MathDB

An array

n \times n

is given, consisting of

n^2

unit squares. A pawn is placed arbitrarily on a unit square. A move of the pawn means a jump from a square of the

k

th column to any square of the

k

th row. Show that there exists a sequence of

n^2

moves of the pawn so that all the unit squares of the array are visited once and, in the end, the pawn returns to the original position.

C4