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.
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.
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. 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.
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.
Subsets and the Bypass
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. In Basic, solving begins immediately. Placements begin immediately. Clues are placed and candidates are removed throughout Basic. It’s just more fun.
Sysudoku Basic begins with the bypass, a way to find clues with clues and other subsets. Only the pencil marks of naked subsets are written on the grid. A subset is a set of n cells in a box or line, containing all candidates of n values, but not all candidates, in the box or a line. No other values can be placed in the subset cells, because these cells must contain the n values. A clue is a subset of n = 1.
In the grid above, there is a subset of 3 values that reserves 4, 8 and 9 values for themselves, leaving 5 as a clue.
In this walkthrough snapshot, we are well underway in the bypass. There are four pencil marks so far. The subset is a naked pair 48. The subset of the box is also a subset in row 3, preventing 4 and 8 candidates in four cells.
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.
The number scan only lists candidates. By abandoning its redundant keypad arrangement of candidates within the cell, Sysudoku Basic does much more to prepare for the Advanced methods required for harder puzzles. Strong links between candidates are marked as they are discovered. A strong link, a.k.a. slink in Sysudoku, is a logical relationship between two candidates that guarantees that at least one of them is a true placement in the solution. If one slink partner proved false, the other must be true.
Strong links are components of many advanced methods. The most frequently encountered slink is the one between the only two candidates of the same value in a box or a line. The unit must contain one of these candidates. A slink is also present in every bi-value cell. These are cells of exactly two values, known in Sysudoku as bv.
The full name of the bypass is the slink marking bypass. The two stages following the bypass write in the slink partners with pencil marks. In the bypass, slinks are recognized and used to find clues and subsets, but only the clues and subsets are written in. The mind sees the consequences of slinks quite readily when not interrupted by writing them down. After the bypass, what is left for the two following stages is reduced by the clues and subsets found.
The second stage of Basic, box marking, concentrates on the unfilled cells in each box in turn, and values excluded from the box by outside clues, slinks, and aligned triples. An aligned triple is a set of three candidates of the same value in a box that are confined to one line.
Box marking is focused on one value at a time. If there is only one cell left unclaimed by outside clues, slinks and aligned triples of a value, then a placement is made of that value. Slink marking gives a second option. Two uncle aimed cells identify a box slink of the value. Three unclaimed cells in the same line identify third option, an aligned triple. Any of these add to the restriction of placements in other boxes.
The third stage, line marking, adds the slinks formed by exactly two candidates of the same value in the line. In addition, line marking 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 bv, are a valued resource in advanced methods, due to their built-in slink. In line marking, bv are marked with green cell borders.
Here is the line marked 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.
Slinks are marked by pencil marks at the top, and the bottom corners of cells. If you’re new to Sysudoku, use this example grid to figure out how box, row and column slinks are distinguished in slink marking. Your analysis will be confirmed in the Box Marking page.
The red arrow symbols in r2 and r5 mark an 8-wing, an advanced elimination method that is available in line marking because the marking action makes X-wings immediately easy to spot. Here, the 8-wing found too early for eliminations was left to avoid adding candidates destined to be eliminated from lines marked later. Very much in the practical spirit of Sysudoku Basic.
So is the positioning of pencil marks. Look again at that first diagram of number scanned candidates. Notice how the logical information highlighted in the line marked diagram is obscured in the keypad 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.
The Basic Trace
Sysudoku pages and posts give readers a compact record of basic moves, a basic trace. With this trace, and a grid diagram, the reader can step through the exact Basic path, seeing the current grid as every move is made. Even better, no explanation is given for any move in the trace. This saves space, but it means that explaining is done by the reader, an ideal situation for gaining solving experience.
Although tracing is very useful when you are sharing solving logic with others, or uncovering where you went wrong when a contradiction occurs, this doesn’t mean that trace writing is a normal part of Sudoku solving. Conventions are observed so that readers can write traces that match with Sysudoku traces for confirmation. These are described in the Sysudoku Traces page on the menu bar. But you don’t need to know them to read Sysudoku traces. The simple rules of trace reading are covered in the walk through example of Begin with the Bypass.
Sounds Like a Plan?
Sysudoku Basic anticipates your exploration and enjoyment of Sudoku of all levels. Please continue down the pyramid of pages of this Guide, starting with the bypass.