Digit Sum Puzzle
Let N be the smallest positive integer whose digits add up to 2015. What is the sum of the digits of N+1?
Age
11 to 14
Challenge level
Problem
Let $N$ be the smallest positive integer whose digits add up to 2015.
What is the sum of the digits of $N+1$?
This problem is taken from the UKMT Mathematical Challenges.
Student Solutions
Answer: 9
$N$ should be as small as possible so smallest number of digits possible. Use as many 9s as possible.
$2015\div9=223$ remainder $8$
$N=8\underbrace{999...999}_{223\text{ }9\text{s}}$
So $N+1=9\underbrace{000...000}_{223\text{ }0\text{s}}$, and the sum of the digits of $N+1$ is $9$.