I have $X$ gold bars, which have different integer lengths $x_i$ ($1 \leq i \leq X$).
I have $Y$ workers, who each get paid in integer lengths of gold $y_j$ ($1 \leq j \leq Y$).
How do I cut the set of gold bars such that each worker gets paid the correct amount, whilst minimising the total number of cuts?
You can view this as a variant of the one-dimensional cutting stock problem. In the standard cutting stock problem, you try to minimize waste, which in this case would be portions of gold bars that end up not being used. Minimizing the number of cuts made would be done somewhat similarly. For instance, you can generate a set of cutting patterns for each of the original X bars and find the "cheapest" set of patterns that would get the job done, where here the "cost" of a pattern is the number of cuts it requires.