# Got Infected Cleavers?

**Discrete Mathematics**Level 4

Jack is playing League of Legends. He chooses Dr. Mundo as his champion for the 5 vs. 5. Mundo's Q spell is Infected Cleaver, which is a skill shot that deals damage based on current health of the first target it hits. Suppose the game is rigged (which it is), and it doesn't like Jack. It will hit if \({ x }^{ 2 }\neq 9 \pmod{10}\), where \(x \le 100\). The probability that the cleaver hits may be expressed as \(\frac { a }{ b } \), where \(a\) and \(b\) share no common factor. What is \(a+b\)?