The New Sudoku Players' Forum

[Camchase]

I have finally gotten down the techniques (one by one) up to an X-Wing and Swordfish and I'm able to solve all of the "Hard" puzzles in Simple Sudoku. I have advanced to the "Expert" ones and find that when "colouring" is needed I cannot solve it.

I've done a search for colouring and I've read the posts. I've also gone to the various help sites and, still, I'm having trouble wrapping my arms (or in this case my brain) around the concept.

Is there anyone out there that can explain it to me (say on a 5th grade level since that seems to be what I might be able to understand). I don't know why I'm having trouble with this next step. I have grasped all the other techniques rather quickly but I'm stumped with this one.

Any help would be appreciated. Thank you.

Cam

[emm]

Hi Camchase - colouring is a beautifully simple technique, it deals with conjugate pairs and with one number at a time. It can be done without solvers.

Label conjugate pairs alternately – say (+) and (-) and because they’re pairs, either the + or the - will be correct.

The rule is that if you find two of the same colour in the same group then they are the incorrect ones.

Code: Select all

+-----------------+-----------------+-----------------+
| 5     19+   7   |  4     3    6   | 19-    8    2   |
| 19-   4     6   |  2     8    5   | 7      19+  3   |
| 8     3     2   |  7     1    9   | 56     4    56  |
+-----------------+-----------------+----------------+
| 4     6     5   |  1     9    7   | 2      3    8   |
| 7     8     3   |  6     4    2   | 159    19-  15- |
| 19+   2     19- |  8     5    3   | 46     7    46  |
+-----------------+-----------------+-----------------+
| 2     7     49  |  3     6    1   | 8      5    49  |
| 6     19-   8   |  5     7    4   | 3      2    19+ |
| 3     5     14+ |  9     2    8   | 14-    6    7   |
+-----------------+-----------------+----------------+ 

You end up with two (-) both in r5 and in c7 => all the (-) are false

The second rule for elimination is that any cell that intersects both a (+) and a (-) must also be false.

Multiple colouring is a more advanced technique.

[Camchase]

I think where I'm having the problem is I'm not sure how to determine which is the + and - . And how you "travel" from one block to another.

Thanks for helping.

Cam

[Crazy Girl]

In em's example, you pick a box/row/column which has two 1's in it and label one (+) and the other (-) it doesn't matter which one has which label, you could label them using 2 colours.

For em's example, say you pick R1C2 as (+) then
R2C1 is (-), so is R1C7 and R8C2, as conjugates of R1C2.
then R2C8 is (+) as conjugate of R1C7(-) / R2C1(-).
You carry on like this, where there are pairs of 1's (in this case) in a unit (box/row/column) until you find that one of them is true and one of them is false.

Code: Select all

+-----------------+-----------------+-----------------+
| 5     19+   7   |  4     3    6   | 19-    8    2   |
| 19-   4     6   |  2     8    5   | 7      19+  3   |
| 8     3     2   |  7     1    9   | 56     4    56  |
+-----------------+-----------------+-----------------+
| 4     6     5   |  1     9    7   | 2      3    8   |
| 7     8     3   |  6     4    2   | 159    19-  15- |
| 19+   2     19- |  8     5    3   | 46     7    46  |
+-----------------+-----------------+-----------------+
| 2     7     49  |  3     6    1   | 8      5    49  |
| 6     19-   8   |  5     7    4   | 3      2    19+ |
| 3     5     14+ |  9     2    8   | 14-    6    7   |
+-----------------+-----------------+-----------------+


[Camchase]

Okay, I think I "got it"!! How's this?

[img] *-----------*
|..6|...|.2.|
|.43|.1.|.7.|
|...|3.7|...|
|---+---+---|
|...|8..|49.|
|86.|...|.57|
|.74|..6|...|
|---+---+---|
|...|2.1|...|
|.9.|.4.|81.|
|.8.|...|5..|
*-----------*


*-----------*
|7.6|...|.2.|
|.43|61.|97.|
|9.8|3.7|64.|
|---+---+---|
|3.1|87.|496|
|869|...|.57|
|.74|..6|.8.|
|---+---+---|
|435|281|769|
|697|543|812|
|182|769|534|
*-----------*


*-----------------------------------------------------------*
| 7 15 6 | 49 59 458 | 13 2 1358 |
| 25 4 3 | 6 1 258 | 9 7 58 |
| 9 125 8 | 3 25 7 | 6 4 15 |
|-------------------+-------------------+-------------------|
| 3 25 1 | 8 7 25 | 4 9 6 |
| 8 6 9 | 14 23 24 | 123 5 7 |
| 25 7 4 | 19 2359 6 | 123 8 13 |
|-------------------+-------------------+-------------------|
| 4 3 5 | 2 8 1 | 7 6 9 |
| 6 9 7 | 5 4 3 | 8 1 2 |
| 1 8 2 | 7 6 9 | 5 3 4 |
*-----------------------------------------------------------*
[/img]

