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'Skip Counting' printed from http://nrich.maths.org/
Alison and Anne of St John's Primary School
sent us in their answers:
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
Thank you very much, Jamie, Alison and