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

Solution

Possible solvepath:

on other forum:
www.dailysudoku.com/sudoku/forums/viewtopic.php?t=9153

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.

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]

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

------------<-----<<->---<------------------->-----<<----------->-----<-
>>-----------<---->--------<<<--->------------------------<-------------


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

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

Total rel count should be 144, should it not?

Yes you are correct !
I over counted the edges

Ri - relationships within a box = 9*12 = 108
Ro - relationships between boxes = 36

.
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)