This is likely a niche topic for puzzle setters, but due to the nature of the sudoku variant I created (Cloku), I've become a collector of sudokus and (mainly) X sudokus with more than one solution because my variant uses a different type of clue to disambiguate between boards with multiple solutions. After finding one board which had a cell with 7 candidates in it and 7 solutions, I became somewhat obsessed with pushing higher, and have now gotten fairly adept at finding boards with 9 candidates in a cell and 9 solutions. Hopefully, it's obvious that these puzzle boards have to have two or more candidates in multiple other cells in order to limit them to precisely 9 solutions. So far, I haven't managed to create one with only one or two candidates in each cell besides the one with 9 clues, but have come within a few cells of that goal, so it may be possible. Anyway, for those who are interested, here are a couple of examples of the 9 solutions for X sudoku boards which I've found:
412385976937246815586791243258167439673954182194832567869513724745628391321479658 1
432795816916348725587261943258617439673954281194832567861529374745183692329476158 2
137985246986742315524361879792614538643857921851293467219536784475128693368479152 3
172435986834692175596871243781264539643957821259318467368549712415723698927186354 4
827365149936741528514289673752694831643817952189532467268953714475128396391476285 5
134985276987246315562731849751692438643857921298413567819364752475128693326579184 6
431285976962743815587691243258167439673954182194832567819576324745328691326419768 7
471835926839642175526871843287164539693257481154398267362589714715423698948716352 8
147985326936742815258361479724619538683257941519834267862193754471528693395476182 9
786195423349726185512384679127869534693457218854231967961578342275643891438912756 1
187294356946735128532861479758619234623457981419328567261983745375146892894572613 2
187394256946725138532861479758619324623457981419238567261983745375146892894572613 3
917485236846327195532169478789613524623754981451298367268531749375946812194872653 4
786591423349726185512384679827169534693457218154238967961875342275643891438912756 5
738615429946327185512489673127863594693754218854291367361578942275946831489132756 6
914785236876324195532169748789613524623457981451298367268531479345976812197842653 7
137894256946725138582361479758619324623457981419238567261983745375146892894572613 8
137984256946725138582361479758619324623457981419238567261893745375146892894572613 9
I managed to get a board with only singles and pairs as clues with nine solutions and nine numbers in a cell.
#4 and #9 (with #2), #1 and #7 (with #5), and #3 and #8 are the most similar, with #6 being less similar to the others.
637584129914263578528179643745391862283647951196852437862935714451728396379416285 1
627385149438719562591264873954837621273641958186592437862953714715428396349176285 2
487265139936817542251349678745691823623784951198532467862953714574128396319476285 3
637285149948713562251469873795834621423671958186592437862957314514328796379146285 4
657384129934261578218579643726495831483617952195832467862953714541728396379146285 5
632594178487213569591687243976435821243871956158962437864759312715328694329146785 6
637584129914263578528719643475391862283647951196852437862935714751428396349176285 7
487365129936217548251849673745691832623784951198532467862953714574128396319476285 8
637485129948217563251963874795834612423671958186592437862759341514328796379146285 9
#4 and #9 (with #2), #1 and #7 (with #5), and #3 and #8 are the most similar, with #6 being less similar to the others.
637584129914263578528179643745391862283647951196852437862935714451728396379416285 1
627385149438719562591264873954837621273641958186592437862953714715428396349176285 2
487265139936817542251349678745691823623784951198532467862953714574128396319476285 3
637285149948713562251469873795834621423671958186592437862957314514328796379146285 4
657384129934261578218579643726495831483617952195832467862953714541728396379146285 5
632594178487213569591687243976435821243871956158962437864759312715328694329146785 6
637584129914263578528719643475391862283647951196852437862935714751428396349176285 7
487365129936217548251849673745691832623784951198532467862953714574128396319476285 8
637485129948217563251963874795834612423671958186592437862759341514328796379146285 9
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Wouldn't it make more sense to share the original puzzles? We can't really tell what they looked like with just the solution grid. In Sudoku it's standard to replace empty cells with either 0 or ., for example:
98.7.....7.6...8...5.......4..8..9......5..3......2..1..74..6......1..5......3..2
A puzzle with 9 candidates in a cell that can be solved with any one of those candidates sounds quite novel.
98.7.....7.6...8...5.......4..8..9......5..3......2..1..74..6......1..5......3..2
A puzzle with 9 candidates in a cell that can be solved with any one of those candidates sounds quite novel.
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The grids are fairly complex to annotate traditionally, because until my most recent one anyway, some cells would have things like 1267 in them to narrow down the choices. Now, I have it narrowed down to only single and double clues, which makes it a bit more tractable. Here's a link for the one with only singles and pairs as clues, as shown by the sudokumaker app: https://sudokumaker.app/?puzzle=N4IgZg9 ... 4XjMYfcYgAbilla wrote:Wouldn't it make more sense to share the original puzzles? We can't really tell what they looked like with just the solution grid. In Sudoku it's standard to replace empty cells with either 0 or ., for example:
98.7.....7.6...8...5.......4..8..9......5..3......2..1..74..6......1..5......3..2
A puzzle with 9 candidates in a cell that can be solved with any one of those candidates sounds quite novel.
My next step is to work towards one which is logically solvable without trial and error methods, which I think I can do with disambiguating clues between the solutions, but I haven't got a version of that completed yet.