MathDB

3

Part of 2016 India PRMO

Problems(1)

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

Source:

8/9/2019
Suppose NN is any positive integer. Add the digits of NN 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≤1000N \le 1000, such that the final single-digit number nn is equal to 55. Example: N=563→(5+6+3)=14→(1+4)=5N = 563\to (5 + 6 + 3) = 14 \to(1 + 4) = 5 will be counted as one such integer.
numbe theoryalgebrasum of digitsDigits