Advanced methods and approaches for solving Sudoku puzzles
Jeff wrote:Thanks Nick, excellent technique. Your post describe the computer algorithm for the advanced colouring technique. I am more interested in how this technique can be applied at a manual level.

In exactly the same way.
Nick70

Posts: 156
Joined: 16 June 2005

Sorry this is not on the subject but it's bothering me - what happened to Nick68 and Nick69?
emm

Posts: 987
Joined: 02 July 2005

Is he related to the sagacious IQ family (PaulIQ etc)?

stuartn
stuartn

Posts: 211
Joined: 18 June 2005

em wrote:Sorry this is not on the subject but it's bothering me - what happened to Nick68 and Nick69?

I just tacked on my birth year to my name ... maybe Nick70
did likewise ... if so that's frustrating, because then I'm 3 years
older, but he's 3 times better at Sudoku!

Jeff wrote:
Code: Select all
`7     58    1    |     2     3     9    |    6     4    586     38    2    |     1     4     5    |    389   89   735    4     9    |     8     6     7    |    23    1    25----------------------------------------------------------4     123  38    |     369   5    136   |    289   7    289      B                           AGF9     235  357   |     37    8    34    |    24    6    1 18    6    78    |     79    2    14    |    489   5    3AB----------------------------------------------------------35    9    356   |     36    1    8     |    7     2    4128  13    368   |     4     7    236   |    5     389  89BCK                               DIE28   7     4     |     5     9    23    |    1     38   6`

Nice work! Few questions to clear my mind.

I realize now that I've got a ways to go before I fully
understand supercoloring. So, please don't take

Is it essential to label non-conjugate candidates such as the 3s in r4c6 and r8c6?

Here, I think it was not essential. In general, I think
it is important to label some non-conjugate candidates.
Is there a way (or is there a need) to distinguish non-conjugate from conjugate candidates?

Nick70's algorithm seems to imply that
it is useful to distinguish the 2 types of candidates.
But, when you are using supercoloring manually,
I'm not sure that it's necessary.
Can elimination be observed without outlining the proofs and what will be the process going through your mind?

I believe the proofs following the coloring are necessary.
One way to look at it: when you create the color table,
you do it by considering relationships between pairs of cells.
When you write the proofs, you are combining these relationships.

Nick70 wrote:
Jeff wrote:Thanks Nick, excellent technique. Your post describe the computer algorithm for the advanced colouring technique. I am more interested in how this technique can be applied at a manual level.

In exactly the same way.

I too am very intrigued about manual supercoloring.
I have these questions:

- When is the right time to use this technique?

- Is there a shorcut version of the algorithm? (Some of
Nick70's posts suggest this. The proofs following the
color tables in these posts are short.)

- Are there any "tricks" for writing the exclusion (or implication) proofs after creating the color table? It seems difficult to spot a "proof goal"
from the color table right away.
Nick67

Posts: 113
Joined: 24 August 2007

[quote="Nick67I'm 3 years older, but he's 3 times better at Sudoku!.[/quote]

I wouldn't have said three times better, old Nick, and anyway you sound way more intelligent than most 48yr olds I know and ponder this - young Nick might actually be a grey-bearded septuagenarian whose brain will soon be going into reverse which means you will actually be passing him somewhere around 2020!
emm

Posts: 987
Joined: 02 July 2005

em wrote:...and anyway you sound way more intelligent than most 48yr olds I know...

Thanks Em! I'll keep tryin' ...
Nick67

Posts: 113
Joined: 24 August 2007

With all of the pair cells and numbers with only two possible patterns, this solves very easily using the Pattern Overlay Method (POM explained here). Start with your 6 possible solution patterns for the number 2. Merge in the pair of patterns for fives using r3c9 as your equation cell. Cell r5c2 will indicate two repeated invalid patterns. Eliminate those patterns and you remove 2 as a possibility in cell r4c7. Keep the resulting grid and merge in four's pair of patterns using equation cell r5c7. Keep the result and merge in one's pair of patterns using equation cell r6c6. Cell r4c2 will contain 2 more invalidated repeat patterns which not only solves for most of the twos, but also, using your pattern equations, solves for all of your ones, fours, and fives as well. This puzzle is a good one for practicing the POM merging technique for successive merges.

Cheers
Myth Jellies

Posts: 593
Joined: 19 September 2005

Myth Jellies wrote:This puzzle is a good one for practicing the POM merging technique for successive merges

With your endorsement, I will definitely try out your POM on this puzzle.

BTW, what do you think about the advanced colouring trechnique? Is it in some way resemble your POM?

If you want to try more puzzles that have been pronounced logical unsolvable, I have a few to share.
Jeff

Posts: 708
Joined: 01 August 2005

em wrote:...and anyway you sound way more intelligent than most 48yr olds I know...

Sorry, I know I've not being paying attention so may have missed something sarcastic/ironic/sardonic, but wouldn't being born in '67 actually make him 38, or at most 39? I only ask 'coz I was born in '71 and I'm fairly sure I'm 33. Unless something really weird and Gregorian happened between '67 and '71. Any Old people care to enlighten me?
Karyobin

Posts: 396
Joined: 18 June 2005

Haven't you got enough puzzles to do, little Watchdog? Everyone is perfectly capable of recognising my mistakes all on their own without having them blasted all over the place by the Scrutineer of Public Arithmetic. Didn’t you read what I said about private whippings only? Actually, I don't think Old Nick did notice all by himself - unless HE was too polite to say (unlike some people) or else he's not quite sure how to take me (most likely).

PS : You’re not missing all that big-red-pen-school-teacher-stuff by any chance, are you?
emm

Posts: 987
Joined: 02 July 2005

Nope. Gonna PM you for that.

(Public bollockings, cool. Think I could get into this BDSM stuff.)
Karyobin

Posts: 396
Joined: 18 June 2005

I always suspected school teachers might like to feel the other end of the ruler!
emm

Posts: 987
Joined: 02 July 2005

Jeff,

I'm not sure if I understand the super-color method completely, but it looks like, in essence, it assigns a color to a specific set of solution patterns and another color to the negation of that set of solution patterns. It then follows the implications of those assertions about looking for crashes from which it can remove possibilities? POM looks for and applies substitution equations whereby you can equate the solution patterns for one number to the solution patterns for another number. After the substitution, it then looks for crashes from which it can remove the invalidated patterns and, potentially, remove number possibilities from the grid. They do appear to have some similarities.
Myth Jellies

Posts: 593
Joined: 19 September 2005

Previous