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# Sudoku/Reviews/Systematic Sudoku/Basic

**DRAFT**

*In Sudoku, the placements you start with, the givens, constrain the possible placements in the other cells in obvious, but also unfathomable, ways. The constraints are eventually expressed as the possible placements in each unfilled cell, the candidates.*

Perhaps this is nit-picking; yes, the givens constraint possible placements, and in a proper sudoku, they *totally constrain* them, such that there is only one possible candidate for each unfilled cell. By "obvious, but also unfathomable," he might mean that the constraints are sometimes obvious, sometimes not, but "unfathomable" is simply not true. All sudoku are solvable using logic, so no sudoku is "unfathomable." By saying this, he is reinforcing the idea that solving is really difficult, perpetuating myths that arose in early solving history.

Given that there is only one actually possible placement for each cell, what does he mean, "all the possible placements"? It means, in practice, all the candidates that have not yet been ruled out by the solver. It's not about the puzzle, but about our process. And it is terrible process to start with "all the possible placements." He's quite aware of that, we will see.

*Solving techniques with names, like X-wing, Sue de Coq and Unique Rectangle, are applied in the Advanced stage following Basic. They are defined by relationships among clues, the current placements, and the candidates. Basic is the stage in which the candidates for each unsolved cell are identified and posted on the grid. Advanced techniques are then applied to remove candidates and make more placements, until all cells are filled.*

These are not really "solving techniques," but rather patterns that may appear. Those are his "relationships." They are called "strategies," which is also a misnomer. A strategy would more ordinarily mean an approach, that then uses what is visible and may include recognizing patterns. For example, suppose one has a list of patterns, describing each one and as well, its characteristics and how it may be recognized. A solving strategy might refer to examining the puzzle for every pattern in the list. That's way crazy, because of the complexity some of the elements in known pattern lists. But this is what solving assistants do, such as the SudokuWiki Solver. Humans are then sometimes led to think they should do the same. Bad Idea.

My Gordian Knot-Cutter, Simultaneous Bivalue Nishio, could be described as "identify bivalue cells or bilocation links, and go down the list of them, coloring the chains from each pair and identifying mutual results (eliminations and resolutions) from each such choice. Repeat as needed." That is a solving strategy that is only weakly pattern-dependent. (Rare puzzles without such pairs, or with very few punproductive ones, are called "unsolvables," and require a more powerful strategy, a universal one that will crack any Sudoku, without exception.)

But, yes, I begin solving with Basics, simultaneously resolving cells and identifying locked candidates, and building to a full candidate list, then, if the puzzle is not solved, I add in an Intermediate strategy (examine box cycles for line pairs with specific relationships, and for ready Nishos), and then proceed to SBN, which handles whatever might remain or even which might have been missed in the Basics.

**The Number Scan**

*Sysudoku approaches the basic stage differently. Most Sudoku writers ignore it, assuming you already have the candidates allowed by the given clues. The method they assume you use, either by computer or by hand, is to eliminate every given value in a cell’s box, row or column, taking all remaining values as candidates. Here we call that the number scan.*

He really should get out more. *No experienced solver does what he describes,* unless using a computer. By hand, Snyder notation (the entry of box doubles as the first step) is almost universal. By computer, some manually enter candidates, again using Snyder.

On paper, I do a full number scan, but quite differently. That is, I record candidates in two ways. Inside the puzzle, I mark box pairs, may supplementally mark naked box pairs and naked box triples as soon as seen, and whatever I do not mark inside the box, I mark outside the box, on the edge (using a blank space on the page for the center box). In this stage, with inside/outside marking, I only need to look at each number once.

So I do quickly build up a complete candidate list, and I check this for completeness by counting the candidates. It is really fast, and avoids certain common errors. With easy puzzles I may skip the outside marking entirely, and with really easy puzzles, I may even skip inside marking, entering only resolutions.

As I am doing this, resolutions fall out of it, and as positions are reduced, candidates are moved from outside to inside and crossed off outside. This system was designed to use ink, it requires no erasures. I eliminate candidates in either list (inside or outside) by covering them with an X.

Eventually all boxes have been checked (literally!) as having 9 candidates inside and outside including givens and resolutions, and then all outside candidates are moved inside, lowest counts first. When all are inside, the puzzle is ready for advanced solving strategy.

