Wrap Around
(Eingestellt am 13. Juli 2024, 21:56 Uhr von Toomas_)
Sudoku:
Place the digits 1-9 in each row, column, and 3x3 box.
Mod 9 Kropki dots:
NOTE: When I write "a ≡ b (mod 9)", this means "a mod 9 = b mod 9".
We say that two digits are "consecutive mod 9" if one of them is one more than the other, modulo 9.
More rigorously, the digits x and y are called "consecutive mod 9" if x ≡ y+1 (mod 9) or y ≡ x+1 (mod 9).
For example, 9 and 1 are "consecutive mod 9" because 9+1 = 10 ≡ 1 (mod 9).
We say that two digits have a "2:1 ratio mod 9" if one of them is double the other, mod 9.
More rigorously, the digits x and y are said to have a "2:1 ratio mod 9" if x ≡ 2*y (mod 9) or y ≡ 2*x (mod 9).
For example, 5 and 7 have a "2:1 ratio mod 9" because 2*7 = 14 ≡ 5 (mod 9).
Two digits separated by a grey dot are "consecutive mod 9" AND have a "2:1 ratio mod 9".
Two digits separated by a white dot are "consecutive mod 9" but DON'T have a "2:1 ratio mod 9".
Two digits separated by a black dot have a "2:1 ratio mod 9" but AREN'T "consecutive mod 9".
For example, 7 and 8 can't be separated by a white dot or a black dot, because they are both "consecutive mod 9" and have a "2:1 ratio mod"; in particular, 8 ≡ 7 + 1 (mod 9) and 2*8 = 16 ≡ 7 (mod 9).
If two dots outside the grid surround a column, then the top and bottom cells of that column are considered to be separated by that dot. Similarly, two dots outside the grid surrounding a row indicate that the left-most and right-most cells of that row are separated by that dot. For example, the pair of black dots surrounding row 3 indicate that R3C1 and R3C9 have a "2:1 ratio mod 9" but aren't "consecutive mod 9".
Not all dots are necessarily given.
Play the puzzle here: SudokuPad
As an aside, the minimum number of given digits for a puzzle with this ruleset is 1.
There's a nice trick to see this.. I might base a future puzzle off it ;)
Lösungscode: Row 8, left to right.
Kommentare
am 16. Juli 2024, 18:47 Uhr von Toomas_
Attempt #2 at fixing the formatting..
am 16. Juli 2024, 18:43 Uhr von Toomas_
Attempted to fix HTML formatting
am 16. Juli 2024, 18:40 Uhr von Toomas_
* Corrected a mistake in the puzzle -- thanks sanabas for finding it and suggesting fixes.
* Clarified the ruleset.
am 15. Juli 2024, 15:40 Uhr von sanabas
The rules aren't very clear, unfortunately. (7)mod9 is identical to (-2)mod9, but that doesn't mean that (7)mod9 = -2. That is what the rules are meant to convey though.
So grey dots are either a 12 pair, or a 78 pair (because -1 and -2 are consecutive and in a 1:2 ratio). Black dots can have the ordinary 24, 48, 36 pairs, but they can also have 75 (as -2 & -4) or 51 (as -4 & -8). White dots can have the normal pairs, excluding 12 and 78, and can also be 19.
So after figuring that out, the puzzle solves ok, just one spot that requires a longish look ahead to work out which set of gray dots are 78 and which are 12. The edge of grid dots are a nice novelty, but only use normal logic, just maybe a little tougher to scan and notice there's a deduction.
Then we reach the final deadly pattern and need to use the final white dot to disambiguate things. Unfortunately, that white dot has a 78 on it, which the rules say isn't allowed, because that is -1 & -2.
If we're allowed to just pick which version to use, say 78 are sometimes -1 & -2 (as on the gray dots) but then 78 when it suits us, then we could equally choose to have 12 on a white dot by saying that's actually -7 and -8. And excluding a 12 option on a white dot was part of the early solve.
That problem with the final clue could be avoided by removing the white dot, and adding a black dot to either a 48 or 36 pair in the same area.
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Hi sanabas, thanks so much for your constructive feedback - I really appreciate it!
I will try my best to update the rules to make it clearer. There was a previous comment which I replied to where I explained what a = b (mod 9) means, but unfortunately it seems they deleted the whole comment afterwards :(
For deducing which grey pairs are 1/2 and which are 7/8, I'll just say that no look-ahead was intented - the logic turns out quite similar to some used in XV Sudokus.
I'm very sorry about the white dot mistake - I completely overlooked it! Thanks for your suggestion as well, I will use it.
Great job finishing the solve despite the everything!
Cheers,
Toomas_
