The reason all the answers can be divided to 9 is simple.The first digit of your chosen number shows the number of the tens,so by subtracting 1 from each ten(of the number) you get 9 for each ten of your number.Only the tens are important,because the other digit(when subtracted) always results in 0.In that way you always get a number that can be divided to 9,because instead of tens(in your original number) after this operation you get nines.Good luck!