Uniqueness - Revision history

Ryokousha: /* Computer-Generated Sudoku Puzzles */

2023-08-03T12:16:57Z

Computer-Generated Sudoku Puzzles

← Older revision		Revision as of 12:16, 3 August 2023
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	Computer-generated sudoku puzzles are common, especially for daily online puzzles and large puzzle packs. These puzzles are typically generated using computer algorithms and validated using computer solvers to ensure they adhere to a well-defined set of criteria, most importantly that they have a unique solution.		Computer-generated sudoku puzzles are common, especially for daily online puzzles and large puzzle packs. These puzzles are typically generated using computer algorithms and validated using computer solvers to ensure they adhere to a well-defined set of criteria, most importantly that they have a unique solution.

	The rating system of computer-generated sudoku puzzles might include Uniqueness Techniques (UT). In these cases, using these techniques could be considered advisable for solvers to experience the puzzle at the intended difficulty level. Refraining from using UT might unintentionally escalate the puzzle's complexity, making it seem more difficult than it was designed to be. I		The rating system of computer-generated sudoku puzzles might include Uniqueness Techniques (UT). In these cases, using these techniques could be considered advisable for solvers to experience the puzzle at the intended difficulty level. Refraining from using UT might unintentionally escalate the puzzle's complexity, making it seem more difficult than it was designed to be.

	== Summary ==		== Summary ==

Ryokousha: added section Computer-Generated Sudoku Puzzles

2023-08-03T12:16:03Z

added section Computer-Generated Sudoku Puzzles

← Older revision		Revision as of 12:16, 3 August 2023
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	In speed solving sudoku competitions, the use of UT is common. These events often feature thoroughly tested puzzles designed to have unique solutions, making the uniqueness assumption more justified. Additionally, the competitive nature of these events encourages solvers to use all available techniques, including UT, to achieve the fastest solving times.		In speed solving sudoku competitions, the use of UT is common. These events often feature thoroughly tested puzzles designed to have unique solutions, making the uniqueness assumption more justified. Additionally, the competitive nature of these events encourages solvers to use all available techniques, including UT, to achieve the fastest solving times.

			== Computer-Generated Sudoku Puzzles ==

			Computer-generated sudoku puzzles are common, especially for daily online puzzles and large puzzle packs. These puzzles are typically generated using computer algorithms and validated using computer solvers to ensure they adhere to a well-defined set of criteria, most importantly that they have a unique solution.

			The rating system of computer-generated sudoku puzzles might include Uniqueness Techniques (UT). In these cases, using these techniques could be considered advisable for solvers to experience the puzzle at the intended difficulty level. Refraining from using UT might unintentionally escalate the puzzle's complexity, making it seem more difficult than it was designed to be. I

	== Summary ==		== Summary ==

Ryokousha: /* The current puzzle has more than one solution */ BUG+1

2023-05-04T14:11:15Z

The current puzzle has more than one solution: BUG+1

← Older revision		Revision as of 14:11, 4 May 2023
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	::- Using the [[Unique Rectangle\|unique rectangle]] in red to eliminate 23 from r7c2 instead results in the conclusion 1r7c2, resolving the green rectangle, thereby leading to a different solution.		::- Using the [[Unique Rectangle\|unique rectangle]] in red to eliminate 23 from r7c2 instead results in the conclusion 1r7c2, resolving the green rectangle, thereby leading to a different solution.

	::- Using the [[Unique Rectangle\|unique rectangle]] in green to eliminate 1 and the [[Unique Rectangle\|unique rectangle]] in red to eliminate 3 from r7c2 results in the conclusion 2r7c2, giving a third solution.		::- Using the [[Unique Rectangle\|unique rectangle]] in green to eliminate 1 and the [[Unique Rectangle\|unique rectangle]] in red to eliminate 3 from r7c2 results in the conclusion 2r7c2, giving a third solution. Alternatively, [[BUG]]+1 can be applied to reach the same conclusion.

	::- Using both [[Unique Rectangle\|unique rectangles]] to eliminate the candidates 123 from r7c2 results in no solutions.		::- Using both [[Unique Rectangle\|unique rectangles]] to eliminate the candidates 123 from r7c2 results in no solutions.

Ryokousha: /* The current puzzle has more than one solution */ how to get 2r7c2 in Sam's example

2023-05-04T13:58:25Z

The current puzzle has more than one solution: how to get 2r7c2 in Sam's example

← Older revision		Revision as of 13:58, 4 May 2023
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	::- This grid does, in fact, have three valid solutions.		::- This grid does, in fact, have three valid solutions.

