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 Post subject: Triankle Killer 2
PostPosted: Tue Oct 08, 2019 10:50 am 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 590
Triankle Killer 2

Please do the vanilla version (V3) first so as to understand the rules (I will answer any questions).
K1 should come next as it is under 1.0 whereas this one is almost an Assassin.

To me this structure works better as a killer. Semi-symmetric works well with it and also fits better as a killer. Hence I will continue producing them on that basis.

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.
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.

There is one cage which can repeat.


Image


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 Post subject: Re: Triankle Killer 2
PostPosted: Thu Oct 31, 2019 10:11 pm 
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Master
Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 199
Location: California, out of London
Phew! Very tough. I ended up with multiple solutions (based on an what may have been an initial faulty premise which luckily worked out) which I could only resolve into one solution using the "Each of the other eight numbers is absent in one and only one nonet" rule. (Edit: Third line fixed)
Solution (I think - I hope):
Code:
     1
    394
   57082
  4908631
 930521876
67812494053
25049131876
 678430529
  1267594
   38570
    162
     4


Pairs [05][14][23][69][78]


Last edited by wellbeback on Mon Nov 04, 2019 9:12 pm, edited 1 time in total.

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 Post subject: Re: Triankle Killer 2
PostPosted: Sun Nov 03, 2019 2:30 pm 
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Grand Master
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Joined: Wed Apr 30, 2008 9:45 pm
Posts: 590
wellbeback

You are correct although you have a typo 3 in the third line.

Did you use the opposite absent pair implication?

Would you care to put a rating number on it?

Maurice


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 Post subject: Re: Triankle Killer 2
PostPosted: Mon Nov 04, 2019 9:33 pm 
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Master
Master

Joined: Tue Jun 16, 2009 9:31 pm
Posts: 199
Location: California, out of London
Thanks for noticing the typo - solution has been edited.
I did not use the implication you mention. I hadn't thought of it!
Regarding a rating: Andrew & Ed have a very good method of rating puzzles based on the specific techniques used in their WTs. I am not as knowledgeable that way and, when asked, base a rating simply on how long it took me to solve. All the Triankles I have tried so far have taken me a looooong time. For example, it took me hours in Triankle 6 to get the 6(3) in c6 down to one set of numbers! Pretty much the only technique I've used so far is to postulate something, see what follows, and see if I get a contradiction. The efficacy of using standard techniques such as '45's and IODs is much reduced in Triankles.
Anyway, that means my rating for Triankle Killer 2 is a hard 1.5. Perhaps I will get better at them with more practice.


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 Post subject: Re: Triankle Killer 2
PostPosted: Tue Nov 05, 2019 8:33 pm 
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Grand Master
Grand Master

Joined: Wed Apr 30, 2008 9:45 pm
Posts: 590
My principle solution technique is building S-S contradiction tables (in Excel). Then doing eliminations between the tables. This takes me back to some of my KiMo puzzles.

I find the sum hint tool in http://www.atksolutions.com/flashgames.html Kakuro game avoids memory of combinations mistakes.

Given your view of difficulty I will not try for harder ones until people are used to them.


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