Shapovalov A.V.

Sasha wrote down the numbers from one to one hundred, and Misha erased some of them. Among the remaining numbers, 20 have the digit one in their notation, 19 have the digit two, and 30 have neither the digit one nor the digit two. How many numbers did Misha erase?
Among the numbers from 1 to 100, the digit 1 appears exactly twenty times: the number 1 itself, ten numbers from 10 to 19, the numbers 21, 31, ..., 91 (eight of them), and the number 100. This means that none of these numbers were erased. Similarly, the digit 2 appears exactly nineteen times: the number 2 itself, ten numbers in the third decade, and 12, 32, 42, ..., 92 (eight of them). Thus, Misha did not erase any of these numbers either. In total, there are $19+20-2=37$ such numbers (we subtract 2 because the numbers 12 and 21 were counted twice). In total, $37+30=67$ numbers remained, and Misha erased $100-67=33$ numbers.

## Answer

33.

## Problem