The Sysudoku Order of Battle, (SYOB) is an adaptive sequence of solving actions recommended in the Sysudoku blog and Guide for puzzles of all human capability levels. A consistent order of solving has many advantages. It minimizes uncetainty about what to do next. SYOB places easier and more immediately productive actions first, an important incentive for DIY (human) solving. Harder puzzles require periods of organiziation to prepare for more advanced methods. These are included in SYOB and MS Office templates for them are available free by email request (see Solving Tools).
Finally, having an Order of Battle is important if you want to document a solution, i.e. have a record of it. Why would you want to do that? For me, to share it with readers. For you, to reproduce it for a friend or later, with yourself. Having a record may be the prevailing reason to use a tool like ©PowerPoint to leave a series of screens and comments as a record, in which you can pick up and try a newly learned method at any point. With an agreed upon SYOB, records made at different times and different people can be compared.
On Sysudoku, everything you see is produced on ©Word and ©P0werPoint, and delivered with ©Wordpress . You can “Do It Yourself“ that way, or on paper, or with some other software. But I do recommend that you consider the technology advantages that show up throughout this site.
The following is a brief description of each stage of SYOB. Its an outline overview of the entire process, and will be here for your reference. For detailed explanations with examples look in The Guide, a pyramid of pages.
If you’re a true newbie, you may need to consult the site glossary, Sysudoku Speak. When that gets too cumbersome, it’s time to move on to details at an earlier stage, and come back later.
Basic solving derives the number placements directly implied by the givens, and the remaining candidates. The givens are the placements that define the puzzle. The candidates are the small numbers in a cell representing the values known to be eligible for placement at the cell. The givens, plus all placements made so far, are the clues. In the process, Basic adds strong links and subsets defined by boxes and lines, which are elements of advanced methods to follow.
Sysudoku Basic divides this task into three successive stages, each concentrating and making progress on a subtask. Each stage has its own type of record, but there is a form of record that is made whenever a new clue is added or a candidate is removed. It is the sequence of follow up moves that bring the puzzle to a stable state or a solution.
In Sysudoku the record of this sequence is called a trace. Traces occur at all stages, and are generated under rules for no other reason than to have everyone generate the same trace for the same input position. The first trace in every published Sysudoku solution covers the first stage of Sysudoku Basic, the bypass.
The term advanced solving generally means using defined techniques or methods beyond basic, when the basic process is completed for all free (unplaced, unassigned) cells. In advanced solving, basic comes back with the same sequence of actions following up on new clues and candidates.
The sequence of actions is the same, puzzle to puzzle, in Sysudoku Basic, though the results vary widely. In Advanced, the sequence adapts more to the current state of solving. The above is a typical “normal” order based on effort, easier steps first.
The advanced flow chart shows a sequence of graphical representations of the puzzle, with a sequence of solving methods along the lines. A process called coloring is started earlier or later, and runs parallel to the left sequence in that the two sequences update each other.
It’s the typical “normal” order based on effort, with easier steps first.
The BV Scan
In Sysudoku, a bi-value cell, one with exactly two candidates, is a bv. The Sysudoku review table, the summary of solutions for the selected puzzles, reports on the number of bv as advanced solving begins. In the bv scan, we look around bv cells for signals that certain bv based techiques can apply. The general theory of the method and possibly the spotting signal for it are on its page but unless an order is specified, you’re looking “simultaneously” for any of them, box by box. A bv is the simplest form of an almost locked set, an ALS. The search for a bv technique that fails can lead to a ALS version that succeeds.
The bv Map
This is a stage in which we pause searching to construct a visual aid. I use a Word table to contain bv cells and their candidates nothing else. It takes little time, and but then it’s available to update when there is any change in the bv field.
The XYZ Scan
We first copy the bv map onto a table with wider fields to look for XYZ and classic WXYZ wings. These methods identify sets of 3 and 4 candidates of the same value, which must contain a true candidate, i.e. a clue of the solution. Again, an ALS can substitute for a bv in the these methods.
The XY Railroad
The SYOB now turns to Alternating Inference Chains, or AIC. These are candidate chains with links alternating between strong links and weak links. The easiest form of AIC to recognize and track is a chain of bv called a XY chain. On the bv map we draw curves which track all current XY chains. We call it a railroad because, when it branches, the alternative branches continue in the same direction, like a railroad switch.
Once the railroads are built on the bv map, every repeated value defines an XY chain. Each one is a potential Almost Nice Loop or ANL. The repeated candidates are on strong link (slink) terminals of an XY chain (as traveled in one direction) and one of them must be true. Even though we don’t know which one is true, any candidate seeing both of them is removed.
Next we build a set of 9 by 9 panels, each one showing the candidates of a single value X. As each panel is completed, we check for line slinks we may have missed, and search the panel for regular, finned fish and kraken fish. There’s an easy progression of analyses for these. Then we scan the panel for X-chains and grouped X-chains. These are AIC of a single value X. Finally, along the edges of the panel, we look for pattern limits for removals and trials.
Coloring is marking a connected network of strong links by adding two colors to candidates. The networks are called clusters. In a cluster, candidates of one color aretrue, and those of the opposing color are false. This leads to candidate removals (traps), related colors(bridging), and cluster merges.
In SYOB, coloring is begun when a potentially significant number of connected strong links is noticed. The new cluster is expanded as much as possible, then maintained. In effect, a parallel solving track is added to the solution path.
When large clusters seem to be stabilized, the technique of lite coloring is used to expand them. Lite coloring identifies candidates which are true when a cluster color is true. Such candidates are then treated as lite colored in that color. Candidates of lite color can trap and induce color bridging and cluster merging even though we don’t know if they, or their full color counterpart candidates, are true or false.
Rather than search AIC of all kinds, Sysudoku treats them as constructions, seeking to build networks of them starting from strong links, with awareness of how AIC starting from a location can end with a candidate removal or clue confirmation. As this proceeds, the networks remaining after these events become self – limiting, and the process ends with a background of AIC segments on the grid. They are assigned a lite blue color and left on the grid as the AIC segments map.
ALS Suset Tables
Sysudoku continues the dominance of construction over searching by reversing these actions in the handling of ALS. ALS are recognized as substitutes in the role of bv throughout the earlier stages, but they occur in such large numbers that it impractical to search for them exhaustively throughout advanced solving. So after all of the above, we exhaustively construct all ALS in rows, columns and boxes in a number string matching process.
Then with these three tables as a resource, we add ALS to one of three graphic ALS maps. As it is added, we copy it to a current grid with AIC segment background , looking first for ways it can be used to extend the segments, then comparing it with ALS already drawn on the ALS maps, we look for ALS_XZ partners, and for the added ALS to be the last one needed for an ALS wing.
If the ALS maps are ever completed we just look for a trial. Coloring failed as well.