What is the sum of the digits of all

2-digit numbers from 10 to 99?

(99) (100) / 2 - (9) (10) / 2 = 4905

Fast way to solve: allow leading zero's temporarily, then first digit can be any of 0 ... 9 and so can second digit, so each digit appears 10 times in each position, so sum is 20 * (9) (10) / 2, except that we must subtract sum of 1 ... 9, so it's 19 * (9) (10) / 2 = 855.