8.1. Three natural numbers are written on the board. Tanya calculated the product of the numbers written on the board and got a number ending in 1010. And Vanya calculated their sum and got the number 9999. Did Vanya make a mistake?
Answer: Mistaken.

Solution: If the sum of three integers is 9999, then either they are all odd (in which case their product ends in an odd digit), or two of them are even and one is odd (in which case their product is divisible by 4, while a number ending in 10 is not divisible by 4).

# Criteria: 

7 points - complete correct solution;

$3-5$ points - partially correct progress in the solution.