This post and the next explore two entries in the online Sudoku composing contest known as the “Patterns Game”. The contest is between Sudoku composers: who can submit first puzzles with unique solutions that fit a “pattern” of givens issued by the referee. The pattern fixes the cell locations, but not the values, of the givens. Computer apps available to the contestants arbitrate the contest rules on difficulty limits and guard against morphs of previous submittals.
One winning Patterns Game entry by Mike Metcalf was previewed last post as ‘mike 1’. The second, ‘mike 2’, will be previewed here and solved next post.
The boundary between the clutter avoiding bypass and line marking is often determined by how many marks you are willing to keep in your head. In this case, let’s say you drew the line at this bypass:
Is that too challenging? It’s a little much for me, but reasonable for many Sysudoku readers. I’m dropping back to full line marking to be sure every reader can appreciate what talented players see in the bypass above. Here’s the box marking grid just before C7 in the box marking trace below.
The 7: list effects trace had to be folded to fit on the screen.
Box marking and line marking don’t require exceptional talent, just patience and enough interest in Sudoku.
The bypass, box marking and line marking cover what is generally known as “singles”, but go further to return cell position marking of all strong links defined by boxes and lines.
Here is the grid on the line marking encounter of a naked triple on the 6th marked line. The removal of 9r2c1 can be interpreted as a box/line removal triggered by the r1 9 removals. Or you may just note that the 9 removals leave 9r2c1 within sight of all remaining 9’s in r1.
In the Patterns Game, all puzzle rules require entry puzzles to be solved by “singles”. Though often used, that term is not well defined. But in the game all participants use the same solver, so “singles” in this rule means what the solver says it is. Since mike1 is a winning entry, we expect unit subset removals must be “singles”.
Line marking is completed with lines r1 and r2, leaving columns c8 and c9 for closing.
The line marked grid hosts two hidden unique rectangles of type 2b. They must be superfluous though, because, looking at the UR table on the Tools page, hidden UR can’t be considered “singles”.
Next, my cluster stalls. Gordon and I independently find an XY ANL with terminals 8r2c1 and 8r2c5. The terminal 8’s on the same line wink to convert the ANL into a nice loop, with extra removals.
Gordon finishes with an enabled XY-wing and a “singles” collapse.
I have to go with my investment in coloring. The cluster expansion, accelerated by nice loop coloring, wraps blue in c8, for a very green solution.
Next week, it’s Metcalf’s Pattern Games second entry, mike 2.
Do you have a third one? To find a pattern game entry, you test set after set of placements on the pattern. If your solver is in human action mode, it stalls over and over. If its in tree traversal mode, you get hundreds of stalls and multiple solutions over and over. Hats off to the patience of patterns gamers.
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Systematic Sudoku 