3. The tennis player and the badminton player got tired of sports tournaments and decided to have a mathematical duel. They wrote down the numbers from 25 to 57 inclusive in a row and agreed to place either “+” or “-” (in any order, but only these signs) between them. If the result of the expression turns out to be even when all the signs between the numbers are placed, the tennis player wins, and if it is odd - the badminton player wins. Who turned out to be the winner and why?

Olympiad for schoolchildren "Hope of Energy". Final stage.

When all the signs between the numbers are placed, the tennis player wins, and if it is odd - the badminton player wins. Who turned out to be the winner and why?
Solution. Among all the given numbers, 17 are odd, and the sum of odd numbers is also odd. The overall result of the expression will then always be odd, regardless of what signs are between our numbers. Therefore, the badminton player will win.

## Answer: badminton player.