A machine dispenses four kinds of tokens. Red tokens are worth points, blue tokens are worth points, green tokens are worth points, and yellow tokens are worth point. The machine never runs out of tokens to dispense. To get tokens from the machine, people enter a total number of points, and the machine will dispense the fewest number of tokens that total that number of points. For example, if someone enters points, the machine will dispense red token and green token, because their total value is points, and this total cannot be obtained using fewer tokens. For how many different total numbers of points will the machine dispense exactly tokens?
https://cemc.uwaterloo.ca/sites/default/files/documents/2024/POTWE-24-N-01-P.html
