The New Sudoku Players' Forum

[palmbay]

Code: Select all

73     6        5  | 4       2       1     | 9     38     378
9      4        2  | 8      73       5     | 367    1     36
1      8       73  | 6       9       73    | 5      4      2
------------------+--------------------+-------------------
378    73     9    | 5       6        4    | 38     2      1
4       5     38   | 17     17        2    | 368    9     368
6       2     1    | 3       8        9    | 4      7     5
------------------+--------------------+-------------------
2      139    6    | 17      4        38   | 378    5      389
5      13     78   | 9       13       78   | 2      6      4
378    379    4    | 2        5        6   | 1     38     3789


Using Angus's program, set on extreme, I am rather puzzled. I came to a grinding halt and had to ask for a hint. It gave me exclusion by colours of number 3 in R4C2. This cell although not coloured, was also NOT in line with any 2 conjugate coloured cells. (Just the one at R8C2). There are 3 cells in box 4 containing the number 3, so no pairs there either. I did it twice to see if there was a mistake and it still comes up with this hint. As a relative newbie, can anyone enlighten me as to why this is, as I know the hint is right, just need to work out why.

[Animator]

Perhaps this helps:

Code: Select all

37     6      5   | 4      2       1   | 9     38    378
9      4      2   | 8      37-     5   | 367   1     36
1      8      37- | 6      9       37  | 5     4     2
------------------+--------------------+-------------------
378    37     9   | 5      6       4   | 38    2     1
4      5      38+ | 17     17      2   | 368   9     368
6      2      1   | 3      8       9   | 4     7     5
------------------+--------------------+-------------------
2      139    6   | 17     4       38  | 378   5     389
5      13-    78  | 9      13+     78  | 2     6     4
378    379    4   | 2      5       6   | 1     38    3789


r3c3 is the opposite of r5c3.
r2c5 has the same value as r3c3. (r3c6 is the opposite of r3c3. r2c5 is the opposite of r3c6)
r8c5 is the opposite of r2c5. (which means it's the same as r5c3)
r8c2 is the opposite of r8c5. (which means it's the opposite of r5c3)

r4c2 sees a + (r5c3) and a - (r8c2). This means it can not contain 3: either r5c3 or r8c2 is the number 3.

[palmbay]

Thanks for the reply, threw me for a while, I have been looking at what is rather than what is not, ie exclusions. and because R5C3 or R8C2 must contain a 3 then R4C4 cannot. Simple logic really, I was trying to use the colour rule as explained in Angus's guide.

[CathyW]

Thanks for posting this query palmbay and for Animator's reply. I think the penny has finally dropped as to where exclusions can logically be made when colouring!

[Animator]

Solving the grid myself showed some other places where colouring should be used.
Since the question is/was about colouring I decided to post them.

What follows is a way to colour the grid to make some more eliminations. (This can be considered a spoiler... so if you want to first try it yourself then you should STOP reading.)

• Colour the number 3:

  Code: Select all

  37-    6      5   | 4      2       1   | 9     38    378

9      4      2   | 8      37+     5   | 367   1     36

1      8      37+ | 6      9       37- | 5     4     2

------------------+--------------------+-------------------

38+    7      9   | 5      6       4   | 38-   2     1

4      5      38  | 17     17      2   | 368   9     368

6      2      1   | 3      8       9   | 4     7     5

------------------+--------------------+-------------------

2      139    6   | 17     4       38+ | 378   5     389

5      13     78  | 9      13      78  | 2     6     4

78     39     4   | 2      5       6   | 1     38    3789


  
  r3c3 is the opposite of r3c6
  r1c1 is the opposite of r3c3 (= r3c6)
  r4c1 is the opposite of r1c1 (= r3c3)
  r4c7 is the opposite of r4c1 (= r3c6)
  
  r2c5 is the opposite of r3c6 : r2c7 now sees a + in r2c5 and a - in r4c7 ==> it can never be the number 3.
  r7c6 is the opposite of r3c6 : r7c7 now sees a + in r7c6 and a - in r4c7 ==> it can never be the number 3.
  
  (Make a few other eliminations)
  
• Colour the number 3:

  Code: Select all

  37     6      5   | 4      2       1   | 9     38    378

9      4      2   | 8      37-     5   | 67    1     36+

1      8      37  | 6      9       37+ | 5     4     2

------------------+--------------------+-------------------

38     7      9   | 5      6       4   | 38    2     1

4      5      38  | 17     17      2   | 368   9     68

6      2      1   | 3      8       9   | 4     7     5

------------------+--------------------+-------------------

2      139    6   | 17     4       38- | 78    5     389

5      13     78  | 9      13      78  | 2     6     4

78     39     4   | 2      5       6   | 1     38    3789


  
  
  r2c5 is the opposite of r2c9
  r3c6 is the opposite of r2c5 (= r2c9)
  r7c6 is the opposite of r3c6 (= r2c5)
  
  r7c9 sees a + in r2c9 and a - in r7c6 ==> it can never be the number 3.
  
  (Make a few other eliminations)
  
• Colour the number 8:

  Code: Select all

  37     6      5   | 4      2       1   | 9     38    378

9      4      2   | 8      37      5   | 67    1     36 

1      8      37  | 6      9       37  | 5     4     2

------------------+--------------------+-------------------

38-    7      9   | 5      6       4   | 38    2     1

4      5      38+ | 17     17      2   | 368   9     68

6      2      1   | 3      8       9   | 4     7     5

------------------+--------------------+-------------------

2      13     6   | 17     4       38- | 78+   5     9

5      13     78- | 9      13      78+ | 2     6     4

78     9      4   | 2      5       6   | 1     38    378


  
  
  r7c6 is the opposite of r7c7
  r8c6 is the opposite of r7c6 (= r7c7)
  r8c3 is the opposite of r8c6 (= r7c6)
  r5c3 is the opposite of r8c3 (= r7c7)
  r4c1 is the opposite of r5c3 (= r7c6)
  
  r4c7 now sees a + in r7c7 and a - in r4c1 ==> it can never be the number 8.
  
  (Solve the rest of the puzzle)
  
  
  Update: last line was incorrect. It said: ... it can never be the number 3... (Thanks Crazy Girl)