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Alison and Anne of St John's Primary School sent us in their answers:

Two pathsTwo paths

They also explained what they thought would limit the number of possible paths.


There are only two $27$ squares, but there are three of every other square apart from $30$, so if you want different paths to have every square apart from $30$ different, you can only have two because there are only two $27$s. If it is okay to have more than just the $30$ the same, then it is still the $27$s that will limit the number of paths that is possible.

And Jamie, aged 7, told us:

You do not need to find paths for the pumpkin people to take to catch Froggie, because any path she takes they can take and any path she can't take they can't take, they just go in the opposite direction. This is because counting down in threes gives you the same numbers as counting up in threes just in the opposite order

Thank you very much, Jamie, Alison and Anne!