Got Infected Cleavers?
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 , where . The probability that the cleaver hits may be expressed as , where and share no common factor. What is ?
The answer is 9.
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1 solution
Ok. Since it is looking for mod 1 0 , you only need to worry about counting the numbers 0 − 9 because it would repeat (this is because mod 1 0 is only counting the last digit). The x 2 for 0 − 9 are 0 , 1 , 4 , 9 , 6 , 5 , 6 , 9 , 4 , 1 , 0 . Only two of these are nines, so 1 − 1 0 2 = 1 0 8 = 5 4 . This means a = 4 and b = 5 . a + b = 4 + 5 = 9