Sudoku Puzzle -- Boxout Pattern

by Ed GLysson
(Morgan Hill, CA)

Sudoku Puzzle -- Boxout Pattern


A true Sudoku Puzzle must be resolvable to only one solution. A Boxout Pattern is a Sudoku Puzzle condition to be avoided as it results in the possibility of two solutions.

A Boxout Pattern is generally only observed in the more challenging Sudoku Puzzles.

First let's examine the attachment "Sudoku Puzzle – Boxout Fragment".

Observe the Space entries that can only possibly contain a 1 or a 9. These are 15, 16, 78, and 79. (Refer to my other article “Sudoku Square and Space Notation” for a description on how I reference Belts, Curtains, Squares, and Spaces within a Sudoku puzzle.) Notice that the four Spaces identified form the shape of a box with one of each subject Space residing in a corner. For proper identification of the Boxout Pattern it is necessary that the Spaces line up in the same rows and columns within one Belt or Curtain.

Notice that if Space 79 were to contain a 19, then a pattern would be created where there would no possiblity of resolving which two Spaces were a 1 and which two were a 9. This means the puzzle would have 2 possible solutions and therefore would be invalid.

The only way for this puzzle to remain valid (one solution) is for Space 79 not to resolve from a 159 to a 19. This means that Spaces 43, 71, and 88 cannot contain a 5.

Let's continue to look at this example in the attachment "Sudoku Puzzle – Boxout Example".

So here we can observe the Fragment we just examined, now within the context of the full puzzle.

The black entries are the start of the Puzzle and the blue entries have been entered by the puzzler. A Space with multiple blue entries identifies the possibilities for that Space. If the blue entry does not have a dash (-) in front of it, then the entries identified are the only possibilities for that Space. If there is a dash (-) in front of a blue entry then what is indicated is that all of the possibilities have not been listed for that Space.

In order to maintain a valid puzzle (a puzzle that has only one solution) Spaces 15, 16, 78, and 79 cannot all contain 19. If they did there would be no way of resolving which two were the 1's and which two were the 9's. This means that none of the Spaces 43, 71, or 88 can resolve to a 5. So Spaces 43 and 71 must resolve to an 8; and Space 88 must resolve to contain either 6 or 7.

Check out the attachment "Sudoku Puzzle – Boxout – Three Fragment Examples" to see other examples of Boxout Patterns. The examples provided here are all in the Belt perspective but are just as valid from the Curtain perspective. A Boxout Pattern will only be found in either a single Belt or a single Curtain; i.e. It will not overlap across Belts or Curtains.

In Summary:

A Boxout Pattern condition creates an unresolvable Sudoku Puzzle and therefore must be avoided. Identify a Boxout Pattern by looking for four Spaces that form a box within a Belt or Curtain that can possibly contain the same two possible entries. Look for a resolution which will avoid the Boxout Pattern.


Ed Glysson
Morgan Hill, CA. Summer 2016

Attachments:
Sudoku Puzzle – Boxout Fragment
Sudoku Puzzle – Boxout Example
Sudoku Puzzle – Boxout – Three Fragment Examples

References:
Article “Sudoku Square and Space Notation”

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