MathDB

For

2n

numbers in a row, Bob could perform the following operation:

S_i=(a_1,a_2,\ldots,a_{2n})\mapsto S_{i+1}=(a_1,a_3,\ldots,a_{2n-1},a_2,a_4,\ldots,a_{2n}).

Let

T

be the order of this operation. In other words,

T

is the smallest positive integer such that

S_i=S_{i+T}

. Prove that

T<2n

C2