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## 'More Children and Plants' printed from http://nrich.maths.org/

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.