MathDB

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 \minus{} 1, |a_{i,j} \minus{} a_{i,{j \plus{} 1}}|\le 1 holds. Find the minimal value of

M

, where M \equal{} max_{1 < i < m}\sum_{j \equal{} 1}^n{a_{i,j}}.

Problem Statement