I Love Sudoku Coloring, but……

Before I get back to may “Nasty1” Series, I wanted to document my new found enjoyment of using Sudoku Coloring as an Advanced Technique.  I have been Using HoDoKu – v2.20 on my MacBook Pro and also on my Dell Studio 15 (Win7-64).    As usual I tend to jump in with both feet right up to my eye-balls!  So I started right in with 3D Medusa.   I think from what I can tell it is Chemistry Professor Bob Hanson  of St. Olaf’s College who named the technique 3D Medusa.

So I thought I had better back off and understand the simpler coloring schemes better.   And I have been using the HoDoKu random puzzles at the “unfair” and even “extreme” levels to test my proficiency on them. Probably from my many years as an electronics design engineer in the r&D world (little r & big D is intentional!) I am always looking to streamline the process.

In Sudoku this means I have been trying to find a few basic systematic ways to do the basic solving and then try to find one or two very sophisticated methods that would “short-cut’ the plethora of advanced techniques.   So I have been learning – mostly the hard way – and trying to find Sudoku Gurus to learn from.    So far I have been attracted to John Welch’s Systematic Sudoku – Human engineered Sudoku Solving site.  The key thoughts I liked:

1. Systematic
2. Human Engineered

After all I am an engineer – at least been claiming to be for the last 37 years or so.  Denis Berthier with his “Hidden Logic of Sudoku” book was my next big discovery.   I bought his book as a long term investment – which seems to be the opposite attitude that some had from Amazon reviews.   They claimed the book was TOO complex.   I usually have the opposite attitude.  Who wants a book that is “too easily” mastered?   Will that kind of book teach me much?   Anyway I digress.   Looks like my next guru may be Bob Hanson.

And this is mainly because I was hearing things like Nice Loops are Soduko’s “theory of everything”   Well I have not been convinced yet of that, but it did seem that “Chains” of some sort were as close to as a technique that would subsume all others as I was going to find.   The problem initially for me was chains seemed so awfully tedious and hard to interpret.  Then the Aha Moment – Coloring was not only colorful, but an appealing and effective way to visualize the effect of chains.    Well as I stepped back from my plunge into 3D Medusa,  I realized some simpler coloring might be useful to visualize some of the Bi-value and Bi-location patterns I was seeing after my basic solving had been exhausted.

Also with HoDoKu I figured out that the candidate coloring was the perfect tool for 3D Medusa (up to that point I had used candidate coloring simply in a forcing chain fashion or even – more honestly – to use as a rT&E method).

Of course if you are into colors then HoDokU has cell coloring which is perfect for the simple coloring and multicoloring of single digit patterns.   So if you ‘google’ Sudoku multicoloring the Suduko Snake site is one of the the first that comes up.  And right away there is this very colorful and attractive explanation of multicoloring that appealed to me right away!   The site explained Type 1 and Type 2 forms.   As usual in my “shoot from the hip” style I immediately thought I had this one down!

I have a saying – at least I invented it  independently from anyone else.   I would tell those interested in engineering that my observation was that the most “damning thing” in engineering was when something worked for all the wrong reasons because it lead you and others to all the wrong conclusions! And one day that will take a big chunk out of your posterior!

Well here is how I got bit:   I thought I totally understoof Type 1 multicoloring.  Here is the puzzle in linear-81 format:

..1.92..3..67…4..5………..23..6.4…..2.7..58………..1..9…83..6..24.8..

I took these steps where the number after the step# is the number highlight button I am pressing on the HoDoKu player.

01 3  r6c8=3bc
02 6  r6c2=6bc
03 2  r6c3=2br
04 3  n3b8r7 => b7r7<>3
05 5  n5b2r2 => b3r2<>5
06 7  n7b5r5 => b6r5<>7

Now I knew there were more simple steps I was missing.  I verified that via the Hint system.   However, I found subset analysis kind of tedious along with many of those “fishy things” And I was seeing some BV and BL (Bi-Location) patterns occurring that seemed perfect for simple chains and multicoloring.  So here is what the puzzle looked like after I put in those few basic clues…

Note:  I have in the digit 4 an orange chain color pair chain and a purple color pair chain.  And obviously just as Sudoku Snake says one of my purple colors sees one of the orange colors E.G.  n4r1c4 is orange and n4r4c4 is purple and then there is the n4r3c4 that is “sandwiched” in between so clearly I can do this:  r3c4<>4 right!  Indeed I can and HoDoKu seems to agree as I have all it warnings turned on and there is no warning!

Well just as Jupiter sometimes aligns with Mars for some obscure reason (at least in this point in the analysis 4 is a valid elimination here, but NOT for the reason I indicate!)

For two color clusters or “webs” as Sudoku Snake calls them to have a “bridge” between them there has to be a strong link somewhere between the orange cluster and the purple cluster.   Well guess what – just because the two cluster share a unit (or house) between them as you can clearly see in column 4 there is NOT a strong link there.  There is nothing that constrains the orange digit and the purple digit from both being false.  In fact r3c4=4 would do just that!   So when Sudoku Snake says:

In Type 1 Multi-Coloring, each color in each web has its counterpart in the other web. This means that at least one candidate in a web shares a unit with a candidate in the other web. Then, any candidate in the puzzle that shares a unit with both of the other colors can be eliminated.

You need to read that very closely – what it means is there MUST be a strong link between them.  One ‘sanity’ check you can do is to set the candidate you think you are excluding to true and see if the logic holds up – if NOT go read those conditions again and this time get all the nuances for they are critical!

Well as Bob Pease one said to me, “May all your problems be middle-sized” so you can find them!

Shalom.