Come let us reason together about regular fishing, i.e. finding X-wings, swordfish, or jellyfish on an X-panel . We look at sets of lines in one direction, then the other. Rows and columns. We seek a set of n lines with a combined total of n line positions to be filled with the panel number. That is a regular fish. In the solution, each of these lines will get one position for the number. Other lines will have other positions for the panel number, but the fish locks up these n positions for itself.
When there are N clues of the panel number on the grid, there are N blank rows and N blank columns on the panel. Of greater significance to fisherpersons, there are 9 – N positions for the clueless n rows and 9 – N for the clueless columns (no insult intended), to house the 9 – N remaining clues to be. That means there is a 9 – N order fish consisting of the clueless rows and another 9-N order fish consisting of the clueless columns. These fish are impressive, and we know where they are, but fisherpersons have no interest in them. They have no victims.
In fishing, we are looking for smaller fish, sets of n lines that combine to lock up n positions for themselves, leaving 9 –N – n positions for the remaining 9 – N – n lines. We are actually trying to divide a big fish into pairs of smaller fish. In Sudoku fishing lore, it is well known that you need only look for a fish of (9 – N)/2 lines or smaller, rounding down. Wise fisherpersons chuckle knowingly if they see anyone fishing for a squirmbag. If there is one, there’s got to be a jellyfish or smaller on the parallel lines. Fish for that instead.
If we have clues for the number ( N>0), regular fishing is even easier. Given three clues, we need only scan lines of three candidates or less, not even looking for jellyfish. Lines of four or five candidates could only be the fin line of a finned fish.
A row fish of n lines reserves n positions, leaving a smaller allocation battle for the remaining rows. But how does finding a row fish effect fishing the columns? To answer that question, let’s call upon a swordfish example Andrew Stuart’s The Logic of Sudoku(order from www.sudowiki.org )? By the way, I am not affiliated with Stuart or Michael Mepham, or any other Sudoku experts, for that matter .
Here is an abstracted panel from Andrew’s Swordfish chapter. All you need to do to follow up on this post is to decide what regular fish to look for. That is, what level of fish are you going after, and what rows and columns are excluded from the scan.
Done that? Fine. Look for the fish before inspecting the diagram that follows this uncommercial break:
So if you are with me on the LA Times weird fish project, you’ll want to compare notes on sysudoku box marking. In the tracing reference page , I’ve modified the notation shown earlier in this blog by dropping all reference to the routine causes of markings, such as dublexi, cross hatches, and box/line reductions. Causes were given, but are dropped now because, after the basic training, readers can find the cause, once reminded where there is something to find.
Speaking of reminders, there are place notation diagrams on the Beginners and Sudoku Speak pages. Boxes are labeled by the compass. Read the trace across lists then left to right down hills, updating a grid as you go. That is the only way you can “read” a trace. Need a template? Ask for one at firstname.lastname@example.org.
Resuming now on Stuart’s swordfish, I marked the victims of the swordfish of columns 1, 3, and 9 with a “v”. The I changed the remaining x’s not in the swordfish or among the victims to lower case letter “o” – an “o” looks nice on the panel. On this diagram, you can verify that the remaining columns do indeed form a squirmbag (8 – 3) with no victims. The complementary fish (o’s) can never have victims, because the only lines outside of this fish are the original fish (x’s), and no ‘x’ can appear between the candidates of the original fish. That last sentence may be gibberish if you are not looking at an example like this one.
Now having accounted for the columns, what about row fish? Notice first that the original fish has taken three columns out of the running. And that the original fish, viewed by rows is now a dead (no victims) swordfish! Why didn’t we see that swordfish before? Because it did not exist before the original victims were removed! This is always going to happen.
Now we get to the row squirmbag (o’s) that is complementary to our new dead swordfish. It has the same victims as the original swordfish, so as a big fish it contributes no removals. And significantly, the row squirmbag is untouched by the removals. This means that if we did find an X-wing/X-swordfish division, these fish should have been found in our initial scan.
But sysudoku fisherpersons have reason to look at the complementary lines of the original fish, in this case the ‘o’ columns for further fish breakdown, because these lines are altered by the removals.
It’s like having a smaller 5 x 5 cove in which the two complementary fish (o’s) are the big fish of that cove. The cross line (rows here) complementary fish is whole, just squeezed into the cove, but the parallel line (columns here) complementary fish is a sliced off piece, unable to avoid the cleaver.
You don’t need to make up a cove panel for the second slice. This one was just to demonstrate the difference between the complementary row fish and column fish after removals. Don’t waste time trying to explain all this to your solver friends. Just send them to this annotated example. And visit Andrew’s site and consider his book. It was ground breaking in 2007.