I am by no means a sudoku expert, but I think your puzzle idea should work.

First, there has to be a grid which fits rule 3 and has a unique solution, because a completely solved grid (with all 81 numbers filled in) has a unique solution (it's already there!) and fits rule 3.

I'd suggest that you start with a solved sudoku grid, then delete given digits one at a time until you reach a point where the puzzle is no longer uniquely solvable. Some existing sudoku solvers, like the one on Sudoku Wiki (see the "Solution Count" button in the top right), tell you how many solutions a puzzle has, so you can determine the exact step in the digit-deletion process where you move from a single solution to many solutions.

Now, I can't guarantee that the resulting puzzle will rate about a 7/10 for difficulty. A solved grid is, of course, really easy, and just removing numbers at random (while following rule 3) will probably leave a pretty easy puzzle. However, at the very least you can find out what the difficulty is, because some sudoku solvers also give you the (approximate) difficulty of a sudoku! (There's a "Grader" button on the Sudoku wiki one.) Maybe there will be a point in your digit deletion at which the solution stays unique, but the difficulty spikes from "doable" to "ridiculous." Stay with the doable version, and you'll have a good puzzle.

You could also try the opposite approach -- start from a blank grid, and add given digits in accordance with Rule 3 until you get a uniquely solvable puzzle. This method would probably get you a higher-difficulty puzzle, but it might be harder for you to generate that puzzle.

I am by no means a sudoku expert, but I think your puzzle idea should work.

First, there has to be a grid which fits rule 3 and has a unique solution, because a completely solved grid (with all 81 numbers filled in) has a unique solution (it's already there!) and fits rule 3.

I'd suggest that you start with a solved sudoku grid, then delete given digits one at a time until you reach a point where the puzzle is no longer uniquely solvable. Some existing sudoku solvers, like the one on Sudoku Wiki, tell you how many solutions a puzzle has, so you can determine the exact step in the digit-deletion process where you move from a single solution to many solutions. (See the "Solution Count" button in the top right of the Sudoku wiki page.)

Now, I can't guarantee that the resulting puzzle will rate about a 7/10 for difficulty. A solved grid is, of course, really easy, and just removing numbers at random (while following rule 3) will probably leave a pretty easy puzzle. However, at the very least you can find out what the difficulty is, because some sudoku solvers also give you the (approximate) difficulty of a sudoku! (There's a "Grader" button on the Sudoku wiki one.) Maybe there will be a point in your digit deletion at which the solution stays unique, but the difficulty spikes from "doable" to "ridiculous." Stay with the doable version, and you'll have a good puzzle.

You could also try the opposite approach -- start from a blank grid, and add given digits in accordance with Rule 3 until you get a uniquely solvable puzzle. This method would probably get you a higher-difficulty puzzle, but it might be harder for you to generate that puzzle.

I just tried a mix of both strategies: I

• started with a blank grid,
• filled in numbers basically at random while following rule 3 until I had a puzzle with exactly one solution, then
• deleted numbers until the "grader" said my difficulty was "Moderate" instead of "Gentle"

That process left me with this puzzle:

Now, that puzzle isn't much to look at, but it is a uniquely solvable sudoku! I'm sure if you take some time with it, you'll find something you're happy with.