Go Fish!

This post defines Sudoku fish and previews the regular and exotic forms of this elimination technique.  This two-post tutorial takes the form of a tour through an aquarium.

It’s economics.  In Sudoku fish, candidates of a single number X compete for a limited supply of line positions in the solution.  Rows compete for column positions; columns, for row positions. For each of its free numbers, a line competes with eight parallel lines for a clue position for one of its candidates.  A clue of that number in a crossing line at any of these positions threatens to take that position from the line.

This competition is exactly like the competition among cells of a unit for fill numbers.  Fish are patterns of n positions locked among n lines, and thereby denied to other parallel lines.

So my title is not demanding that you draw a card from the deck.  It’s about the family of elimination patterns known as X-wing, swordfish, jellyfish, and  (ugh) squirmbag.  X-wings are the locked pairs,  and swordfish, the locked triples, etc., of the line position competitions.

maestro-4-sword-gridHere is the display in the main lobby of the aquarium, a regular fish, the swordfish from Maestro 4. The fishy icons mark a column fish. We might say the fish is in columns 2, 5, and 9. These 3 columns must share row positions 3, 6 and 9 since they have no 2-candidates outside of these rows. Each gets one of these positions in the solution. We don’t know which, but we do know that none of these 3 positions are available for other columns. Hence the removals.

Rows compete for positions in the same way.  Later we will show how fish economics extends to boxes.

Aside from a brief mention of X-wing spotting in line marking,  I’ve neglected  fish.  I placed them behind bv analysis methods in the SOB, the sysudoku order of battle,  for two related reasons.  Compared to X-wings, higher order fish eliminations occur less frequently.  Secondly,  the bv analysis methods use the same bv map tool, so there is synergy in exploiting the constrictions of the bv net in many ways before constructing X-panels for fish.

When you reach for the X-panel tool, I advocate using all X-panel methods together by considering all of them as each panel is generated.  I’ll go further and add that methods for a panel should be prioritized to suit the panel itself, with the option to skip unpromising methods on the current panel in favor of analyzing a more promising panel first. This compromises a little on one sysudoku principle of reaching closure on a method before moving on to the next method, but it does that to honor another honored principle of efficiency:  Pick the low hanging fruit first.

Along with box marking, line marking and the bv scan, let’s consider panel analysis as phase of sysudoku solving.  X-chains and fishing as components.  A third component, pattern analysis, awaits us.

In addition to regular fish mentioned above, we have finned, multi-finned,  kraken and sashimi fish.  Let’s walk through the aquarium and check them out. We’re going to be looking for them all on our X-panels, and the exotic ones are actually not that rare, compared to regular ones.

Regular x-wing exampleIn this regular X-wing, candidates r2c5 and r6c1 are removed, because rows r1 and r4 demand positions 1 and 5 along the row.  On the grid, we mark the fish candidates with two-way arrows, victims with diamonds, as usual.  The double arrows point along the line of victims.  They are copied and dragged in on the puzzle template.  Don’t they look a little “fishy”?



We deal later with the task of recognizing such patterns in a sea of candidates on the X-panel .  Right now we continue our tour with the more exotic fish. In Sudoku fish talk, a fin is one or more extra candidates in one line of a fish.  I use a rounded square or rectangle on the template to mark the fin.

finned x-wing with box victimIn a finned fish, the fin allows the fish to eliminate a victim sharing its box, because the  finned line can use the extra position of the fin for X if one of its positions is taken by a competing row. Without the fin in this finned X-wing, if the Xr6c1 candidate is true,  it takes the r1c1 position, but r1 can take fin position r1c4, leaving position r1c5 for r4. Xr6c1 can be true, and is not removed.

However, candidate r2c5 remains a victim despite the fin, because it sees  the fin.  If it is true, it denies r1 position r1c4 as well as position r15. Rows 1 and 4 are left with only position c1.  Can’t happen, so  Xr2c5 has to go. One can say that a candidate that would have been a victim, absent the fin, remains a victim of the finned fish if it is in the same box as the fin.

double finned x-wingThe fin is not necessarily confined to one cell. Two cells of the fin can be seen by a victim in the same box, as in the example here. This candidate remains a victim. You could say it takes four positions from the five on the two rows, leaving them to share one.  The X-candidate in r2c5 is removed.

Readers following my blog to this point can anticipate the next exotic fish, although its tank is still around the corner in our aquarium tour.  Let’s pause and have an opportunity for that personal discovery.  It’s about victim vision. The tour continues on my next post.


About Sudent

My real name is John Welch. I'm a happily married, retired professor (computer engineering), timeshare traveling, marathon running father of 3 wonderful daughters and granddad to 7 fabulous grandchildren. The blog is about Sudoku solving. It covers how to start, basic solving to find candidates efficiently, and advanced solving methods in an efficient order of battle. It is about human solving methods, not computer solving.
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