	::- However, using the [[Unique Rectangle\|unique rectangle]] in green results in the conclusion 3r7c2, resolving the red rectangle, leading to one specific solution.		::- However, using the [[Unique Rectangle\|unique rectangle]] in green to eliminate 12 from r7c2 results in the conclusion 3r7c2, resolving the red rectangle, leading to one specific solution.

	::- Using the [[Unique Rectangle\|unique rectangle]] in red instead results in the conclusion 1r7c2, resolving the green rectangle, thereby leading to a different solution.		::- Using the [[Unique Rectangle\|unique rectangle]] in red to eliminate 23 from r7c2 instead results in the conclusion 1r7c2, resolving the green rectangle, thereby leading to a different solution.

	::- Using ~~both~~ [[Unique Rectangle\|unique ~~rectangles~~]] ~~eliminates~~ the ~~candidates 12 and 23~~ from r7c2, ~~resulting in no solutions~~.		::- Using the [[Unique Rectangle\|unique rectangle]] in green to eliminate 1 and the [[Unique Rectangle\|unique rectangle]] in red to eliminate 3 from r7c2 results in the conclusion 2r7c2, giving a third solution.

	::- ~~The solution with 2r7c2 is not found applying these uniqueness techniques~~.		::- Using both [[Unique Rectangle\|unique rectangles]] to eliminate the candidates 123 from r7c2 results in no solutions.

	=== The current puzzle has exactly one solution ===		=== The current puzzle has exactly one solution ===

Ryokousha at 09:10, 24 April 2023

2023-04-24T09:10:15Z

← Older revision		Revision as of 09:10, 24 April 2023
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	== Summary ==		== Summary ==

	As a single-player game, sudoku allows solvers to employ any technique they prefer. However, it is essential to understand the logical assumptions underpinning UT to ensure their correct application in specific situations.		As a single-player game, sudoku allows solvers to employ any technique they prefer. However, it is essential to understand the logical assumptions underpinning [[Solving Techniques#Uniqueness Techniques\|Uniqueness Techniques]] (UT) to ensure their correct application in specific situations.

	Additionally, the appropriateness of using UT may vary depending on the social context and community. For instance, a puzzle setter may not desire solvers to bypass particularly elegant parts of a solution by applying UT.		Additionally, the appropriateness of using UT may vary depending on the social context and community. For instance, a puzzle setter may not desire solvers to bypass particularly elegant parts of a solution by applying UT.

Ryokousha: /* Speed Solving and Competitions */

2023-04-23T21:05:35Z

Speed Solving and Competitions

← Older revision		Revision as of 21:05, 23 April 2023
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	== Speed Solving and Competitions ==		== Speed Solving and Competitions ==

	In speed solving ~~and~~ sudoku competitions, the use of UT is common. These events often feature puzzles designed ~~with~~ unique solutions, making the uniqueness assumption more justified. Additionally, the competitive nature of these events encourages solvers to use all available techniques, including UT, to achieve the fastest solving times.		In speed solving sudoku competitions, the use of UT is common. These events often feature thoroughly tested puzzles designed to have unique solutions, making the uniqueness assumption more justified. Additionally, the competitive nature of these events encourages solvers to use all available techniques, including UT, to achieve the fastest solving times.

	== Summary ==		== Summary ==

Ryokousha: /* Uniqueness in Puzzle Setting */

2023-04-23T20:51:40Z

Uniqueness in Puzzle Setting

← Older revision		Revision as of 20:51, 23 April 2023
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	Uniqueness Techniques (UT) depend on the assumption that a puzzle has a single valid solution '''''at the time of application'''''. This premise often does not hold for incomplete puzzles during the incremental process of setting a puzzle. In such cases, applying UT leads to incorrect, or at best useless deductions, even if subsequent clue additions ultimately render the puzzle unique.		Uniqueness Techniques (UT) depend on the assumption that a puzzle has a single valid solution '''''at the time of application'''''. This premise often does not hold for incomplete puzzles during the incremental process of setting a puzzle. In such cases, applying UT leads to incorrect, or at best useless deductions, even if subsequent clue additions ultimately render the puzzle unique.

