# Sum of digits of numbers

Let S be a function such that S(N) is the sum of digits of N. N belongs to natural numbers, and N < 10²³. N does not contain a zero digit in it. The numbers are in base 10.

Find the number of N that satisfies the equation: S(N) = S(S(N))

• Discussion of this question on meta May 24, 2022 at 14:25

• Shouldn't it be $2^{k-1}$ ways? May 23, 2022 at 11:37