2023 IOQM/Problem 20
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For any finite non empty set X of integers, let max(X) denote the largest element of X and |X| denote the number of elements in X . If N is the number of ordered pairs (A, B) of finite non-empty sets of positive integers, such that max(A) × |B| = 12; and |A| × max(B) = 11 and N can be written as 100a + b where a, b are positive integers less than 100, find a + b .
