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 Post subject: Triankle Killer 11
PostPosted: Sat May 07, 2022 5:00 am 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 658
Triankle Killer 11

Hi All
I have just taken a job in Saudi Arabia where there is no alcohol. Hence I have significant free time, so I will be posting again.
I am currently creating Triankle 11 (not sure what happened to 8, 9, and 10), My four stage process is:
1. find a solution (not that easy) preferably with a balance between same symmetry and anti-symmetry;
2. apply the semi-symmetric pairing in JSudoku and create a killer that solves;
3. add cages so that the semi-symmetric pairs can be derived; then
4. solve the puzzle perhaps removing unnecessary cages.

I am at stage 2 on this one and realized that is is an easier puzzle in its own right, so I decided to post it as an introduction to Triankles.

I will post the full puzzle soon.

Rules
The numbers are from 0 to 9.
There are 8 triangular nonets covering twelve rows and 11 columns.
The two different 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.
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 (this is provable).


Triankle Killer 11 Given

The red numbers are missing from the nonet.
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


Last edited by HATMAN on Tue May 17, 2022 8:38 am, edited 2 times in total.

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 Post subject: Re: Triankle Killer 11
PostPosted: Tue May 17, 2022 8:25 am 
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Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 658
Triankle Killer 11 Full Puzzle

This is not too hard, but I like it because it is the first one where I discovered the pairs as I solved. In previous ones I derived the pairs first.
The 4/3 cage is in r5c56,r6c6 the 8/2 cage is in r5c67 and the 6/3 cage is in r6c567.

For an easy puzzle you can include the missing number clues above - if you have not done a Triankle before I recommend this approach.

Rules
The numbers are from 0 to 9.
There are 8 triangular nonets covering twelve rows and 11 columns.
The two different 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.
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 (this is provable).


Triankle Killer 11 Full Puzzle
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


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