MathDB

Three children wanted to make a table-game. For that purpose they wished to enumerate the

mn

squares of an

m \times n

game-board by the numbers

1, ... ,mn

in such way that the numbers

1

and

mn

lie in the corners of the board and the squares with successive numbers have a common edge. The children agreed to place the initial square (with number

1

) in one of the corners but each child wanted to have the final square (with number

mn

) in different corner. For which numbers

m

and

n

is it possible to satisfy the wish of any of the children?

Problem Statement