Problem 7.1. Petya wrote 20 natural numbers 1, 2, .., 20 on the board. Vasya first erased all even numbers, and then erased all numbers that give a remainder of 4 when divided by 5. How many numbers are left on the board
Answer: 8.

Solution. After erasing all even numbers, the following remain on the board:

$$
\begin{array}{llllllllll}
1 & 3 & 5 & 7 & 9 & 11 & 13 & 15 & 17 & 19 .
\end{array}
$$

Among them, exactly two give a remainder of 4 when divided by 5 - these are 9 and 19. After erasing these as well, 8 numbers remain on the board.