There was more than one solution to this problem and many of you sent in several of them. It was rather difficult to describe in words what changes were being made and quite a number of diagrams were sent to us. This problem required that you thought differently about lines, or more specifically line segments.

Kathryn Henderson of Higher Bebington Junior School, wrote, "As soon as I stopped thinking of only vertical and horizontal rows it appeared obvious". That was the key! She worked out a solution to the 'trees' problem on her 11th birthday! Here is her solution:

Written descriptions of the solutions were sent in by Keiichi Isyama, Adam Knowles, Elliot Sutcliffe and Anthony Hayward, Chris G., Matt B., David S., Adam F., as well as Emma Horrocks, Abigail James and Perry and Paul Anderson.

Jordan Maxwell aged 7 and Michael Hellon aged 6, from Cummersdale School, explain two of the possible moves that can be made:

"Move the pink tree and put it left of the light green tree.
Move the top tree to the right to get one diagonal/one
horizontal/ and one vertical row of trees. It also works if you move the top tree to the left."

Christina Ivanova from Malborough Primary School, Kristian Kasi from Zurich, Kristine Heald, Kathryn Henderson, plus Emma Horrocks and Abigail James, from Moorfield Juniors, sent in diagrams to show the changes they made to reach their solutions. Below is Helena Manning's diagram of the four ways she found to rearrange the trees.