There were seven boxes. In some of them, seven more boxes (not nested within each other) were placed, and so on. In the end, there were 10 non-empty boxes.

How many boxes are there in total?
At each operation, one empty box is filled. Since there are now 10 non-empty boxes, 10 operations have been performed. With each operation, seven boxes were added. Therefore, in the end, there are $7 + 10 \cdot 7 = 77$ boxes.

The Russian national football team won against the Tunisian national team with a score of $9: 5$. Prove that at some point during the match, the Russian team had to score as many goals as the Tunisian team had already scored.

## Solution

Consider the moment in the match when a total of 9 goals were scored. Let the Russian team have scored $n$ goals by this point; then Tunisia had scored

$9-n$ goals. But the Russian team still had to score exactly $9-n$ goals, which is what was required to be proven.