1. (M. Evdokimov) Given three distinct non-zero numbers. Petya and Vasya form quadratic equations by substituting these numbers as coefficients, but each time in a new order. If the equation has at least one root, Petya gets a candy wrapper, and if it has none, the wrapper goes to Vasya. The first three wrappers went to Petya, and the next two to Vasya. Can we determine who will get the last, sixth wrapper?
Solution: A quadratic equation has at least one root if and only if its discriminant is non-negative. If the first and last coefficients are swapped, the discriminant does not change. Therefore, the six equations can be divided into pairs, in each of which either both equations have roots or both do not. Thus, the number of equations that have roots is even. Therefore, the last candy will go to Pete.

## Criteria.

“+” - a correct and justified solution is provided;

“+.” - a correct solution is provided, but some non-essential details are omitted or not explained;

“土” - a reasoning about equations with the same discriminant is provided and the correct answer is obtained, but a significant part of the solution is not explained or omitted, or an arithmetic error is made in deriving the discriminant formula;

“干” - a reasoning about equations with the same discriminant is provided, but due to errors in reasoning, the correct answer was not obtained, or a reasoning about equations with the same discriminant is provided and the correct answer is obtained, but an incorrect discriminant formula is used without proof;

“-” - all other cases.

## Criteria.