## Varient

Notes on possible new logic puzzles

### Varient

Yo people

I have this new varient and am unsure if it has been done before

It is inequality-sudoku

Below is an example.

It would be great if someone could brute force it to check that it is not valid without the inequalities being taken into consideration

Anyone like this varient[/img]
Last edited by Pi on Mon Apr 03, 2006 12:30 pm, edited 2 times in total.
Pi

Posts: 389
Joined: 27 May 2005

Reply no longer necessary, so have removed.

MCC
Last edited by MCC on Fri Apr 14, 2006 11:42 am, edited 1 time in total.
MCC

Posts: 1275
Joined: 08 June 2005

Pi,

I checked your puzzle and 77 cells can be solved with naked singles only, not using the inequalities.

Ruud.
Ruud

Posts: 664
Joined: 28 October 2005

Thanks, i am working on creating some more of these puzzles, hopefully with less clues, i assume that it should be possible to make some with less than 17 clues
Pi

Posts: 389
Joined: 27 May 2005

### Greater/Less Sudoku

Greater/Less Sudoku are not new you can find examples in
Ed Pegg Jr.'s article, in the rule paper of the 1st Sudoku World Championship (PDF) and on my sudoku variant page (look for Greater/Less Sudoku). There is also a similar puzzle type called Sudoku Chain.
Pyrrhon

Posts: 240
Joined: 26 April 2006

### Re: Varient

Pi wrote:It would be great if someone could brute force it to check that it is not valid without the inequalities being taken into consideration

You could keep just the one inequality between r9c4 & r9c5, and delete all the rest -- the puzzle would still have only one solution, and be very easy to solve. (But deleting them all would produce a puzzle with two solutions.)

Personally, I prefer the type of inequality puzzle in which all the digits are absent, and there are inequalities between adjacent cells within each box. Every completed number-grid converts of course to exactly one (possibly invalid) inequality puzzle of that type.

It might be interesting to try to make a variant of that kind, going one step further and deleting as many inequalities as possible -- with the intention of having a unique-solution puzzle with only blanks and a minimum number of inequalities.
r.e.s.

Posts: 337
Joined: 31 August 2005