The New Sudoku Players' Forum

[Kim154]

Hi All,

I'm a beginner. The third or "Tough" level puzzles in the Dummies book have me completely stumped. I would love help with puzzle 169. The answer is in the back of the book, of course, but I would like to know what techniques of logic would help me solve this one. Here is what I have:

9*31*5746
*****41*5
1**7*6*83

218*43**7
57***8314
3**5718*2

83*412**9
4**8*7**1
**1**94*8

Thanks,
K

[Carcul]

Hi Kim154.

Welcome to this forum. A technique that can be used in solving your puzzle is Colors, a simple form of Nice Loops. This technique uses conjugate nodes, which are cells in a unit (row, column, or box) that are the only two possible places for a given candidate in that unit. In your puzzle, we can use this technique with candidate "2": if you look carefully, you see that there are in column 3 only two cells available for "2" (r2c3 and r8c3: "r" stands for row and "c" stands for column); the same thing happens in column 7 - only r3c7 and r8c7 can contain a "2". Now, let's imagine that r2c8 is "2": this means that r2c3 cannot be "2" and so r8c3 must be "2", which means that r8c7 cannot be "2" and so r3c7 is "2" - but now we have two "2s" in box 3 because we start by assuming that r2c8 is "2". This is a contradiction, and so r2c8 cannot be "2". From this deduction the puzzle is easily solved.

Hope this helps.

Regards, Carcul

[CathyW]

Hi Kim and welcome to the Sudoku forum.

There are undoubtedly other ways forward that I don't yet fully understand but one way is to use a technique known as multiple colouring - in this case on 2s:

Code: Select all

 *-----------*
 |9.3|1.5|746|
 |...|..4|1.5|
 |1..|7.6|.83|
 |---+---+---|
 |218|.43|..7|
 |57.|..8|314|
 |3..|571|8.2|
 |---+---+---|
 |83.|412|..9|
 |4..|8.7|..1|
 |..1|..9|4.8|
 *-----------*
 *--------------------------------------------------------------------*
 | 9      28     3      | 1      28     5      | 7      4      6      |
 | 67     268   A267    | 239    2389   4      | 1     b29     5      |
 | 1      45     45     | 7     b29     6      | B29    8      3      |
 |----------------------+----------------------+----------------------|
 | 2      1      8      | 69     4      3      | 569    569    7      |
 | 5      7      69     | 269    269    8      | 3      1      4      |
 | 3      469    469    | 5      7      1      | 8      69     2      |
 |----------------------+----------------------+----------------------|
 | 8      3      567    | 4      1      2      | 56     567    9      |
 | 4      2569  a2569   | 8      356    7      |b256*   2356   1      |
 | 67     256    1      | 36     356    9      | 4      23567  8      |
 *--------------------------------------------------------------------*


Colouring is where you label or colour conjugate pairs i.e. where there's only two instances of that candidate in a row, column or box. We know that either A or a is true, and that either B or b is true. Note that A and b share a row so in addition either A or b is true. Accordingly, at the intersection of a and B marked with *, this cannot be true and the 2 can be eliminated from this cell. It's a bit complex but there are more posts on multiple colouring in the "Advanced Techniques" section which might explain things better than I have done.

After the 2 in r8c7 is removed, the rest of the puzzle solves with singles.

Hope that helps

Edit: Carcul beat me to it! But I'll leave this here as well anyway.

[tarek]

another approach is to used the finned fish technique.....

Just checking that you managed to find this naked double first...

Code: Select all

*-----------------------------------------------------------------*
| 9      28     3     | 1      28     5     | 7      4      6     |
| 67     268    267   | 239    2389   4     | 1      29     5     |
| 1     -245   -245   | 7     *29     6     |*29     8      3     |
|---------------------+---------------------+---------------------|
| 2      1      8     | 69     4      3     | 569    569    7     |
| 5      7      69    | 269    269    8     | 3      1      4     |
| 3      469    469   | 5      7      1     | 8      69     2     |
|---------------------+---------------------+---------------------|
| 8      3      567   | 4      1      2     | 56     567    9     |
| 4      2569   2569  | 8      356    7     | 256    2356   1     |
| 67     256    1     | 36     356    9     | 4      23567  8     |
*-----------------------------------------------------------------*
r3c2 Must only have 45 as valid Candidates (29 is a Naked Double in Row 3)
r3c3 Must only have 45 as valid Candidates (29 is a Naked Double in Row 3)

then the fish comes into place....

Code: Select all

*-----------------------------------------------------------------*
| 9      28     3     | 1      28     5     | 7      4      6     |
| 67     268   *267   | 239    2389   4     |*1     -29     5     |
| 1      45     45    | 7      29     6     |#29     8      3     |
|---------------------+---------------------+---------------------|
| 2      1      8     | 69     4      3     | 569    569    7     |
| 5      7      69    | 269    269    8     | 3      1      4     |
| 3      469    469   | 5      7      1     | 8      69     2     |
|---------------------+---------------------+---------------------|
| 8      3      567   | 4      1      2     | 56     567    9     |
| 4      2569  *2569  | 8      356    7     |*256    2356   1     |
| 67     256    1     | 36     356    9     | 4      23567  8     |
*-----------------------------------------------------------------*
Eliminating 2 From r2c8 (Finned XWing in Columns 37)

& solves the puzzle

Tarek