Using the 2s and 5s if R2C1 is + then R3C2 is -
Then if R2C1 is + then R6C1 is -
Then if R6C1 is - then R6C5 is +
Then if R6C5 is + then R4C6 is -
and since R2C1 is + then R2C6 is -
That makes R4C6 a - and R2C6 a - meaning they are false and all -'s can be removed.

Is this right?

Cam

[Crazy Girl]

Okay, I think I "got it"!! How's this?

Code: Select all

 *-----------*
 |..6|...|.2.|
 |.43|.1.|.7.|
 |...|3.7|...|
 |---+---+---|
 |...|8..|49.|
 |86.|...|.57|
 |.74|..6|...|
 |---+---+---|
 |...|2.1|...|
 |.9.|.4.|81.|
 |.8.|...|5..|
 *-----------*

Code: Select all

 *-----------*
 |7.6|...|.2.|
 |.43|61.|97.|
 |9.8|3.7|64.|
 |---+---+---|
 |3.1|87.|496|
 |869|...|.57|
 |.74|..6|.8.|
 |---+---+---|
 |435|281|769|
 |697|543|812|
 |182|769|534|
 *-----------*

Code: Select all

 *----------------------------------------------------*
 | 7    15    6   | 49   59    458  | 13    2    1358 |
 | 25-  4     3   | 6    1     258  | 9     7    58   |
 | 9    125+  8   | 3    25-   7    | 6     4    15   |
 |----------------+-----------------+-----------------|
 | 3    25-   1   | 8    7     25+  | 4     9    6    |
 | 8    6     9   | 14   23    24   | 123   5    7    |
 | 25+  7     4   | 19   2359  6    | 123   8    13   |
 |----------------+-----------------+-----------------|
 | 4    3     5   | 2    8     1    | 7     6    9    |
 | 6    9     7   | 5    4     3    | 8     1    2    |
 | 1    8     2   | 7    6     9    | 5     3    4    |
 *----------------------------------------------------*

Using the 2s and 5s if R2C1 is + then R3C2 is -
Then if R2C1 is + then R6C1 is -
Then if R6C1 is - then R6C5 is +
Then if R6C5 is + then R4C6 is -
and since R2C1 is + then R2C6 is -
That makes R4C6 a - and R2C6 a - meaning they are false and all -'s can be removed.

Is this right?

Cam

Colouring only applies to one number, and the deduction that follow only apply to the single number under consideration so you can't use colouring on 2's and 5's, you need to apply colouring to a single number and see if there are any deductions, if not try another number.

Also note that you can only apply simple colouring when there are 2 cells of the number under consideration, (what was referred to as conjugates) in a unit (box/row/column) to say 'if this one is true then this one is false' or vice versa.

your statement

Then if R6C1 is - then R6C5 is +

is false as you did not consider R6C7, and Row 6 has 3 cells that could be 2 and not *two* cells.

If you look at your example again, looking at the 2's, and see what you can conclude on cells R5C5 R6C5

[emm]

Yes Camchase, you are confused over the term conjugate pair. Remember we are talking about one number ie 2s or 5s not both.

A conjugate pair is when a number has only ONE other buddy in its row column or box - in your example the conjugate pairs of 2s are

r2c1 and r2c6 (row2)
r2c1 and r3c2 ( box 1)
r3c2 and r3c5 (row 3)
r2c6 and r3c5 (box 2)
r3c2 and r4c2 (column 2)
r4c2 and r4c6 (row 4)
r4c2 and r6c1 (box 4)

Since two (+) end up in c6 all the (+) are false.
Since r6c5 intersects with- a (+) and a (-) it is also false.

Code: Select all

*-----------------------------------------*
| 7  15  6 | 49  59    458 | 13   2  1358 |
|-25 4   3 | 6   1    +258 | 9    7  58   |
| 9 +125 8 | 3  -25    7   | 6    4  15   |
|----------+--------------+---------------|
| 3 -25  1 | 8   7    +25  | 4    9  6    |
| 8  6   9 | 14  23    24  | 123  5  7    |
|+25 7   4 | 19  2359  6   | 123  8  13   |
|----------+----------------+-------------|
| 4  3   5 | 2   8     1   | 7    6  9    |
| 6  9   7 | 5   4     3   | 8    1  2    |
| 1  8   2 | 7   6     9   | 5    3  4    |
*------------------------------------------* 
 

[Camchase]

Thanks Em, for taking it step by step. I think I've got it now. (Famous last words). I need to try and get another Simple Sudoku puzzle to come up with "coloring" and I'll let you know how it goes. You have been so patient and very, very helpful. Thank you, again, so much. Thank you so much to all who have contributed. I'll let you know if I do have it down.

