A Minimal Cyclic Product Sum

Problem

Let $\delta=(a_1,a_2,\dots,a_n)$ be a permutation of $\{1,2,\dots,n\}$ , and define

F(\delta)=\sum_{i=1}^{n}a_ia_{i+1},\qquad\text{where }a_{n+1}=a_1.

Find $\min_{\delta}F(\delta)$ .

Answer

Solution

Difficulty	8/10
Topics	combinatorics, Recursion, Induction

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