## Multiple Coloring??

Advanced methods and approaches for solving Sudoku puzzles
yasmin wrote:1. Doesn't it matter which of the two conjugates I call "a" and which "A", which "b" and which "B" and so on?

No. Both colors (the upper and lower cases) alternately represent both true and false. We (usually) just don't know which yet.

Lummox JR wrote:Now in the basic form, you can do the following: 1) If the same color appears twice in a box/column/row, it is false and you can eliminate it. 2) If two conjugates intersect at another choice, eliminate it.

2. IN the final paragraph of the last reply, "eliminate IT" - does that mean eliminate the colour or the candidate?

There are two "eliminate IT" statements in that paragraph, and they are different.

For the first, it means ALL candidates on the grid having the "same color" may be eliminated, which effectively eliminates that color as well.

For the second, the candidate is not colored and is often said to "see" both conjugate colors. Since one or the other of those colors ultimately represents true, that ONE candidate cannot be true and may be eliminated. Of course, there may be several candidates that "see" both conjugate colors.

Ron
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

thanks Ron, that makes it clearer.

I have another question in this regard:

I'm trying to apply colouring to conjugate pairs and often find several smaller chains of conjugate pairs that don't automatically lead one to the other. I colour them separately using 2 different sets of colours (say, yellow and purple for one chain, orange and green for the other etc).

In the Sudokus I'm trying now, there doesn't seem to be any compulsive connection between the different chains (which pertain to the same number-candidate though). Is there a way to establish such a connection?

It seems to me that such a situation only opens up multiple possibilities that I can't conclusively solve in any way. In each chain, I don't know which is the false and which is the true, and it doesn't contradict itself in any way.

Is there a way to establish a forcing connection between such separate chains? or can't one say generally?

(Maybe I'll post my current problem-Sudoku for all to help - it's the first one I haven't managed to solve so far and it's really frustrating).
yasmin

Posts: 20
Joined: 24 February 2006

yasmin wrote:Is there a way to establish a forcing connection between such separate chains? or can't one say generally?

(Maybe I'll post my current problem-Sudoku for all to help - it's the first one I haven't managed to solve so far and it's really frustrating).

Try this link for starters. (Handle 'rkral' there is me. ) Don't let the A+, A-, B+ and B- labels there throw you. They're just another way of designating colors in lieu of A, a, B, and b.

A specfic example can't hurt.

Ron
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

yasmin wrote:
Is there a way to establish a forcing connection between such separate chains? or can't one say generally?

Here is a rule-of-thumb for multiple colouring ie one number, two different conjugate chains.

Label the two chains differently eg Aa and Bb

If two from different chains (say A and B) share a group they can’t both be true so either a or b or both a and b are true and any cell that shares a group with both a and b is false.

If A shares a group with both B and b (which are conjugates so one is true) then A is false. (vv with the others)
sweetbix

Posts: 58
Joined: 10 December 2005

Thanks for the cool explanation Sweetbix, I knew the logic somehow escaped me...
Ronk the link didn't open yet for some reason, I'll try later.
I'm still figuring out how to post real examples here.
yasmin

Posts: 20
Joined: 24 February 2006

yasmin wrote:Ronk the link didn't open yet for some reason, I'll try later.

That link at the Programmers' Forums worked for me just now. I stay logged on there and not sure what would happen if you weren't registered there.

Ron
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Hi,

Here is an example of a puzzle I got a bit stuck with, maybe it was just being tired (I'm expecting a baby really soon...).

Please try the link below and tell me if it works. The small coloured squares are for all different conjugates (the 6's are light blue), the larger colouring is for a chain of conjugate 6's.

Would you say that I can safely eliminate the 6 in c1r5?

Thanks for any other patterns you notice and which I may have missed.

Yasmin

http://www.yasminscreations.com/sudoku/sudoku.01.doc
yasmin

Posts: 20
Joined: 24 February 2006

yasmin wrote:Would you say that I can safely eliminate the 6 in c1r5?

Yes, you can. Pretend you're standing in c1r5. You're looking about, but your vision is restricted to the row, col, and 3x3 box in which you stand. As you look about, you list *all* the colors you see. If *any* pair in that list is a pair of conjugate colors ... you're eliminated.

This "seeing" thing works in reverse too ... kinda like simultaneously being in the sights of both the CIA and the KGB. One of them is going to be the big guy on the block (row, col, box) ... and there just won't be room for anyone else.

Ron

P.S. Your site worked AFAICT. A few suggestions though: 1) make the puzzle available in ASCII form too, so viewers can copy and paste the puzzle into other solvers, 2) avoid putting candidates on the grid with different layouts, and 3) reduce the size so the entire grid fits on the screen.

