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'Plants' printed from http://nrich.maths.org/
The first solutions we rceived seemed to focus on getting $3, 4$ and $5$ plants in the different areas while sharing one. Perhaps we made it look as though there was some calulating to do.
To achieve solutions for the three children getting $5, 6$ and $7$ using just $10$ plants, the most successful solutions were practical. Kagan at St. Michael's Sandhurst used buttons in circles to show a good example of a correct solution - well done, and here it is.
We've also had a number of other responses which focused on working systematically to get all the solutions. The best results so far have been from Misha and Marjolaine of Highgate School, who both found 34 different arrangements!
Some years ago the same challenge generated these solutions from a group of children in Somerset: