Is there a 10-clue SudokuP puzzle?

While we're at it, I hope to collect a complete set of 11-clue puzzles if possible.

I've been busy with preliminaries, assembling a toolset, scoping the problem, deciding on feasibility, etc. I'm nearly ready to begin the computational phase, so I'll describe the general approach and the initial state of play:

1. General Approach

The plan is to use the methodology employed by Gary McGuire in "There is No 16-clue Sudoku". This essentially involves testing all relevant grids, using UA set methods to determine minimum clue requirements, solving the associated Hitting Set problem to generate all possible 10-clue puzzles, and finally testing those puzzles with a solver.

All fairly straight-forward, really ...

As you know, the McGuire group solved the Sudoku problem in a mere YEAR, with a 320-node cluster, using a total of 7 million CPU-hours (give or take a few).

I have a single desktop PC with 4 hyper-threaded cores, so what makes me think I can do this? Well, mainly the reduction in complexity afforded by the SudokuP variant. We have only 200 million grids to test, and the number of 10-clue possibilities is far less than the number of 16-clue possibilities. I have run some critical scoping jobs which suggest the project is indeed feasible.

I'll get to that later.

2. Toolset

The major software tools needed are:

- a fast SudokuP solver. Brian Taylor's BB solver is not only fast, but easily modified to add the extra constraint dimension for SudokuP

- a fast UA set generator. I have combined a stand-alone UA6 function excellently coded by dobrichev, which does the basic work, and I have added my own function (less excellent, but sufficient) to generate additional UA sets, using Pittenger-style cycle generation

- a reasonably efficient Hitting Set generator to identify the 10 (or 11) clue sets that need to be tested for each grid

3. Feasibility Study

Why does this job look feasible? I'll outline my reasoning in the next post ...