CouNTing to 100 | Math Problem

Website Discussion
1

Click here to read the complete problem statement.

2

Recipe for solving this
Inclusion Exclusion is the way,

  1. Count combinations without restrictions with stars and bars
  2. Minus if x divides, \times 3 (why? something to do with symmetry)
  3. Plus if x, y both divides
  4. NO INTERSECTION
  5. Don’t be sad, it took me a solid 15 minutes and 3 failed attempts to figure this out
3

I am pretty sure the problem was on National BDMO 2025 Junior category. (I was one of the contestants there)