MathDB

The sequence

a_1,a_2, ..., a_{2n}

of integers is such that each number occurs in no more than

n

times. Prove that there are two strictly increasing sequences of indices

b_1,b_2, ..., b_{n}

and

c_1,c_2, ..., c_{n}

are such that every positive integer from the set

\{1,2,...,2n\}

occurs exactly in one of these two sequences, and for each

1\le i \le n

is true the condition

a_{b_i} \ne a_{c_i}

. (Anton Trygub)

10.7