	Assuming we have determined whether a partial puzzle has a single or multiple solutions by accurately applying non-uniqueness techniques and/or using a computer solver to enumerate the solutions, the following non-mutually exclusive situations may occur:		Assuming we have determined whether a partial puzzle currently has a single or multiple solutions by accurately applying non-uniqueness techniques and/or using a computer solver to enumerate the solutions, the following non-mutually exclusive situations may occur:

	=== The current puzzle has more than one solution ===		=== The current puzzle has more than one solution ===

Ryokousha: /* The current puzzle has more than one solution */

2023-04-23T20:39:50Z

The current puzzle has more than one solution

← Older revision		Revision as of 20:39, 23 April 2023
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	; Applying Different UTs Leading to Different Solutions		; Applying Different UTs Leading to Different Solutions

	: There may be situations where multiple different uniqueness techniques can be applied to a non-unique puzzle, ~~resulting~~ in different solutions depending on which UT is used. It's also possible that applying multiple UTs simultaneously may lead to the conclusion that there are zero solutions. This further demonstrates the potential pitfalls of using UT during the puzzle-setting process, as it can introduce inconsistencies and inaccuracies.		: There may be situations where multiple different uniqueness techniques can seemingly be applied to a non-unique puzzle, but result in different solutions depending on which UT is used. It's also possible that applying multiple UTs simultaneously may lead to the conclusion that there are zero solutions. This further demonstrates the potential pitfalls of using UT during the puzzle-setting process, as it can introduce inconsistencies and inaccuracies.

	: [[File:Classic_Sudoku_17.png\|300px\|right\|link=MediaWiki\|frameless\|Contradictory uniqueness deductions]]		: [[File:Classic_Sudoku_17.png\|300px\|right\|link=MediaWiki\|frameless\|Contradictory uniqueness deductions]]

Ryokousha: /* The current puzzle has more than one solution */

2023-04-23T19:59:15Z

The current puzzle has more than one solution

← Older revision		Revision as of 19:59, 23 April 2023
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	; Applying a UT leads to zero solutions		; Applying a UT leads to zero solutions

	: Similar to the previous case, this contradiction confirms the puzzle is not unique.<br />We establish the implication <code>unique => no solutions</code>, but the consequence is not necessarily true since the premise is false.		: Similar to the previous case, this contradiction confirms the puzzle is not unique.<br />We establish the implication <code>unique => no solutions</code>, but the consequence is not necessarily true since the premise is false.<br />The contrapositive <code>one or more solutions exist => not unique</code> has a true premise, but yields information we already possessed.
	The contrapositive <code>one or more solutions exist => not unique</code> has a true premise, but yields information we already possessed.

	; Applying Different UTs Leading to Different Solutions		; Applying Different UTs Leading to Different Solutions

Ryokousha: /* The current puzzle has more than one solution */

2023-04-23T19:58:46Z

The current puzzle has more than one solution

← Older revision		Revision as of 19:58, 23 April 2023
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	; Applying a UT leads to zero solutions		; Applying a UT leads to zero solutions

	: Similar to the previous case, this contradiction confirms the puzzle is not unique~~, information we already possessed~~.<br />~~In analogy to the first case, we~~ establish the implication <code>unique => no solutions</code>, but the consequence is not true since the premise is false.		: Similar to the previous case, this contradiction confirms the puzzle is not unique.<br />We establish the implication <code>unique => no solutions</code>, but the consequence is not necessarily true since the premise is false.
			The contrapositive <code>one or more solutions exist => not unique</code> has a true premise, but yields information we already possessed.

	; Applying Different UTs Leading to Different Solutions		; Applying Different UTs Leading to Different Solutions

← Older revision		Revision as of 14:11, 4 May 2023
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	::- Using the [[Unique Rectangle\|unique rectangle]] in red to eliminate 23 from r7c2 instead results in the conclusion 1r7c2, resolving the green rectangle, thereby leading to a different solution.		::- Using the [[Unique Rectangle\|unique rectangle]] in red to eliminate 23 from r7c2 instead results in the conclusion 1r7c2, resolving the green rectangle, thereby leading to a different solution.

	::- Using the [[Unique Rectangle\|unique rectangle]] in green to eliminate 1 and the [[Unique Rectangle\|unique rectangle]] in red to eliminate 3 from r7c2 results in the conclusion 2r7c2, giving a third solution.		::- Using the [[Unique Rectangle\|unique rectangle]] in green to eliminate 1 and the [[Unique Rectangle\|unique rectangle]] in red to eliminate 3 from r7c2 results in the conclusion 2r7c2, giving a third solution. Alternatively, [[BUG]]+1 can be applied to reach the same conclusion.

	::- Using both [[Unique Rectangle\|unique rectangles]] to eliminate the candidates 123 from r7c2 results in no solutions.		::- Using both [[Unique Rectangle\|unique rectangles]] to eliminate the candidates 123 from r7c2 results in no solutions.