The New Sudoku Players' Forum

[Uncrypted]

Hi all, been stuck on this puzzle for half a day, tried a number of techniques looking at various forums, still can't advance!

Would appreciate a hint from someone for the next move together with an explanation of the technique used.

Thank you in advance!

[StrmCkr]

Code: Select all

+----------------+------------------+-----------------+
| 9   2     6    | 17    17   8     | 4     3     5   |
| 8   5     1    | 9     4    3     | 2     7     6   |
| 4   7     3    | 6     5    2     | 9     8     1   |
+----------------+------------------+-----------------+
| 26  1     4589 | 458   36   7     | 35    59    289 |
| 27  3     458  | 458   9    45    | 6     1     27  |
| 67  89    589  | 2     36   1     | 357   4     789 |
+----------------+------------------+-----------------+
| 5   4689  2789 | 47    278  4(6)  | 1     9-6   3   |
| 3   46    27   | 1457  127  9     | 8     (56)  47  |
| 1   4689  789  | 3     78   4(56) | 7(5)  2     479 |
+----------------+------------------+-----------------+

M-Wing: 6 r7c8 -6- r7c6 =6= r9c6 =5= r9c7 -5- r8c8 -6- r7c8 => r7c8<>6

singles to the end...

[JC Van Hay]

You could start from one of the 3 units having 2 solutions : B1, C1, C8.

In details :
1r1c4 -> 5 singles; 7r1c4 -> 0 solution
2r4c1 -> 6 singles; 6r4c1 -> 0 solution
5r4c8 -> 1 solution; 9r4c8 -> 0 solution
In the last case, the solved C8 immediately gives r9c6=5 AND r9c6=6
In short, r7r8=6 -> r7c6≠6, r9c6=6, r9c6≠5, r9c7=5, r8c8≠5 and r8c8≠6 (or r8c8={})

Forbidding Matrix Notation :

Code: Select all

6r7c8
6r7c6 6r9c6
      5r9c6 5r9c7
6r8c8       5r8c8

[Leren]

Puzzle solved cell status in line format : 926..8435851943276473652981.1...7....3..9.61....2.1.4.5.....1.33....98..1..3...2.

Code: Select all

*---------------------------------------------*
| 9   2    6    | 17   17   8   | 4    3  5   |
| 8   5    1    | 9    4    3   | 2    7  6   |
| 4   7    3    | 6    5    2   | 9    8  1   |
|---------------+---------------+-------------|
| 26  1    4589 | 458  36   7   | 35   59 289 |
| 27  3    458  | 458  9    45  | 6    1  27  |
| 67  89   589  | 2    36   1   | 357  4  789 |
|---------------+---------------+-------------|
| 5   4689 2789 | 47   278  46  | 1    69 3   |
| 3   4-6  27   | 1457 127  9   | 8   a56 47  |
| 1  d4689 789  | 3    78  c456 |b57   2  479 |
*---------------------------------------------*

M Wing Type 7A Eureka notation : (6=5) r8c8 - r9c7 = (5-6) r9c6 = (6) r9c2 => - 6 r8c2; stte

In words : If cell a r8c8 is not 6 it is 5, so cell b r9c7 is not 5, so cell c r9c6 is 5 and in particular it's not 6, so cell d r9c2 is 6.

Since r8c2 can see both cells a and d, at least one of which must be 6, it can't be 6. This solves r8c2 and the puzzle solves with a cascade of singles from there (stte).

An M Wing is a particular type of Alternating Inference Chain (AIC) Type 1, which you can read more about here.

Leren

[eleven]

Hi all, been stuck on this puzzle for half a day, tried a number of techniques looking at various forums, still can't advance!

Knowing a short solution from a program, it looks easy. But if i would solve it manually, i probably would make some eliminations, which turn out not to be very helpful.
The first to spot for me is the UR 17 (type 4) in r18c45. Since the 1 is restricted to the 4 cells, the 7 must be outside somewhere, e.g. in row 8 only possible in r8c3 or r8c9. So you can eliminate 7 in r8c45.

