## Kurzhals’ Easter Monster Volley in SetLink

This post exhibits SudokuOne’s setlink diagram of Steve Kurzhal’s  in sysudoku format, showing the direct correspondence to Sudoku Snakes naked double loop. The chute loop is known as an SK-1 Loop on the New Player’s Forum.  A matrix version of the attack is cited also.

I did swear off the rank field version of Set Link Graphs, but I’m not allergic to those without triple set and cover intersections.  Rank theory does offer an alternative justification for the opening salvo on the Easter Monster, and SudokuOne’s keypad SLG appears on his page http://www.sudokuone.com/sweb/extra/steaster/steaster.htm .

Here is the sysudoku formatted version.  It is a rank = 0 structure, with 16 truths and 16 covers. Removed candidates are in no truth set, and in one cover.

The structure corresponds directly to the naked double loop, but with no apparent dependence on the candidate pairs other than 1267.

The four box structure is known outside the Sudoku Snake tent as an SK-1 Loop, undoubtedly in honor of Steve Kurzhals, but I’m depending here on my chance encounters with Sudoku history.

I hasten to add, that this SLG demonstration is not evidence that rank theory is a reasonable vehicle for human solving. Once the arguments of the previous two posts have been made, and we know which truths to select, and where covers are needed, the SLG is graphic justification of the removals.  But only a computer can try out truths and covers until something like this emerges for us to marvel at.

In a similar vein I should mention yet another technique  receiving a demonstration inspired by the Easter Monster opening salvo.  On the same blog, Sudoku.com.au, Steve presents  an article titled Matrices in Sudoku, in which the Easter Monster free line candidates are arrayed in a pigeonhole matrix, and the salvo eliminations are justified by a logical property of these matrices.  The theory is a mapping of rank = 0 theory, but without the nice visual picture.  Again, if you know which cell contents to enter, you can prove you are right, but  in my opinion, you’re never going to find the right combinations without an external  guide.

Well, it’s time to move beyond the opening salvo and face the Easter Not Quite As Monstrous. You can start me off on that road by finding, immediately after the 13 removals, a naked triple that enables another naked triple.  Also get out your x-panels and freeform pattern enumeration tools.  I’m going to need some LPO on this one.