Find the number of 10-digit numbers, where the sum of the digits is divisible by 3.

This one is easy:

The first number whose digits sum is divisible by 3>>1,000,000,002

The last number whose digits sum is divisible by 3>>9,999,999,999

[9,999,999,999 - 1,000,000,002] / 3 + 1 ==3,000,000,000 - integers whose digits sum up to 3.