Box Canonicalization of a Floor - Revision history

127.0.0.1: /* Steps to normalize a starting permutation */

2021-10-29T12:10:08Z

Steps to normalize a starting permutation

← Older revision		Revision as of 12:10, 29 October 2021
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	* Sort the [[column]]s in box 2 so that r1c4=4, r1c5 < r1c6		* Sort the [[column]]s in box 2 so that r1c4=4, r1c5 < r1c6
	* Sort the columns in box 3 so that r1c7 < r1c8 < r1c9.		* Sort the columns in box 3 so that r1c7 < r1c8 < r1c9.

			=== Notes ===

			There are a total of 36288 different configurations for a normalized floor, 416 of which are unique.

	== Compare results ==		== Compare results ==
	* The numbers to compare can be found in cells a-q below:		* The numbers to compare can be found in cells a-q below:

127.0.0.1 at 11:45, 26 October 2021

2021-10-26T11:45:22Z

← Older revision		Revision as of 11:45, 26 October 2021
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	* Of the 108 starting permutations, choose the one with the lowest numerical value		* Of the 108 starting permutations, choose the one with the lowest numerical value
	* For all possible configurations of the 27 numbers in a band, there are only 416 essentially different ones.		* For all possible configurations of the 27 numbers in a band, there are only 416 essentially different ones.
	~~== External Links ==~~
	~~[https://web.archive.org/web/20120918031713/http://www.setbb.com/phpbb/viewtopic.php?p=13455&mforum=sudoku#13455 Post by '''blue'''] in ''The Sudoku Programmers' Forum''~~

127.0.0.1 at 11:43, 26 October 2021

2021-10-26T11:43:59Z

← Older revision		Revision as of 11:43, 26 October 2021
Line 24:		Line 24:
	* Of the 108 starting permutations, choose the one with the lowest numerical value		* Of the 108 starting permutations, choose the one with the lowest numerical value
	* For all possible configurations of the 27 numbers in a band, there are only 416 essentially different ones.		* For all possible configurations of the 27 numbers in a band, there are only 416 essentially different ones.
			== External Links ==
			[https://web.archive.org/web/20120918031713/http://www.setbb.com/phpbb/viewtopic.php?p=13455&mforum=sudoku#13455 Post by '''blue'''] in ''The Sudoku Programmers' Forum''

127.0.0.1 at 11:41, 26 October 2021

2021-10-26T11:41:40Z

← Older revision		Revision as of 11:41, 26 October 2021
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	For a Sudoku grid with only [[given]]s a different algorithm is used, to account for missing [[digit]]s.		For a Sudoku grid with only [[given]]s a different algorithm is used, to account for missing [[digit]]s.
	== Steps to find all 36 starting permutations ==		== Steps to find all 108 starting permutations ==

			* Try each of the 3 [[box]]es as box 1. (3 permutations)
	* Permute the 3 [[row]]s. (6 permutations)		* Permute the 3 [[row]]s. (6 permutations)
	* Permute the 3 [[~~box~~]]es. (6 permutations)		* Permute the 3 [[column]]s in box 1. (6 permutations)
	*

	== Steps to normalize a starting permutation==		== Steps to normalize a starting permutation==
Line 17:		Line 17:
	* Sort the [[column]]s in box 2 so that r1c4=4, r1c5 < r1c6		* Sort the [[column]]s in box 2 so that r1c4=4, r1c5 < r1c6
	* Sort the columns in box 3 so that r1c7 < r1c8 < r1c9.		* Sort the columns in box 3 so that r1c7 < r1c8 < r1c9.
			== Compare results ==
			* The numbers to compare can be found in cells a-q below:
			1 2 3 \| 4 a b \| c d e
			4 5 6 \| f g h \| i j k
			7 8 9 \| l m n \| o p q
			* Of the 108 starting permutations, choose the one with the lowest numerical value
			* For all possible configurations of the 27 numbers in a band, there are only 416 essentially different ones.

127.0.0.1: Created page with "A band of 3 rows from a Sudoku solution grid can be modified to its minimum lexicographic equivalent. For a Sudoku grid with only givens a different algorit..."

2021-10-26T10:19:01Z

Created page with "A band of 3 rows from a Sudoku solution grid can be modified to its minimum lexicographic equivalent. For a Sudoku grid with only givens a different algorit..."

New page

A [[floor|band]] of 3 rows from a Sudoku solution [[grid]] can be modified to its minimum lexicographic equivalent.

For a Sudoku grid with only [[given]]s a different algorithm is used, to account for missing [[digit]]s.
== Steps to find all 36 starting permutations ==

* Permute the 3 [[row]]s. (6 permutations)
* Permute the 3 [[box]]es. (6 permutations)
*

== Steps to normalize a starting permutation==

* Relabel the numbers so that box 1 reads:
123
456
789
* Sort box 2 and 3 so that box 2 contains 4 in the top row.
* Sort the [[column]]s in box 2 so that r1c4=4, r1c5 < r1c6
* Sort the columns in box 3 so that r1c7 < r1c8 < r1c9.