127.0.0.1: Created page with "In a 9 by 9 sudoku, a '''Reverse BUG''' is a state of the grid where every solved cell of two particular digits form an unavoidable set of less than 18 cel..."

2021-10-25T13:34:29Z

Created page with "In a 9 by 9 sudoku, a '''Reverse BUG''' is a state of the grid where every solved cell of two particular digits form an unavoidable set of less than 18 cel..."

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In a 9 by 9 [[sudoku]], a '''Reverse BUG''' is a state of the [[grid]] where every solved [[cell]] of two particular [[digit]]s form an [[unavoidable set]] of less than 18 cells, without the presence of [[Hidden Single|hidden singles]].

If we assume that a [[valid]] sudoku must contain a [[Uniqueness Controversy|unique]] solution, then a Reverse BUG cannot occur. Thus, as a [[solving technique]], we can [[eliminate]] [[candidate]]s from [[cell]]s that cause a Reverse BUG to appear.

== Proof ==

For any two [[digit]]s, we have an [[unavoidable set]] of 2''n'' cells involving these two digits if and only if these cells occupy exactly ''n'' [[row]]s, ''n'' [[column]]s, and ''n'' [[box]]es. Suppose we have a Reverse BUG of 2''n'' cells with ''n'' < 9, then we have an unavoidable set occupying ''n'' rows, ''n'' columns, and ''n'' boxes. Now, the remaining 9 - ''n'' rows, 9 - ''n'' columns, and 9 - ''n'' boxes will contain another unavoidable set of 18 - 2''n'' cells. As this latter unavoidable set contains no [[given|placements]], it is a [[deadly pattern]] which implies that this sudoku puzzle does not have a unique solution. Therefore, a Reverse BUG cannot occur in a valid sudoku puzzle.

== Example ==

This example is taken from the [http://www.sudoku.com/boards/viewtopic.php?t=4431 at Sudoku Players' forums].

*-----------------------------------------------------------*
| 189 7 -18 |*2 4 5 | 3 19 6 |
| 6 3 *2 |*1 8 9 | 4 5 7 |
| 19 5 4 | 3 7 6 | 129 129 8 |
|-------------------+-------------------+-------------------|
| 1238 1289 1378 | 5 6 12 | 129 78 4 |
| 124 1249 6 | 8 12 7 | 5 1239 39 |
| 5 128 178 | 9 3 4 | 6 78 12 |
|-------------------+-------------------+-------------------|
| 7 128 138 | 6 5 12 | 1289 4 39 |
| 123 6 9 | 4 12 8 | 7 123 5 |
| 1248 1248 5 | 7 9 3 | 128 6 12 |
*-----------------------------------------------------------*

If R1C3 = 1, then R12C34 forms a Reverse BUG on the digits 1 and 2. Therefore, 1 can be [[eliminate]]d from R1C3.

== Reference ==

* [http://www.sudoku.com/boards/viewtopic.php?t=4431 ''The Reverse-BUG'' at Sudoku Players' forums]

== See Also ==

* [[Bivalue Universal Grave|BUG]]
* [[Reverse BUG Lite]]

[[Category:Uniqueness]]
[[Category:Solving Techniques]]

Reverse BUG - Revision history

127.0.0.1: Created page with "In a 9 by 9 sudoku, a '''Reverse BUG''' is a state of the grid where every solved cell of two particular digits form an unavoidable set of less than 18 cel..."