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A knight is placed on each square of the first column of a

2017 \times 2017

board. A move consists in choosing two different knights and moving each of them to a square which is one knight-step away. Find all integers

k

with

1 \leq k \leq 2017

such that it is possible for each square in the

k

-th column to contain one knight after a finite number of moves.
Note: Two squares are a knight-step away if they are opposite corners of a

2 \times 3

3 \times 2

board.

Problem Statement