MathDB

We have a chessboard and we call a

1\times1

square a room. A robot is standing on one arbitrary vertex of the rooms. The robot starts to move and in every one movement, he moves one side of a room. This robot has

2

memories

A,B

. At first, the values of

A,B

are

0

. In each movement, if he goes up,

1

unit is added to

A

, and if he goes down,

1

unit is waned from

A

, and if he goes right, the value of

A

is added to

B

, and if he goes left, the value of

A

is waned from

B

. Suppose that the robot has traversed a traverse (!) which hasn’t intersected itself and finally, he has come back to its initial vertex. If

v(B)

is the value of

B

in the last of the traverse, prove that in this traverse, the interior surface of the shape that the robot has moved on its circumference is equal to

|v(B)|

Problem Statement