## Triankle Sudoku

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Triankle Sudoku

I've been trying for a long time to get a workable 10 digit sudoku. 10 by 10 does not really work, I've come up with a couple of jigsaw structures that are OK but not fully satisfactory. This is my latest attempt which I think works, but I would welcome your views.

Triankle Sudoku rules:
The numbers are from 0 to 9.
There are 8 triangular nonets covering twelve rows and 11 columns.
The two numbers in the centre two grey cells repeat horizontally and vertically. I.e. in row six there are eleven numbers so nine different numbers with the grey number twice and row seven the same. In column 6 there are 12 numbers eight different numbers with the two grey numbers twice.
The other eight numbers do not repeat anywhere.
The repeating numbers are present in every nonet.
Each of the other eight numbers is absent in one and only one nonet.

Semi-symmetric is not an absolute necessity but given that it fits very well, I will be using it in all my early puzzles. So Semi-symmetric.
There are five pairs of numbers which are unknown.
If a cell contains a number the opposite cell must contain it or its partner.

These can be put together in JSudoku. If anyone wants guidance on how to do it I will post how.

Triankle Vanilla 3

If you wish to solve in JSudoku:
open as a 12 by 12 Latin Square from 0 - B
enter the eight nonets as killer cages with no sum (c, then choose operator "none")
select a cell in C6: ctrl right click select remove and then C6
select a cell in R6: ctrl right click select remove and then R6
select a cell in R7: ctrl right click select remove and then R6 (JS has renumbered the rows)
select all the nonet cells shift A then shift B to remove the A & B pencilmarks
do a set of solves to put A B in every cell around the diamond.
select r67c6 as a twin killer cage with no sum (twin killer is easier to see)
select r6 c1-5 & c7-11 as a twin killer cage 45/10
select r7 c1-5 & c7-11 as a twin killer cage 45/10
select r1-5&r8-12 c6 as a twin killer cage 45/10
Last edited by HATMAN on Tue Oct 15, 2019 3:01 pm, edited 2 times in total.
HATMAN

Posts: 272
Joined: 25 February 2006
Location: Nigeria

### Re: Triankle Sudoku

Well done on latest efforts. I haven't looked closely at your latest postings as my latest free sudoku related time has mainly focused on the sukaku explainer project.

tarek

Posts: 3748
Joined: 05 January 2006

### Re: Triankle Sudoku

Thanks tarek

Do you have any memory of semi-symmetric being discussed before?

Maurice
HATMAN

Posts: 272
Joined: 25 February 2006
Location: Nigeria

### Re: Triankle Sudoku

HATMAN wrote:Thanks tarek

Do you have any memory of semi-symmetric being discussed before?

Maurice
No not really. I trust you already looked at gurth’s Symmetric placement and any related threads as it is the only thing that comes to my mind when you mention “symmetric”. There had been some vanilla puzzles that were posted to demonstrate symmetry of solution grid but I never encountered the term “Semi symmetric before”

Tarek

tarek

Posts: 3748
Joined: 05 January 2006

### Re: Triankle Sudoku

OK I'll look those up again.
Given for 9by9 with nonets n5 is asymmetric, symmetry cannot be achieved, for a latin square might it be possible? Could the other eight nonets be symmetric - probably not.
10by10 with symmetric tenets can be symmetric - I've made some.
I played with asymmetric 9by9 but did not find that it made interesting puzzles.
HATMAN

Posts: 272
Joined: 25 February 2006
Location: Nigeria