RE 1) All clues on one line in ASCII is fine, with either dots (periods) or zeroes for empty locations.
RE 2) The layout is sometimes all in a row, sometimes all in a column, and sometimes on a grid. If there's a reason for that, I didn't deduce it.
RE 3) IE6 users can use zoom to fit to a page, but it's not fun to have to switch back and forth as one browses. All JMO, of course.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Thanks for your helpful reply Ron. What's ASCII, is this the code many use here? If so, do you just type it that way in - say - word and then copy it in?

there was no good reason for the different layouts. It was my first trial and suffers from "1st pancake syndrome"... (usually gets burned or crumpled...), i.e. I tried both ways and couldn't decide which was best.

I'll try reducing the overall size, I too find it annoying to have to go back and forth.
yasmin

Posts: 20
Joined: 24 February 2006

yasmin wrote:Thanks for your helpful reply Ron. What's ASCII, is this the code many use here? If so, do you just type it that way in - say - word and then copy it in?

For this purpose, ASCII simply means plain text. Typically, an 81-character long string which represents a puzzle. This way it's easy to copy and paste to and from different solver programs. An example:
Code: Select all
`2.7..3.5....4.........9..8159.......8.62.54.....6......2.98...3....1..7..6.....4.`

which represents this puzzle:
Code: Select all
`+-------+-------+-------+| 2 . 7 | . . 3 | . 5 . | | . . . | 4 . . | . . . | | . . . | . 9 . | . 8 1 | +-------+-------+-------+| 5 9 . | . . . | . . . | | 8 . 6 | 2 . 5 | 4 . . | | . . . | 6 . . | . . . | +-------+-------+-------+| . 2 . | 9 8 . | . . 3 | | . . . | . 1 . | . 7 . | | . 6 . | . . . | . 4 . | +-------+-------+-------+`

... "1st pancake syndrome"...

That is a brilliant expression! Hereby adopted.

Vidar
vidarino

Posts: 295
Joined: 02 January 2006

yasmin wrote:What's ASCII, is this the code many use here?
Sorry, I should have said 'text'. Oops, I see vidarino already answered.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Yasmin - going back to your question - you've only used 2 colours but there are 2 separate chains, right?

Code: Select all
` A-a . | . . . | . . .  . | . | . . . | . . .  . | . | . . . | . . . ---|---+-------+------  *.| . | ./b . | . . .  . A . | B . . | . . .  . . . | . . . | . . . -------+-------+------  . . . | . . . | . . .  . . . | . . . | . . .  . . . | . . . | . . .`

Ron - I can't see how the elimination is at r5c1 - wouldn't it be r4c1?
emm

Posts: 987
Joined: 02 July 2005

em wrote:Ron - I can't see how the elimination is at r5c1 - wouldn't it be r4c1?

Sorry, I based my elimination on yasmin's coloring without checking if the coloring was correct. The complete correct coloring of 6s is ...
Code: Select all
` A a . | . . . | . . .  . . . | . . . | . . .  . . . | . . . | . . . -------+-------+------  B . . | . b . | . . .  6 A . | B . . | . . .  . . . | . . . | . . . -------+-------+------  . . . | . . . | . . .  . . . | . . . | . . .  . . . | b B . | . . .`

... and *no* elimination can be made.

Since we only know A (true) excludes B (true) and v.v., there are three possible outcomes. Either A is false, or B is false, or both A and B are false. If A and B are both false, uncolored r5c1 must be true. Therefore, we cannot validly deduce r5c1<>6.

Ron

P.S. I eliminated your '-----' indications for strong links as the 'A-a' and 'B-b' color pairing already conveys that information.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Hi guys, last night, frustrated by not having solved it yet, I re-wrote this puzzle in big format and worked out all the candidates anew trying the bean method. I discovered my mistake myself, these are 2 separate chains (originally there were actually three but they can be solved) and the said 6 can't be eliminated.

If I can't solve this within the next day I'll re-post and ask your help.

My preliminary question is whether you sometimes use trying-out long chains of "if x is true then y is true then z is true then a is true....... to find out contradictions down the line, because there's just no other way of solving a certain puzzle. Or should I post this under a different thread?
yasmin

Posts: 20
Joined: 24 February 2006

yasmin wrote:If I can't solve this within the next day I'll re-post and ask your help.

It's a very tough puzzle, at least at the start. If I had a clue on how to proceed (with a logical step), I'd pass it on ... but I've none.

Ron
Last edited by ronk on Wed Oct 11, 2006 12:08 pm, edited 1 time in total.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

PreviousNext