Sysudoku Basic

Sudoku puzzles are solved in a step by step process. In Sysudoku this process is divided into three successive stages: Basic, Advanced and Extreme. Extreme can be left for later, but Basic and Advanced are best considered together. 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 limit placements, until all cells are filled. If no way to do this by logic is found, a logic-based trial is a last resort.

In relation to human abilities and effort, there is a right way to identify the candidates. The worst way is to start each cell with all possible candidates and eliminate the candidate of every given number in the cell’s box, row or column. This method is so much assumed by many writers, they give it no name.  Here we call it the number scan.

The number scan is the simplest logic possible, but generates the most candidates before removals begin. A cloud of candidates hinders human solving because it requires the most removals, while it obscures the relationships among candidates that techniques rely on, making removals harder.

Sysudoku Basic does the opposite.  Clues are placed and candidates removed throughout Basic. It is designed to find the most clues with the least candidates. To do this, Basic is divided into three successive stages, the bypass, box marking, and line marking.

The Begin Page demonstrates how the bypass finds clues, and aligned candidates that work together with the givens to allow only the most essential candidates onto the grid. The number scan uses only the givens, and adds candidates only.

The full name of the bypass is the slink marking bypass. Except for subsets, the bypass defers the posting of candidates to the grid. Subsets reserve cells for their member numbers, and are therefore essential to the function of the bypass.

In all stages of Sysudoku, new clues are followed up in the same manner as the bypass, with depth first, cause and effect posting and tracing. After the bypass, however, new candidates are written in as they are identified.

With the second basic stage, box marking, preparations begin for the event that the puzzle survives Basic.  To the candidates of closed subsets within boxes, and lines, we add box slinks, these are pairs of candidates of the same number within a box. The restriction to exactly two establishes a logical relationship between them, the strong link. This candidate link is so important we give it short nickname, the slink. If one of the slink partners is false, the other one is true, because the box must have one true candidate of the slink’s number. Slinks are fundamental to many advanced methods.

The third stage, line marking, completes the identification and marking of all remaining candidates of the surviving puzzle. By placement of candidates within the cell, line slink candidates are distinguished from other candidates; row slinks from column slinks. Cells with two candidates only, the bi-value cells, are valued resources in advanced methods. In Sysudoku posts, they are called bv, and are marked with green borders.