MathDB

In the

25

squares of a

5 \times 5

square, zeros are initially written. in the every minute Ionel chooses two squares with a common side. If they are written in them the numbers

a

and

b

, then he writes instead the numbers

a + 1

and

b + 1

a - 1

and

b - 1

. Over time he noticed that the sums of the numbers in each line were equal, as well as the sums of the numbers in each column are equal. Prove that this observation was made after an even number of minutes.

Problem Statement