MathDB

There is a chip in one of the squares on the checkered board. In one move, she can move either

1

square to the right, or diagonally

1

to the left and

1

up, or

1

to the left and

3

down (see Fig.). The chip made

n

moves and returned to the starting square. Prove that a)

n

is divisible by

2

, b)

n

is divisible by

8

. K.A.Sukhov

Problem Statement