Now that we have established the number of of
SudokuX grids, and the number of EDX grids, we turn our attention to the minimum-clue questions.
Ruud's
SudoCue website has a collection of 7193 x 12-clue puzzles (
http://www.sudocue.net/minx.php). This formed the initial catalog.
I've been running an RMW (random morph walker), and when the "new grid find" rate had slowed to only one new grid per hour, it was terminated and a "backfill" process applied that filled in all {+1, -1} (PM1) morphs of the known puzzles.
The end result was a catalog of
15,626 puzzles on
12,010 EDX grids.
A "PM2 backfill" is in progress to expand the catalog by looking for {+2, -2} morphs. This is a slow process, and is expected to take about one week to complete. At the 2000 puzzle mark, this process has found over 5000 new grids/puzzles, so it looks as though the size of the catalog will at least triple.
The key questions, both of which remain open, are:
- how many 12-clue puzzles are there?
An estimate at this stage looks difficult. We will probably get some idea of the size of the {+2, -2}-connected puzzle set in a week or so, when the initial PM2 job is finished and we start a second pass (on the new entries).
The size of the EDX grid pool (1.5 billion) means that an estimate based on sampling is going to be very difficult.
- do any 11-clue puzzles exist?
All 12-clue puzzles found so far are minimal (otherwise you would cetainly hear about it!). This, and the low ratio of 12-clue puzzles / grids, suggest that an 11-clue puzzle is unlikely.
