Interesting Differences

Take 1 an even number of times, subtract from the number thus formed a series of 2s half the length of the first number, and

11 - 2 = 9 = 3^2

1111 - 22 = 1089 = 33^2

111111 - 222 = 110889 = 333^2

11111111 - 2222 = 11108889 = 3333^2

1111111111 - 22222 = 1111088889 = 33333^2

you'll always get a square.