MathDB

Every square of

1000 \times 1000

board is colored black or white. It is known that exists one square

10 \times 10

such that all squares inside it are black and one square

10 \times 10

such that all squares inside are white. For every square

K

10 \times 10

we define its power

m(K)

as an absolute value of difference between number of white and black squares

1 \times 1

in square

K

. Let

T

be a square

10 \times 10

which has minimum power among all squares

10 \times 10

in this board. Determine maximal possible value of

m(T)

Problem Statement