## Greater than Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Greater than Sudoku

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

sobspaour@tapi.re

Posts: 1
Joined: 26 May 2022

### Re: Greater than Sudoku

Solution
Hidden Text: Show
Code: Select all
`587162934369754218214893756643918527175246389892375641956431872721589463438627195`

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.`
creint

Posts: 340
Joined: 20 January 2018

Pat

Posts: 3968
Joined: 18 July 2005

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.
1to9only

Posts: 4073
Joined: 04 April 2018

### Re: Greater than Sudoku

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]
coloin

Posts: 2219
Joined: 05 May 2005
Location: Devon

### Re: Greater than Sudoku

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
`------------<-----<<->---<------------------->-----<<----------->-----<->>-----------<---->--------<<<--->------------------------<-------------`

Mathimagics
2017 Supporter

Posts: 1901
Joined: 27 May 2015
Location: Canberra

### Re: Greater than Sudoku

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

Posts: 2219
Joined: 05 May 2005
Location: Devon

### Re: Greater than Sudoku

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

Total rel count should be 144, should it not?

Mathimagics
2017 Supporter

Posts: 1901
Joined: 27 May 2015
Location: Canberra

### Re: Greater than Sudoku

Yes you are correct !
I over counted the edges

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

Posts: 2219
Joined: 05 May 2005
Location: Devon

### Re: Greater than Sudoku

.
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)

Mathimagics
2017 Supporter

Posts: 1901
Joined: 27 May 2015
Location: Canberra