The SOB, the Sysudoku Order of Battle, is the recommended sequence of solving actions. The sequence is designed to place easier and more productive actions first. Exceptions can be made with reasons noted, but having a generally optimum sequence means that the solver always knows what to do next. The SOB also helps sysudokies compare solving experiences, and is a basis for rating the difficulty of puzzles on a common scale.
The SOB takes three additional factors into account. These are
- The timely introduction of Sysudoku visual tracking ©PowerPoint templates.
- The benefit of completely exploiting an easier method before attempting a more difficult one.
- Some methods assemble multiple candidates for trial. The SOB includes a trial policy allowing for powerful early trials, while preserving the ability to discover more direct results later in the SOB.
Arbitrary selection of candidates for trial is never justified in sysudokie society. This is the very definition of T&E, i.e. trial-and-error, for us. It allows puzzles to conceal their secrets. “My guess X at row r, column c was correct” reveals nothing, and spoils the mystery for anybody else. T&E perpetrators must give up their sysudokie badges.
Basic solving derives clues and all remaining candidates. This enables advanced solving, which uncovers logical contradictions among candidates, and removes candidates causing them. Basic solving is mechanical, in that every step is taken, and makes some progress. Advanced methods may fail, and may be skipped when unpromising. Advanced techniques earlier SSOB come back into play as solving advances. Basic marking and tracing continues in follow up on each decisive candidate removal or clue confirmation.
The remainder of this page is for reference primarily. It is full of sysudokie jargon and very terse descriptions . The jargon is decoded on the “Sysudokie Speak” page, and the techniques are described, justified and demonstrated in detail in the posts. Relevant posts can be located on the “Find It” page, and accessed by date on the list to the right.
Basic solving derives clues and all remaining candidates. This enables advanced solving, which uncovers logical contradictions among candidates, and removes candidates causing them. Basic solving is mechanical, in that every step is taken, and makes some progress. Advanced methods may fail, or may be skipped when unpromising. Advanced techniques earlier SOB may come back into play as solving advances. Basic marking and tracing continues in follow up on each decisive candidate removal or clue confirmation.
Box marking derives the clues and slinks (strong links) that can be directly determined from clues and slinks(marks), as they sweep into boxes, excluding candidates. We use all marks of one number at a time, reducing the box cells available to that number. When the available cells are reduced to one or two, clues or slink markings for missing numbers are added . When only a chute is left, slink and aligned triple marks are added.
Boxes are reviewed for naked locked sets as the number of marks approaches the number of free cells.
It is an engaging challenge, and often more efficient, to divide box marking into two stages. Before recording slinks in regular box marking, the slink making bypass is a scan through the numbers, but marking only the clues and naked pairs. This bypasses the recording and tracing of slinks that are replaced by clues before they produce solving effects.
Sysudoku offers an efficient method of tracing exact steps in basic solving and follow up marking. It is described in detail on the traces page, along with a modification used for trials. To match checkpoint traces in blog posts, do your box marking in number order, 1 through 9 and follow the tracing rules. When tracing, it isn’t necessary to divide the bypass trace into separate lists by number.
To match checkpoint 2-D traces, do box marking in number order, 1 through 9. A checkpoint trace immediately exploits each new marking, listing all immediate effects. Effects on the cause number are listed first, then numerical order. Effects become causes left to right, after all effects of earlier listed causes are completed.
In tracing the bypass, the effects list is not divided into separate lists by number.
Line marking identifies remaining candidates, and marks bv (bi-value cells) and strong links along rows and columns (line slinks). The order of processing is from the smallest number of free (unsolved) cells to the largest. But that order keeps changing as clues are discovered, and box marked.
Line marking is an efficient way to enumerate candidates, much more efficient than the generally endorsed method. A string of possible candidate numbers is placed beside the line, and compared at each free cell along the line, with marks on the crossing line and enclosing box.
