More children and plants
Problem
This is seen as a possible follow-on from Plants.
In "Plants" we had three children sharing $10$ plants in the three overlapping circles.
This particular challenge is about extending that, so that we consider four and then maybe five children in a similar way.
In considering these larger numbers we have to examine a different arrangement of the circles (possibly changed into slightly different shapes).
You will need to draw these four (first of all) areas in such a way that there is a section for each of the sharing situations. In the case of plants there were seven sections - allowing for each child to have an overlapping part with each and all of the other children.
Once you have drawn an arrangement for four areas I suggest that you start with allocating $4, 5, 6, 7$ to the areas.
As before, where can a certain number of plants go? I suggest you start with a number like $19$ for the total number plants.
Find all the answers that satisfy the requirements of having $4, 5, 6, 7$ shared in the different regions using $19$ plants.
Want to go still further? Then go to More Plant Spaces.
Getting Started
In order to have four overlapping areas we need something like this:
showing $15$ areas.
Or, when moving on to five we need something like this:
Showing $31$ areas.
These are just suggestions and there are other ways of constructing a suitable arrangement.
Student Solutions
Well done Jess and Casey, that's really good work, I wonder how long it took you? I really hope you enjoyed the journey of solving it!
This is what they sent:
