Since the final, cease-and-desist will receive the sum of the claps of all the previous articles, and is not counted in the answer, then the clap-value of each article can be doubled.

Brute force is the intended solution. Add $2X$ to a total clap count and subtract $Y$ from $X$ per iteration. Iteration should stop when either the $X$ value hits $0$ (articles will no longer count for claps) or when the sum of claps reaches the goal.