Problem

Source: Iran MO 3rd round 2016 mid-terms - Combinatorics P1

Tags: Iran, permutations, combinatorics



Find the number of all $\text{permutations}$ of $\left \{ 1,2,\cdots ,n \right \}$ like $p$ such that there exists a unique $i \in \left \{ 1,2,\cdots ,n \right \}$ that : $$p(p(i)) \geq i$$