Rooted: 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

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..."

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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:
* Relabel the 9 [[digit]]s
* Swap any 2 [[row]]s in a floor
* Swap any 2 [[column]]s in a tower
* Swap any 2 [[floor]]s
* Swap any 2 [[tower]]s
* Swap rows with columns (i.e. matrix transpose operation)

In other words, two [[Sudoku]] puzzles are '''mathematically equivalent''' if they have the same [[canonical form]].

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.

A [[symmetrical]] puzzle can be mathematically equivalent to an [[asymmetrical]] puzzle. From an aesthetic point of view, these puzzles are completely different.

== See Also ==
* [[Scramble]]
* [[canonical form|Canonicalize]]

Mathematically equivalent - Revision history

Rooted: 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..."