2.2. Premises, Inferences and Searching

2.2.1. Premises and Inferences

Source: http://sudopedia.enjoysudoku.com/Inference.html

Solving Sudoku puzzles involves asserting a premise, and deducing what conclusions can be inferred.

The most basic assertion of a premise is on the state of a Ccell. For example:

3r7c2 - Asserts 3 in r7c2 to be True, similarly.

3!-r7c2 - Asserts 3 in r7c2 to be False

When a cell state is inferred, other cell states may be inferred:

3r7c2 => 3r7c8 => 5r7c8

Asserting 3r7c2 True, infers 3r7c8, which in turn infers 5r7c8. An inference string may lead to the placement or elimination of a candidate.

5!-r2c7 => 5r2c2 => 5!-r6c2 => 5r6c7 => r34c7-=5

Asserting 5r2c7 False infers 5r2c2 is True, 5r6c2 is False, leading to the elimination of candidate 5 from Cells r3c7 and r4c7.

2.2.2. Searching

Searching is the process of cascading inferences to find a solution. Often referred to as Forcing Chains in the Sudoku literature, it is a type of Trial and Error technique, not a guessing. It is the application of logic to test a premise.

However, exhaustive searching becomes a mechanical process, replacing skill with brute force to find a solution. Searching finds it own place in conjunction with other criteria, logic and/or pattern solving techniques that have isolated a few conditions to search.

A Verity is where two search different paths from the same condition, find another candidate to be True in both cases. A Contradiction where two different search paths from the same condition find another candidate to be False in both cases. A verity / contradiction could also be the testing for a strong or robust link.