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Triankle Sudoku
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Author:  HATMAN [ Thu Sep 26, 2019 5:58 pm ]
Post subject:  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. For clarity: the ten numbers from 0 to 9 are put in five pairs. Part of the solution process is to work out what these pairs are. Then to work out which of these pairs is the repeating one in r67c6.
If a cell contains a number the opposite cell must contain it or its partner.

These can be put together in JSudoku, see below.

Triankle Vanilla 3

Image

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
Save as your TRIANKLE BASE
Author:  azpaull [ Mon Oct 07, 2019 11:57 pm ]
Post subject:  Re: Triankle Sudoku
I :salute: your continued creativity! Will try this this week!
Author:  Andrew [ Tue Oct 29, 2019 8:21 pm ]
Post subject:  Re: Triankle Sudoku
HATMAN wrote:
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.
Since this puzzle uses the numbers 0 to 9, does that mean that the pairs are 0,9, 1,8, 2,7, 3,6 and 4,5? So that, if one cell of those five pairs of numbers contains, for example, 3 the other will contain 3 or 6?

You say "There are five pairs of numbers which are unknown." Does that mean that none of the given numbers is part of a semi-symmetric pair?
Author:  HATMAN [ Wed Oct 30, 2019 2:51 pm ]
Post subject:  Re: Triankle Sudoku
Andrew

For clarity: the ten numbers from 0 to 9 are put in five pairs. Part of the solution process is to work out what these pairs are.
Then to work out which of these pairs is the repeating one in r67c6.

Maurice
Author:  Andrew [ Wed Oct 30, 2019 6:29 pm ]
Post subject:  Re: Triankle Sudoku
HATMAN wrote:
For clarity: the ten numbers from 0 to 9 are put in five pairs. Part of the solution process is to work out what these pairs are.
Then to work out which of these pairs is the repeating one in r67c6.

Thanks for that! I think I understand that condition now, having also looked at SudokuSolver's solution (not steps) for Semi-Symmetric Killer 1 which I haven't yet tried.

All corresponding cells contain either one of the pairs of numbers or both contain the same number.

This is different from Rotational Symmetry which was used some years ago in udosuk's Assassin 123 "Roulette" and I think one or two other Assassins.
Author:  HATMAN [ Wed Oct 30, 2019 6:53 pm ]
Post subject:  Re: Triankle Sudoku
That was of course where I got the idea from. At the time I made some anti-symmetric puzzles but never found that it added any interest.

I've just been trying to do NC and Semi-Symmetric but even on a Latin Square I am not finding solutions.
Author:  Andrew [ Tue Nov 26, 2019 2:32 am ]
Post subject:  Re: Triankle Sudoku
As recommended in the Triankle Killer 2 post, I've tried Vanilla 3 first, now that I understand what the semi-symmetry rule means. It's very helpful.

My solving outline:
Numbers are 0 to 9.
The numbers in the grey cells repeat horizontally and vertically and are present in every nonet.
No repeats in any other rows or columns.
Each of the other numbers is missing from one and only one nonet.
Five pairs of unknown numbers are semi-symmetric, with the corresponding cell containing the same number or its partner.

7 missing from N7 -> all other nonets must contain 7

The only number in all cells corresponding to cells containing 7 is 2 -> 2,7 must be a pair
From semi-symmetry since 7 is missing from N7 -> 2 must be missing from N2

5 in N2 corresponds to 4 in N7 -> 4,5 must be a pair
From semi-symmetry since 5 is missing from N5 -> 4 must be missing from N4

Hidden single 4 in R6, 8 in N5 for R7

From N2 and N7, 3,6 must be a pair
6 missing from N6 -> 3 missing from N3

The only number in cells corresponding to cells containing 9 that do not contain 9 is 0 (since it cannot be paired with 6) -> 0,9 must be a pair

Remaining pair must be 1,8
1 missing from N1, 8 missing from N8

Solution:
Attachment:
Triankle Vanilla 3.jpg
Triankle Vanilla 3.jpg [ 38.36 KiB | Viewed 7748 times ]

Pairs: [2,7], [4,5], [3,6], [0,9] and [1,8]
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