# Solved 2000+ problems

Discrete Mathematics Level 4

Let $$\pi$$ be a permutation of $$\{1, 2, . . . , 2000\}$$.

Find the maximum possible number of ordered pairs $$(i, j)\in\{1, 2, . . . , 2000\}^2$$ with $$i < j$$ such that $$\pi(i).\pi(j)> i. j$$.

This problem is adapted from HMMT.

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