### Plants

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?

### Junior Frogs

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

### More Plant Spaces

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

# More Children and Plants

##### Stage: 2 and 3 Challenge Level:

This activity has been particularly created for the most able. (The pupils that you come across in many classrooms just once every few years.) It 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.