Bosnia and Herzegovina EGMO TST 2017 Problem 1
Source: Bosnia and Herzegovina EGMO Team Selection Test 2017
September 19, 2018
Sequenceiterationscombinatorics
Problem Statement
It is given sequence wih length of which consists of first positive integers in arbitrary order (every number occus exactly once). Let us consider a first term from sequence, let it be . From given sequence we form a new sequence of length 2017, such that first elements of new sequence are same as first elements of original sequence, but in reverse order while other elements stay unchanged. Prove that if we continue transforming a sequence, eventually we will have sequence with first element .