Here we look at similar problems of distributing a certain number of items across a larger number of sets, each needing a particular number of items.

 

So, set yourself a challenge like;

"Distribute $15$ objects among four sets having $3$ in one, $4$ in another, $5$ in another and $6$ in the last."

Then take this further by having five sets with the extra set having just $1$ object.

You'll be able to think of your own examples too.

Perhaps most important is to formulate some generalisations that can tested.

 

One of the interesting and creative parts of this challenge may be to design the arrangement of sets. Here are some examples to start you off. Two for each of $4, 5$ and $6$ sets.