I've just been putting numbers in the grid again, using the numbers before the : as the coordinates and then writing the number after the : into the square.
After doing just the first set of numbers, the grid reminded me of a game I had played a long time ago, but I can't remember what it's called now. The game involved drawing lines, starting in each box with a number in, and the number specified how long the line had to be. You had to fill the whole grid without overlapping lines.
Interestingly this first set of numbers seems to have a valid solution. I know my explanation is very bad, but I have attached my solution to the game.
All done in the finest MS paint with the pencil tool
The only problem is that the result is not the only possible valid one, although it very nearly is. The only bits that could be changed for another valid result would be the two lines of length 3 in the bottom left. This makes me think it might just be a coincidence and im on the wrong track completely.
Also it doesn't really show much at the moment, not anything helpful anyway. Maybe the other sets of coordinated create lines to overlay on top of these?
I'm now going to try the second set to see what happens there.
EDIT:
Well that idea was a complete failure, doesn't work at all with the second set of numbers.