Let us try to find the digit sum of numbers starting from 1, 2, 3, 4, and so on.
Number: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21 . . . 51, 52, 53, . . .
Digit Sum: 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 2, 3, 6, 7, 8, . . .
If you see the above Digit Sums, then a new pattern is created. The digit sums keep cycling from 1 to 9. And when we plot this, then a circle of 9 is formed.
Also, if we add 9 or a multiple of 9 to any number, it is the same as adding 0 in digit sum.
For example:
Digit Sum of 17 is 1+7 = 8
Now, Digit Sum of 26 (17+9) is 2+6 = 8.
Effectively, 0 and 9 are same in Digit Sums.
