solution

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Fang-jh wrote: Let $ m > 1$ be an integer, $ n$ is an odd number satisfying $ 3\le n < 2m,$ number $ a_{i,j} (i,j\in N, 1\le i\le m, 1\le j\le n)$ satisfies $ (1)$ for any $ 1\le j\le n, a_{1,j},a_{2,j},\cdots,a_{m,j}$ is a permutation of $ 1,2,3,\cdots,m; (2)$ for any $ 1 < i\le m, 1\le j\le n - 1, |a_{i,j} - a_{i,{j + 1}}|\le 1$ holds. Find the minimal value of $ M$, where $ M = max_{1 < i < m}\sum_{j = 1}^n{a_{i,j}}.$ Aren't $ M = max_{1 < i < m}\sum_{j = 1}^n{a_{i,j}}.$ and $ 1 < i\le m, 1\le j\le n - 1, |a_{i,j} - a_{i,{j + 1}}|\le 1$ typos?? Following solution also considered them as $ M = max_{1\le i\le m}\sum_{j = 1}^n{a_{i,j}}.$ and $ 1\le i\le m, 1\le j\le n - 1, |a_{i,j} - a_{i,{j + 1}}|\le 1$

It's definitely a typo!