## CIMC 2022 Part A - Question 5, CEMC UWaterloo

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#### Difficulty: 5

#### This problem is tagged with cimc, cimc22, highschool.

**(Canadian Intermediate Mathematics Contest 2022, Part A, Question 5, CEMC - UWaterloo)**

Magnus and Viswanathan play a game against each other three times:

- In each game, each player’s score is a positive integer. The players’ scores at the end of the three games are six different integers.
- In each game, the winner’s score is at least $25$ points. If the winner’s score is $25$, their opponent’s score must be at most $23$. If the winner’s score is greater than $25$, their opponent’s score must be exactly $2$ less than the winner’s score.
- Viswanathan wins either the first game or the second game, but not both.
- Viswanathan wins the third game with a score of $25$.
- Each player’s score in the second game is the average of their scores in the first and third games.

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