Why do this problem?
is one that requires working systematically because it is necessary to try and improve as you find the way through the network. It is also a good activity for promoting discussion between learners working together. This sheet, which can be photocopied, gives two copies of the network for working on.
Why don't you make a list of the numbers from $1$ to $9$ and cross them out as you go?
Which number can you not use until the end?
Children who do this quickly could find other ways through the network. Can they find all the possible ways?
You could suggest crossing out all the numbers from which you can't start. This sheet
gives two copies of the network for working on.