly five numbers with odd digit sum and five numbers with even digit sum. Thus, among the integers 0, 1, . , 999999 we have equally many numbers of both kinds. After substituting 1000000 instead of 0 we shall have more numbers with odd digit sum.