Code: Select all

+----------------+------------------+-----------------+
| 9   2     6    |#17   #17   8     | 4     3     5   |
| 8   5     1    | 9     4    3     | 2     7     6   |
| 4   7     3    | 6     5    2     | 9     8     1   |
+----------------+------------------+-----------------+
| 26  1     4589 | 458   36   7     | 35    59    289 |
| 27  3     458  | 458   9    45    | 6     1     27  |
| 67  89    589  | 2     36   1     | 357   4     789 |
+----------------+------------------+-----------------+
| 5   4689  2789 | 47    278  46    | 1     96    3   |
| 3   46   *27   |#1457 #127  9     | 8     56   *47  |
| 1   4689  789  | 3     78   456   | 75    2     479 |
+----------------+------------------+-----------------+

Next there is a w-wing 46 in cells r7c6 and r8c2, with a strong link for 6 in row 9. If r9c2=6, then r8c2=4, and if r9c6=6, then r7c6=4. So one of r8c2 and r7c6 must be 4, and you can eliminate it from r7c2 and r8c4.

Code: Select all

+----------------+------------------+-----------------+
| 9   2     6    | 17    17   8     | 4     3     5   |
| 8   5     1    | 9     4    3     | 2     7     6   |
| 4   7     3    | 6     5    2     | 9     8     1   |
+----------------+------------------+-----------------+
| 26  1     4589 | 458   36   7     | 35    59    289 |
| 27  3     458  | 458   9    45    | 6     1     27  |
| 67  89    589  | 2     36   1     | 357   4     789 |
+----------------+------------------+-----------------+
| 5   4689  2789 | 47    278 #46    | 1     96    3   |
| 3  #46    27   | 145   12   9     | 8     56    47  |
| 1  *4689  789  | 3     78  *456   | 75    2     479 |
+----------------+------------------+-----------------+

But now it's getting harder. There are several other eliminations, which are not very useful, you migt find.
And you might find StrmChkr's or Lreen's M-Wing.
Or look at 47 in r8c9 and row 9:

Code: Select all

+----------------+------------------+-----------------+
| 9   2     6    | 17    17   8     | 4     3     5   |
| 8   5     1    | 9     4    3     | 2     7     6   |
| 4   7     3    | 6     5    2     | 9     8     1   |
+----------------+------------------+-----------------+
| 26  1     4589 | 458   36   7     | 35    59    289 |
| 27  3     458  | 458   9    45    | 6     1     27  |
| 67  89    589  | 2     36   1     | 357   4     789 |
+----------------+------------------+-----------------+
| 5   689   2789 | 47    278  46    | 1     96    3   |
| 3   46    27   | 15    12   9     | 8     56   #47  |
| 1   4689 @789  | 3    @78   456   | 75    2    @479 |
+----------------+------------------+-----------------+

If r8c9=4 you get a triple 789 in r9c359.
So the 7 must be in one of these cells or r8c9, can't be in r9c7.
Look for ALS XZ to find the general technique for this move.

[Leren]

Code: Select all

*-----------------------------------------------*
| 9   2     6    | 17    17  8   | 4    3   5   |
| 8   5     1    | 9     4   3   | 2    7   6   |
| 4   7     3    | 6     5   2   | 9    8   1   |
|----------------+---------------+--------------|
| 26  1     4589 | 458   36  7   | 35   59  289 |
| 27  3     458  | 458   9   45  | 6    1   27  |
| 67  89    589  | 2     36  1   | 357  4   789 |
|----------------+---------------+--------------|
| 5   4689  2789 | 47    278 46  | 1    69  3   |
| 3   4-6   27   | 1457  127 9   | 8   a56  47  |
| 1  b4689 b789  | 3    b78  456 |b57   2  b479 |
*-----------------------------------------------*

Here is another very well known technique that you might find easier to spot :

ALS XZ Rule: X = 5, Z = 6: (6=5) r8c8 - (5=6) r9c23579 -> - 6 r8c4; stte. You can read about this technique here or here.

Leren