*The number scan is the simplest logic possible, and many beginners invent it for themselves. But there are problems with generating all allowed candidates before removals begin. That is inefficient, because it requires removal of many candidates that we can more easily avoid generating. The number scan is also poor human engineering. It is boring, and its unnecessary candidates hinder human solving, by obscuring the relationships that basic and advanced techniques rely on.*

Of course. "Boring" is an reaction, actually a choice, and does not exist in the thing itself. It could be said that for an expert, all sudoku solving is "boring," but pastimes are not boring, and may in fact be used to address boredom. The reality here is that excessive entry of candidates into the puzzle can function to obscure relationships. This is exactly why no experienced solver enters all candidates at the beginning unless using autofill, which isn't boring, it is easy and fast.

It can obscure relationships, still, but then autofill brings with it other advantages that outweigh this. I use Snyder for paper solving, and autofill for Hodoku solving, because candidate highlighting, which is meaningless -- or misleading -- if one doesn't have a full candidate list -- is very powerful for basic solving, being weak only in identifying hidden multiples, and there is a strategy for finding them, requiring a one-time scan and then review whenever there have been resolutions and eliminations. Overall, the benefit of candidate highlighting far outweighs that loss of simplicity.

*Here is the puzzle you will be invited to walk through on the Begin With the Bypass page, as number scanned by Andrew Stuart’s Sudokuwiki solver. It’s a 5-star Sunday puzzle solved early in Basic. One cell has a single candidate, and that clue leads to several others.**As in most Sudoku literature, the candidate pencil marks are placed in keypad positions. Here, the font size is the same as Sysudoku grids, and that makes the logical fog more apparent. Generally in keypad grids, the pencil marks are made smaller. That make the logical fog less apparent, but it’s just as real.*

This is outrageous. There is no actual "logical fog," there is chaotic data in which patterns are difficult to see, creating confusion if one expects to see patterns. Yet that single candidate is very visible. A newcomer will look at the center of a puzzle like this and may feel hopeless. An experienced user will *ignore* that center and look at the simpler regions.

When one uses autofill, autoerase is generally used also. So as the simpler areas of the puzzle are resolved, candidates disappear and the remainder of that "fog" clears up. One can actually watch the patterns appear.

But Welch has used his own larger numbers, plus they are a script font, not the small simple numbers that are standard. This makes it look considerably more confusing. Below right is the SW Solver version of that same puzzle.

*Sysudoku Basic is in every way the opposite of the number scan. It follows the advice of Wayne Gould, a well known Sudoku composer, who said, ”If you are writing too many pencil marks, it means you are not understanding how the puzzle works.” Sysudoku Basic is designed to find the most new clues with the least candidates. The number scan is a burdensome task to be completed before solving begins.*

This is a straw man argument. Nobody with any experience does that. Gould was talking about solving on paper, "writing." Many of the people who ask for help on r/sudoku have used Snyder, they only noted box double-positions. And they are mostly holding onto that too long, not wanting to add the rest of the notes because it would be "too confusing." But the simplicity of the incomplete candidate list is an illusion. Yes, marking up a puzzle sanely keeps the notes to a minimum, until what can be seen with that runs out of steam. With easy puzzles, Snyder and what it reveals can go all the way. But with more difficult puzzles, the blank space conceals the patterns that exist under it.

Snyder is box-oriented. Welch does something like Snyder, but he combines box naked sets with row and column naked sets. Ultimately, a solver must consider the line sets, but a box is a confined area, it can all be seen, and all the numbers or marks in it can be read without scanning. I follow a rule: do not mark any candidate in a box unless all positions for that candidate are marked.

Referring to solving on paper, what I do is "number scan," all right, but I'm not marking all those candidates in all the cells. Rather, I am only marking, inside boxes, pairs, and I mark, outside the box all numbers not written inside, as I have looked at the positions of that number. So this is approaching one-ninth of the writing. It's very simple, and error-tolerant, I'm much more careful about what I write inside the puzzle.

Welch deprecates positional notation, because it is allegedly redundant, thus inefficient, but does not use position as far as I can tell to provide what it so usefully provides in standard positional notation: geometry for pattern recognition.

Welch claims to use candidate position for additional information. He essentially asks the reader to figure it out, he doesn't explain it on this page.

It appears that the Sysudoku method is not practical for solving with ink on paper. Yes, he does a lot of analysis. More than I understand as yet. However, what I do cracks all ordinary sudoku with no fuss; in the paper version I have often used ink only, but of later I started using pencil for coloring, because I can run alternate colorings then, without restriction. The eraser just removes the pencil marks, not the candidate marks -- which are converted to "elimination marks" (X) if not overwritten by a resolution number.