Sudoku Variants Series (408) - Greater grey consecutives
(Eingestellt am 24. Januar 2025, 12:00 Uhr von Richard)
Logisch lösbar
Greater grey consecutives
Dieses Rätsel ist von Abdul the Killer inspiriert.
Solve online in Penpa+ or in Sudokupad.
Wie alle meine Sudoku-Varianten kann dieses Rätsel rein logisch gelöst werden. Raten ist nicht erforderlich, und es sind auch keine ausgefeilten Lösungstechniken nötig; es genügen einfache Sudoku-Schritte und natürlich die Logik, die diese spezielle Variante zu bieten hat. Falls du diese Logik nicht findest oder nicht weiterkommst, kannst du in den Kommentaren unter diesem Rätsel nach einem Tip fragen, und ich werde dir gerne helfen.
Verwende die üblichen Sudoku-Regeln.
Immer wenn zwei aufeinanderfolgende Ziffern in Feldern stehen, die sich orthogonal oder diagonal berühren und im gleichen 3x3-Block sind , ist das Kästchen mit der größeren der beiden Ziffern schattiert. Kästchen, für die das nicht zutrifft sind nicht schattiert.
Lösungscode: Spalte 9.
Kommentare
am 26. Januar 2025, 07:34 Uhr von Richard
Added instructions to German text too.
am 25. Januar 2025, 13:02 Uhr von WildEnte
lovely!
am 25. Januar 2025, 12:34 Uhr von nunc
I always loved the ATK puzzles, and love this one too. Thanks for sharing.
am 25. Januar 2025, 09:17 Uhr von galium_odoratum
As an ATK enjoyer I am happy that there are now others puzzles with this ruleset thank you for setting!
am 25. Januar 2025, 04:54 Uhr von Richard
Thanks for the comments to the puzzle. I have added the suggested extra words to the instruction.
My doubts about the addition are that
- a normal sudoku does not contain grey cells;
- in this case the sudoku does contain grey cells and they play an important role;
- one of my goals with writing sudokus is that players have fun with it;
- therefor it is not in my interest to add extra grey cells for no reason to confuse players, which would certainly take away some of the fun in solving.
But I don't have any problem with the addition too! :-)
am 25. Januar 2025, 04:44 Uhr von Richard
Completed the rules based on players comments.
am 25. Januar 2025, 00:45 Uhr von Lorena
@geronimo92 “In all cases where” does NOT mean if and only if. I’m reluctant to give you an example because you seem to have misunderstood my previous one entirely, but regardless:
“In all cases where there was illness, death followed”. That means illness implies death, but it does not mean death implies illness. There could very well be people who died of natural causes and the sentence would still hold true.
Let's break it down:
Statement A: Two consecutive digits are placed in cells that touch each other orthogonally or diagonally in the same box.
Statement B: The cell contains the greater digit of the two mentioned in Statement A.
Statement C: The cell is shaded.
The rules say A and B imply C. In a English, the addition of “in all cases” at the beginning of the sentence doesn’t change its logical meaning. If the rules had said “In all cases where a cell is shaded it it’s because [statements A and B]” then the implication would be reversed, but that wasn’t the case.
As the rules currently stand, there is absolutely nothing preventing ANY and ALL cells in the puzzle from being shaded, since the rule forces certain cells to be shaded but it doesn’t force any shells to be unshaded. Clearly, this is a hypothetical, since we can see not all cells in the puzzle are shaded. However, the fact that no cells are forced to be unshaded does impact the solve because (e.g) there is nothing preventing a 9 that doesn’t touch an 8 from being shaded. The rule says “if A and B then C”, but if A doesn’t happen at all, we cannot conclude anything about the state of C.
am 25. Januar 2025, 00:11 Uhr von Lorena
@Nylimb I’m really glad that my comment helped! I like how you expressed it, the shaded cells being “genuine”, that’s exactly what I meant.
am 24. Januar 2025, 23:08 Uhr von geronimo92
@Lorena : "in ALL cases where...." means exactly if and only if ! Furthermore every single cell cant be shaded in the puzzle and the reason why is trivial
am 24. Januar 2025, 14:52 Uhr von Piatato
Neat!
am 24. Januar 2025, 13:40 Uhr von Lorena
I had never encountered this ruleset and I really enjoyed it, thank you. It might be worth adding to the rules that otherwise, cells are unshaded, which was in the rules of the inspiration puzzle and is needed in order for this one to be solvable.
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Reply: thanks for the solve and your kind words! :-)
I don't think it's necessary mention the 'otherwise unshaded'-part since that is already captured by the negative constraint: 'ALL cases'. This means automatically that the constraint doesn't hold for unshaded cells.
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Indeed, the constraint doesn’t hold for unshaded cells. However, that doesn’t necessarily mean that all shaded cells have to be subjected to that constraint. I’ll give you an example: if every single cell in the puzzle were shaded, then it would still be true that “in all cases where two consecutive digits are placed in cells that touch each other orthogonally or diagonally in the same box the cell containing the greater digit of the two is shaded”. In all cases of X, Y happens is a one-directional implication that doesn’t necessarily mean that Y cant happen without X. For that, you would need and “if and only if” statement, which is what Abdul expressed with his “otherwise”.
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Thanks for pointing that out. It didn't even cross my mind that it is possible to have grey cells that don't have a lower consecutive neighbour attached to it, but the initial wording indeed doesn't rule that out. So I added your suggestion to the instruction text now. Thx!
