This post reveals that the symmetries and supersymmetries of THLS, as applied to subsets and fish, are identical to a Sysudoku tool that reduces these Sudoku entities to numerical input for a well-known algorithm. This shows conclusively that maintaining extra grids for symmetry transformations is not a practical way to detect these entities.
First, the homework on the hidden triples of Royle 17-32227. The basic trace to the point of collapse reveals only naked triples,
and the grid at the second one, in line marking, reveals the reason.
Without the candidates uselessly introduced before solving even begins, the hidden triples are replaced by naked triples.
Is THLS symmetry more of a problem than a solution? The required number scanning and symmetric grid surveillance are a BIG problem for human solvers.
Now we can turn to the super hidden transformations of THLS, and Berthier’s suggestion that they belong in every solver’s tackle box. We start with the super hidden pair, the regular fish we have been stubbornly referring to as an X-wing.
In Royle 17-6973, Denis Berthier shows us the puzzle in in nrc space and in rcn space. We get to see it, after the LI_0 elaboration, when most of the number scanned candidates have been removed, and when SudoRule rules are reported to have revealed a 5-wing. You can find the wing in Figure 8, page 105 in my THLS edition, and the naked triple transformed hidden triple on the Figure 9 grid, page 106. You’ll know just where to look after reading a little farther.
Here is the same 5-wing, as it appeared in our almost completed line marking. I was on r1, when I realized that I was adding the last and second 5 in c7 and the slink matches the 5’s in c1, creating the 5-wing.
Spotting X-wings is that easy in the follow up to every marked line.
Now to look at it through supersymmetric glasses, let’s go to the X-panel, where we look for higher order fish, among other phenomena. There, at least we have all basic candidates and can see the 5’s alone.
At left is the 5-panel with blank line markers for the column fish (|) and the removal rows(+). Is the 5-wing harder to see than a naked pair? Not much.
At right is the corresponding naked pair in r5. Row 5 represents the distributions of 5’s in all columns. In fact, the row is the starting suset list for generating all column wise 5-fish. Of course the full rnc grid would have the mapped other numbers into into all columns. Besides the 5-wing, all column-wise regular fish of 5-candidates are represented in these numbers.
Yes, I was into supersymmetric fishing in 2012, and didn’t know it. It was long before encountering THLS. In Casting for Regular Fish, you’ll see a suset list I used before discovering the much easier blank line tally. I left that in for tough cases, and later, applied suset enumeration to the finned, kraken and mutant fish that are missing from THLS.
When you interchange number and row for supersymmetry transformation, you are recording the column positions for true candidates of the panel number. Interchange number and column for a suset list of row fish. And by the way, we do this mapping only on the candidates remaining after basic, and bv scan. And only when the fish are a lot less evident than here.
And speaking of row fish, it so happens Royle 7-6973 provides an example, undisclosed by THLS. On the 5-panel is a row oriented swordfish. For row regular fish, the supersymmetric mapping is to interchange number and column. Can you spot the 3 numbers in only 3 lines that mark the swordfish, without looking at the left panel? If so, you just did a suset enumeration, pilgrim.
For row or column fish, the supersymmetries list the positions along the line, the very resource the lines are competing for in a regular fish. When there are n lines needing n positions, no other lines can have one of the n positions. That is how fish should be explained.
But as shown many times in these posts, the THLS symmetries and supersymmetries are totally unnecessary for regular fish. If the blank line tally on the X-panel leaves any doubt, list the line positions as susets, and do the enumeration, starting with the sparser lines, of course.
But perhaps you’re unconvinced because we only saw the X-wing and swordfish in Royle 17-6973?
In that case, let’s spend one more post on it, and take up a very challenging THLS example, the super hidden quad or jellyfish example, Royle 17-1007. Follow the SOB. You’ll find three naked quads on your way through line marking, and may encounter a unique rectangle, and a twisted Sue de Coq. Skip the rest of the bv scan and go directly to the X-panel for the jelly, and come back afterwards for the finish. We’ll blank line tally the jelly, and do a full suset enumeration on it, just to show off the sysudokie tackle box