https://www.sudopedia.org/index.php?title=Mathematically_equivalent&feed=atom&action=historyMathematically equivalent - Revision history2022-08-13T06:43:16ZRevision history for this page on the wikiMediaWiki 1.34.1https://www.sudopedia.org/index.php?title=Mathematically_equivalent&diff=453&oldid=prevRooted: Created page with "Two Sudoku puzzles are '''mathematically equivalent''' if one can transform the first into the second via a series of zero or more operations, where the allowed operations..."2022-01-20T03:29:00Z<p>Created page with "Two <a href="/wiki/Sudoku" title="Sudoku">Sudoku</a> puzzles are '''mathematically equivalent''' if one can transform the first into the second via a series of zero or more operations, where the allowed operations..."</p>
<p><b>New page</b></p><div>Two [[Sudoku]] puzzles are '''mathematically equivalent''' if one can transform the first into the second via a series of zero or more operations, where the allowed operations are:<br />
* Relabel the 9 [[digit]]s<br />
* Swap any 2 [[row]]s in a floor<br />
* Swap any 2 [[column]]s in a tower<br />
* Swap any 2 [[floor]]s<br />
* Swap any 2 [[tower]]s<br />
* Swap rows with columns (i.e. matrix transpose operation)<br />
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In other words, two [[Sudoku]] puzzles are '''mathematically equivalent''' if they have the same [[canonical form]].<br />
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If a puzzle '''P''' can be solved using a set of [[solving technique]]s, then any puzzle that is mathematically equivalent to '''P''' can also be solved using the same set of solving techniques. However, [[Sudoku Programs]] may rate two mathematically equivalent puzzles slightly differently because a different [[solving path]] is used. When a program checks for patterns one [[digit]] at a time, relabeling the digits may cause the solver to find patterns of similar nature in a different order.<br />
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A [[symmetrical]] puzzle can be mathematically equivalent to an [[asymmetrical]] puzzle. From an aesthetic point of view, these puzzles are completely different.<br />
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== See Also ==<br />
* [[Scramble]]<br />
* [[canonical form|Canonicalize]]</div>Rooted