2005 PMWC Problems/Problem T1
Problem
Call an integer "happy", if the sum of its digits is . How many "happy" integers are there between and ?
Solution
We have a three digit integer in the form ABC. The number of happy integers per hundred is the number of positive integer solutions to
For the one hundreds:
B+C=9: 10 solutions
two hundreds:
B+C=8: 9 solutions
so on, until there are two solutions in 9 hundreds.