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2023 SSMO Team Round Problems/Problem 5

Problem

Joshy is playing a game with a dartboard that has two sections. If Joshy hits the first section, he gets $20$ points, and if he hits the second section, he gets $23$ points. Assume Joshy always hits one of the two sections. Let $a$ be the maximum value that Joshy cannot achieve. Let $b$ be the number of positive integer scores Joshy cannot achieve. Let $c$ be the number of ways for Joshy to achieve $2023$ points. Find $(a-b)c$.

Solution

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