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Invalid

An invalid or improper Sudoku does not have a unique solution, which means that it either has no solution at all or it has multiple solutions. A Sudoku with a unique solution is a valid Sudoku.

Invalid Sudokus are often the result of transcription errors, either by the maker, the publisher or a player. When a source frequently publishes invalid Sudokus, the generation process (manually or by computer) may be incorrect.

No Solution

There is little debate about Sudokus without any solution. At some point in the solving path, a contradiction will be found, which is not based on a prior assumption (see Trial & Error). From there, the puzzle can not be completed by the solver.

Multiple Solutions

When there are multiple solutions, a player who does not employ techniques that rely on a unique solution has the advantage. At some point, there are no further deductions that can be made, and the puzzle cannot be solved completely. A player who uses uniqueness-based techniques may draw the wrong conclusion from certain patterns, either resulting in a contradiction or the discovery of only one of the possible solutions.

Computer Programs

When the contradiction is directly caused by two or more givens for the same digit in a single house, most Sudoku Programs will not accept the puzzle. Programs which automatically verify each puzzle will also refuse puzzles that do not have a solution. Most programs will issue a warning when you load a puzzle that has multiple solutions.

This page was last modified 17:44, 7 November 2006.  

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