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Find the number of six-digit numbers, where the sum of the digits is divisible by 10.

 Aug 7, 2023
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A number is divisible by 10 if and only if its last digit is 0. So, we need to count the number of six-digit numbers whose digits add up to a multiple of 10.

The sum of the digits of a six-digit number can be any number from 1 to 60, inclusive. For each such sum, there are 9 choices for the first digit (any digit except 0), 10 choices for each of the second, third, fourth, and fifth digits, and 2 choices for the sixth digit (0 or 10). So, the total number of six-digit numbers whose digits add up to a multiple of 10 is 9 * 10^4 * 2 = 180,000.

 Aug 7, 2023

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