As it is marked, each line is reviewed for new slinks, and its bv (bi-value) cells are highlighted. The line candidates are scanned for locked sets, both naked and hidden, and new line slinks are compared with those of parallel marked lines, for X-wings. X-wing symbols are left in place until possible removals from as yet unmarked lines are recorded. As boxes are covered by marked lines, they are reviewed for naked and hidden locked sets among box candidates.
Line marking concludes with line closure. When all lines are covered in one direction, lines not processed in the other direction are reviewed for line slinks and locked sets.
Advanced solving techniques depend on a full set of remaining candidates in each cell. They are divided into six phases based on the visual tools being used. Tools are prepared for each phase.
Sysudoku recommends ©PowerPoint, or equivalent officeware, for following traces and comparing results. The readers’ own solving experiences with a puzzle are can be saved in presentation files. See the tools page for information about Sysudoku template files.
The bv scan is done on the grid and with a ©Word bv map template.
X-panel analysis requires a template of 9 panels. I use a ©Word template with 12 panels and copy the panel contents to a ©Powerpoint template of larger panels for blog reporting. Limited Pattern Overlay(LPO) requires X-panels sized for detailed freeform analysis, or lettering tables for overlays.
Trials are tests of a large number of candidates logically determined to be all true, or all false. Trials are conducted with trial tracing and graphic follow up. If the trial result is graphically obvious, then the trial result is used immediately, even if it collapses the puzzle. Else the trial is noted on a trial list for possible use when all logically determining methods are exhausted.
The bv scan
Unique rectangles and remote pairs are very distinctive on the grid, and are therefore done first. Then comes a box by box scan for Sue de Coq chutes. Complete the classic two alternate form of SdC immediately with eliminations. The Sysudoku single alternate SdC employs a trial to confirm the elimination by disproving an alternative chute solution.
Prior to completing bv maps, a scan is made for APE, N-sets, WXYZ-wings, simple ALS toxic pairs and Death Blossoms. Simple ALS are bent combinations of bv and ALS set. For N-sets, look for n numbers in n cells in a union of a line and box. Examine remainder cells for BNS0 and BNS1 cases. Examine unit members for n-1 restricted commons, a BARN.
The completed bv map is copied for the testing of XYZ hinges, which includes searching the grid for forcing chains to complete XYZ wings and for identifying victims.
The XY railroad curves are drawn on the original bv map, and traced to find the toxic terminals of XY-chain ANL. XY nice loops are left for coloring.
Regular and finned fish are identified via blank line (-|+) marking .
Kraken analysis confirms victims of finned fish. Suset enumeration is used to identify hard to spot finned and regular fish, and to confirm franken fish.
For X-chains and loops, note slinks and use freeforms or curves to map x-chains on the panel. Complete chains and loops by grouping. Nice loops are left after eliminations, for later coloring.
Watch starting edges for easy LPO orphans.
Bv slinks are included in Medusa coloring. Traps are candidate eliminations. Wraps eliminate one color and confirm the other. Bridging associates colors in two clusters fro trapping. Merges combine clusters, recoloring the two colors of one cluster. Leave cluster coloring in place. Add nice loop and direction extension coloring combine with Medusa slink net coloring.
Remaining clusters provide associated slinks from each member to every opposing member. Repeat forcing chain wink searches with these shortcut slinks,
Alternate Inference Chains
AIC hinges are marked on the grid, allowing for slink extensions and bv node reversals in AIC building. Chains are extended by grouping and ALS nodes. Nice loops are extended in both directions with coloring. Fully extended nice loops are given archived trials, for later invocation under Sysudoku trial rules.
ALS Toxic Set Enumeration
Enumerate ALS unit by unit, with suset scratchpad. For each one, look for ALS partners with restricted commons and toxic sets. For nearby bv and triple candidate stem cells, watch for ALS Death Blossoms .
Limited Pattern Overlay
Examine X-panels to identify LPO opportunities . Copy X-panels to LPO ©PowerPoint panels for freeform analysis to remove orphans and map patterns. Divide patterns via pink/olive slicing. Apply pattern slinks.
From the deferred trials list, apply the latest decisive trial. If none, the latest indecisive trial. If there are no decisive results, apply an available trial generator, such as an exocet .