Logic in Xsudo

Logic is simply reasoning. Although different kinds of reasoning and notation are used in Sudoku, at some level they are much the same. Xsudo represents all solving methods with one system using truths and links.

What is a truth?

· A truth is group of candidates where at least one candidate must be in the solution (true).

What is a link?

· A link connects 2 or more candidates that see each other in a row, column, box, or cell.

Example

The solving method below, called a two string kite, has 2 truths and 3 links. It eliminates the red candidate in cell r8c8.

Truths

· The two 8s in row 2 form a truth because one must be true.

·  The two 8s in column 4 form a truth because one must be true.

Links

· The two truths are linked in box 2  forming a short chain.  

·  The two ends of the chain see the candidate in r8c8 through a column link and a row link .

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The reasoning is simple. The two truths contain two 8s. The box link cannot contain two 8s so the other 8 is forced into either the row link or the column link. Either way,  it prevents the 8 in cell r8c8 so the red candidate can be removed.

Single Example

A single is the simplest form of logic with one candidate in one truth. The digit 4 in cell r4c5 is the only 4 in the column so it forms a truth in the column. (short green bar) All the red candidates see the 4 through row, column, and box links.