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palindromes from 10,000 - 999,999 with even sum of digits, and how many

Source: Caucasus 2015 9.5

April 26, 2019
number theorycombinatoricspalindromessum of digits

Problem Statement

Let's call a natural number a palindrome, the decimal notation of which is equally readable from left to right and right to left (decimal notation cannot start from zero; for example, the number 12211221 is a palindrome, but the numbers 1231,12121231, 1212 and 10101010 are not). Which palindromes among the numbers from 10,00010,000 to 999,999999,999 have an odd sum of digits, which have an one even, and how many times are the ones with odd sum more than the ones with the even sum?
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