MathDB

For each integer

n>0

, a permutation

a_1,a_2,\dots ,a_{2n}

1,2,\dots 2n

is called beautiful if for every

1\leq i<j \leq 2n

a_i+a_{n+i}=2n+1

and

a_i-a_{i+1}\not \equiv a_j-a_{j+1}

(mod

2n+1

) (suppose that

a_{2n+1}=a_1

). a. For

n=6

, point out a beautiful permutation. b. Prove that there exists a beautiful permutation for every

n

Problem Statement