Greater than Sudoku

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Greater than Sudoku

Postby sobspaour@tapi.re » Thu May 26, 2022 3:09 pm

Can't seem to crack this greater Sudoku. Can you help me?

Image
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Re: Greater than Sudoku

Postby creint » Sun May 29, 2022 9:11 am

Solution
Hidden Text: Show
Code: Select all
587162934
369754218
214893756
643918527
175246389
892375641
956431872
721589463
438627195

Possible solvepath:
Hidden Text: Show
Code: Select all
Digits 1 and 9 can be found first. All digits 1 and 6 of 9. Next step is 2 and 8. Then 3 and 7.
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Postby Pat » Mon May 30, 2022 3:39 am

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Postby 1to9only » Mon May 30, 2022 7:04 am

If anyone is interested in similar clueless 'greater than' sudokus there are daily ones at https://puzzlemadness.co.uk/greaterthansudoku/.
Dont know if the OP posted is from that website.
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Re: Greater than Sudoku

Postby coloin » Mon May 30, 2022 10:55 am

Code: Select all
+---+---+---+
|587|162|493|
|369|754|821|
|214|893|675|
+---+---+---+
|643|918|752|
|175|246|938|
|892|375|164|
+---+---+---+
|956|431|287|
|721|589|346|
|438|627|519|
+---+---+---+


would this puzzle solution have a more difficult start [ no 1 or 9 in a middle cell]
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Re: Greater than Sudoku

Postby Mathimagics » Tue May 31, 2022 9:19 am

In 2016 there was a discussion of what I call Sudoshiki puzzles.

In the parlance that I suggested, the "clueless" puzzles mentioned above might be categorised as SI(N = 9, G = 0, R = 144).

For 9x9 Sudoshiki, with no givens (G = 0), then fully-specified puzzles, that is, when all relationships are specified (R = 72 + 72 = 144), uniqueness of solution is not necessarily guaranteed.

And from blue, we have this R = 19 puzzle, which has the lowest known R count:

Code: Select all
------------<-----<<->---<------------------->-----<<----------->-----<-
>>-----------<---->--------<<<--->------------------------<-------------
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Re: Greater than Sudoku

Postby coloin » Tue May 31, 2022 12:56 pm

Very good

Ri - relationships within a box = 9*12 = 108
Ro - relationships between boxes = 72

I can just about see that even with Ri at 108 there may well be multiple solutions ... row or column swaps do not usually preserve the puzzle
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Re: Greater than Sudoku

Postby Mathimagics » Tue May 31, 2022 1:16 pm

coloin wrote:Ri - relationships within a box = 9*12 = 108
Ro - relationships between boxes = 72

Total rel count should be 144, should it not? :?
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Re: Greater than Sudoku

Postby coloin » Tue May 31, 2022 3:50 pm

Yes you are correct !
I over counted the edges

Ri - relationships within a box = 9*12 = 108
Ro - relationships between boxes = 36
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Re: Greater than Sudoku

Postby Mathimagics » Wed Jun 01, 2022 5:02 pm

.
I have now checked the 19R puzzle given by blue which I quoted above, and it seems to be not valid, there are multiple solutions.

I will post details in the original thread, where he posted it (here)
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