I'm one of a group of people building a big puzzle hunt. I have what I think is a pretty good idea for a puzzle, but I'm having trouble constructing it. Basically, what I need to do is make a sudoku but it needs to fit the following criteria:
It needs to be challenging, but not fiendishly so (about 7 out of 10 for difficulty would be perfect).
It needs to have a unique solution.
All the clue numbers need to either be connected to the edge of the puzzle, or need to be connected either horizontally or vertically to a number connected to the edge of the puzzle.
That third criteria is pretty hard to explain so here's a couple of examples which might help.
This grid fits the 3rd criterion because, moving horizontally or vertically, you can trace a direct line from any number to the edge of the grid.
This grid, on the other hand, breaks the 3rd rule in several places. None of the squares in the second box on the top row connect directly to the border. The 4, the 9, and the 3 in the left box on the middle row don't work. In the centre square, the numbers 9, 5, 2, 3, and 8 don't work but the 6 and the 4 do, because the 6 and the 4 can be linked to the edge of the puzzle in a straight line by the 5, 3, and 2 in the box underneath.
I hope this makes the 3rd rule a bit clearer.
The trouble I'm having is I'm finding it really hard to create a grid which fits rule 3 and has a unique solution. I've been working on it for a couple of days now and I'm starting to think it's not possible. Is such a puzzle possible? If it is, is there a formula for making them that's more effective than trial and error?