MathDB

2016 preRMO p3, adding digits of N and so on until you get single digit

Source:

August 9, 2019

numbe theoryalgebrasum of digitsDigits

Problem Statement

Suppose

N

is any positive integer. Add the digits of

N

to obtain a smaller integer. Repeat this process of digit-addition till you get a single digit numbem. Find the number of positive integers

N \le 1000

, such that the final single-digit number

n

is equal to

5

. Example:

N = 563\to (5 + 6 + 3) = 14 \to(1 + 4) = 5

will be counted as one such integer.