MathDB

9\times 9

board has a number written on each square: all squares in the first row have

1

, all squares in the second row have

2

\ldots

, all squares in the ninth row have

9

. We will call special rectangle any rectangle of

2\times 3

3\times 2

4\times 5

5\times 4

on the board. The permitted operations are:

\bullet

Simultaneously add

1

to all the numbers located in a special rectangle.

\bullet

Simultaneously subtract

1

from all numbers located in a special rectangle.
Demonstrate that it is possible to achieve, through a succession of permitted operations, that

80

squares to have

0

(zero). What number is left in the remaining box?

6