We have had two solutions to this and both were very well described in different ways. Well done Joe. Here is his solution. The other one was from Sarah.

Clement Chan from Sha Tin College in Hong Kong has found 13 ways. He says:

I first tried to find all the possible lines I could make on the grid than looked at each one carefully for example:

I want to make a vertical line from the 1, I check whether the 21 can go in anywhere and if it can I check whether the 3 can go anywhere, and then the 2 and put the 1 on to finish the line.

If I want to make a line diagonally from the 5 then I check it in the same way, and if I want to make a horizontal line from the 15 I check it the same way etc.

Perhaps there are more than 13 lines... If you find any more and can list them, email us.