Cam

[Camchase]

It WORKED!!! I'm so thrilled. Actually, it was an "intersection" of a + and -. Thanks for including that.

Now I'm so into looking for advanced techniques that I missed a simple naked quad.

Thanks again for everyone's patience.

Cam

[Camchase]

I had to let you know that, while looking for info on coloring, I read something about a deadly pattern from a rectangle. I just glanced over it, thinking that it was far from what I needed to know. I just had a puzzle that had it and I was able to apply it. I don't know what it is called but it goes like this:


xyz . . . . . . . . xyz
.
.
.
xyz . . . . . . . . xyz
a


The solution was a. I hope this is a technique and not a lucky guess.

Any comments very welcome.

Thank you.

Cam

[Crazy Girl]

Cam,

What you have found is called Uniqueness, for a puzzle to only have one solution (one assumes it is a valid puzzle with one solution) one has to have 'a' in the bottom right, otherwise you will get multiple solutions.

[Camchase]

Wonderful, Crazy Girl. Thank you. That makes sense now that you point it out. I can't remember seeing it in any other puzzle but I'm sure it has been there. It's just one more thing for me to remember.

Again, thanks,

Cam

[bradles]

I too am completely bamboozled and lost with this technique.
Em, I have quoted one of your replies below and marked it up in bold with my comments. i was wondering if you wouldn't mind trying another way of explaining it to me so that I might be able to wrap my head around this?

Yes Camchase, you are confused over the term conjugate pair. Remember we are talking about one number ie 2s or 5s not both.

A conjugate pair is when a number has only ONE other buddy in its row column or box - in your example the conjugate pairs of 2s are

r2c1 and r2c6 (row2)
r2c1 and r3c2 ( box 1)
r3c2 and r3c5 (row 3)
r2c6 and r3c5 (box 2)
r3c2 and r4c2 (column 2)
r4c2 and r4c6 (row 4)
r4c2 and r6c1 (box 4)

I follow you up to here

Since two (+) end up in c6 all the (+) are false. <-- I lose it here
Since r6c5 intersects with- a (+) and a (-) it is also false. <-- and here

Code: Select all

*-----------------------------------------*
| 7  15  6 | 49  59    458 | 13   2  1358 |
|-25 4   3 | 6   1    +258 | 9    7  58   |
| 9 +125 8 | 3  -25    7   | 6    4  15   |
|----------+--------------+---------------|
| 3 -25  1 | 8   7    +25  | 4    9  6    |
| 8  6   9 | 14  23    24  | 123  5  7    |
|+25 7   4 | 19  2359  6   | 123  8  13   |
|----------+----------------+-------------|
| 4  3   5 | 2   8     1   | 7    6  9    |
| 6  9   7 | 5   4     3   | 8    1  2    |
| 1  8   2 | 7   6     9   | 5    3  4    |
*------------------------------------------* 
 

[emm]

Hi bradles - I hope I can!

Each group (row, column or box) can have only one cell of any number.

With conjugates (only two of that number in a group) either one is true or the other is true. They can’t both be true. We label them + / - or chalk / cheese or anything we like to identify them. We don't know which is true and which is not. We just know that if one is true then it's conjugate will be false.

After colouring the 2s we find that -
in c6 you have two (+) They are the both the same value and they can’t both be true otherwise you would have two 2s in that group (c6). Therefore they must both be false. The extension is that therefore all (+) must be false.

In r6c5 you have a 2 that ‘sees' both a (+) and a (-). Now since either (+) or (-) is true, then r6c5 cannot also be true. Otherwise you would end up with two 2s in either row 6 or column 5.

I hope this is clearer. You can read the Simple Sudoku explanation - http://angusj.com/sudoku/hints.php - or ask for further clarification if you need.

[bradles]

Thanks em,

I think I'm getting it. I've had to go over and over a number of different explanations to get my head around it and find something that I can understand if that makes sense.

I use simple sudoku as a way of trying to learn all the techniques so i checked the site again. After your explanation, I was able to understand their explanation. <--- quite ironic eh...almost like a sudoku in itself.

Hopefully I'm starting to get a grip on the technique now.
Thanks again.
Brad