Sudoku puzzles are solved in a step by step process. In Sysudoku this process is divided into three successive stages: Basic, Advanced and if necessary, trials. Techniques given names, like X-wing, Sue de Coq, or Unique Rectangle are applied in the Advanced stage. They are defined by relationships among candidates, the known possible placements of numbers in cells. They depend on knowing all the possible candidates of the cells involved. 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 placements, until all cells are filled. If no way to do this by logic is found, a logic-based trial is a last resort.
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.
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. It is also poor human engineering. A large cloud of candidates hinders human solving because it obscures the relationships among candidates basic and advanced techniques rely on.
Here is the puzzle you will be invited to walk through on the Sysudoku Basic 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 numbers, the pencil marks are placed in keypad positions. Here, the font size is the same as Sysudoku grids, and the logical fog factor is very apparent. Generally in pencil marked grids, the pencil marks are made smaller.
Sysudoku Basic is in every way the opposite of the number scan. It carries further the human solving philosophy 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.”
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. In Basic, solving begins immediately. Clues are placed and candidates are removed throughout Basic. It begins with the bypass, a challenge to find clues without candidates other than subsets.
In this walkthrough snapshot, we are well underway in the bypass. There’s one subset so far, a naked pair 48. In the walkthrough, you will know exactly how Basic gets here. The point is, these clues are discovered on a fog free grid, with only the givens and a few clues. It’s the level of Sudoku that is actually practical to do by pen on a paper grid.
And finally, the number scan only lists candidates. Basic does much more to prepare for the Advanced stage. It uses subsets and marks strong links for Advanced methods. A subset is a set of cells reserved for the same number of values. A strong link is a logical relationship between two candidates that guarantees that at least one of them is a placement in the solution. If one slink partner is false, the other must be true.
Systematic Sudoku Basic is a human engineered organization of the work of marking candidates, strong links and subsets to avoid repetition, and to require attention to one task at a time.
The first stage bypass is a stimulating challenge of combined observations. Beginners can skip it at first, but should get to the bypass early, because it is an incentive to prepare for the harder advanced challenges.
The full name of the bypass is the slink marking bypass. It bypasses writing in candidates, except sets of candidates reserving sets of cells for themselves, the subsets. Slink is the Sysudoku abbreviation for strong link.
With the second Basic stage, , new clues and subsets are sometimes found, but mostly it is preparing for the event that the puzzle survives Basic. To the subset candidates, we add box slinks. When there are exactly two candidates of the same value in a box or a line, they form a slink. If one of the slink partners is false, the other one is true, because the box must have one true candidate of that value. Slinks are fundamental to many advanced methods.
The third stage, line marking or LM, adds the slinks formed by exactly two candidates of the same value in the line. In addition, LM completes the identification and marking of all remaining candidates of the surviving puzzle. Box slink partners, row slink partners, and column slink partners are distinguished by the positioning of candidates within their cells.
Cells with two candidates only, the bi-value cells, are a valued resource in advanced methods. In Sysudoku posts, they are called bv. Think about it, bv have a built-in slink. In Sysudoku LM, bv are marked with green borders.
We can illustrate the final Basic product, the line marked grid, only with a puzzle that survives it to reach Advanced. Here is the LM grid of James Forest’s Classic 48, recently reviewed.
The givens are supplemented by 17 clues, and six more placements are locked into three naked pairs, subsets of two values confined to two cells.
To count the slinks you need to know how they are positioned in their cells. Box slink partners go along the top, in identical positions. Row slinks go bottom left and column slinks, bottom right. When a candidate partners in more than one slink, the box slink has priority.
The red arrow symbols mark an 8-wing, an advanced elimination method that is included in LM because the action of line marking makes X-wings easy to spot. Here, the 8-wing found early in two lines was left to avoid adding candidates destined to be eliminated from lines marked later. Very much in the practical spirit of Basic.
So is the positioning of pencil marks. Look again at that first diagram of number scanned candidates. Notice how the logical information in the LM diagram is obscured in the kypad cloud. Note how wasteful it is to be digging this information out of the keypad display, as it gradually melts away. The same values are reported twice. Once by symbol and again by position. Sysudoku uses position for useful information.
Sysudoku Basic anticipates your exploration and enjoyment of Sudoku of all levels. Please continue down the pyramid of pages of this Guide