Sudoku Variants Series (408) - Greater grey consecutives
(Published on 24. January 2025, 12:00 by Richard)
Logic solvable
Greater grey consecutives
Inspiration for this type comes from Abdul the Killer.
Solve online in Penpa+ or in Sudokupad.
Like all of my sudoku variants, this puzzle can be solved by logic alone. Guessing is not required and also no sophisticated solving techniques are necessary; just plain and easy sudoku steps and of course the intrinsic logic this specific variant has to offer. In case you don't find that logic or get stuck, feel free to ask for a hint in the comments below this puzzle and I'll be happy to help you.
Apply classic sudoku rules.
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, and otherwise unshaded.
Solution code: Column 9.
Comments
on 26. January 2025, 07:34 by Richard
Added instructions to German text too.
on 25. January 2025, 13:02 by WildEnte
lovely!
on 25. January 2025, 12:34 by nunc
I always loved the ATK puzzles, and love this one too. Thanks for sharing.
on 25. January 2025, 09:17 by galium_odoratum
As an ATK enjoyer I am happy that there are now others puzzles with this ruleset thank you for setting!
on 25. January 2025, 04:54 by 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! :-)
on 25. January 2025, 04:44 by Richard
Completed the rules based on players comments.
on 25. January 2025, 00:45 by 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.
on 25. January 2025, 00:11 by 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.
on 24. January 2025, 23:08 by 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
on 24. January 2025, 14:52 by Piatato
Neat!
on 24. January 2025, 13:40 by 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.
---
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.
————-
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”.
---
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!
