The New Sudoku Players' Forum

[kiyoshige]

Here's the original puzzle with my grid. If it's a turbot fish, X-Y wing or other, please explain because I don't understand those advanced techniques (even after looking on the advanced techniques pages)! Thanks! Sorry, Len, yes you are correct r4c8 should be 23457

Code: Select all

 *-----------------------------------------------------------------------------*
 | 57      6       59      | 389     3489    49      | 2       1       578     |
 | 8       23      123     | 5       7       12      | 69      46      49      |
 | 1257    279     4       | 12689   1689    1269    | 578     57      3       |
 |-------------------------+-------------------------+-------------------------|
 | 2457    234789  2358    | 12789   1589    12579   | 13579   23457   6       |
 | 2567    1       256     | 4       569     3       | 579     8       2579    |
 | 9       23478   23568   | 12678   1568    12567   | 1357    23457   2457    |
 |-------------------------+-------------------------+-------------------------|
 | 3       28      128     | 1679    1569    15679   | 4       267     27      |
 | 46      49      69      | 37      2       8       | 357     357     1       |
 | 12      5       7       | 136     1346    146     | 368     9       28      |
 *-----------------------------------------------------------------------------*


[Len]

I get 23457 for r4c8 in the code? Corrected - thanks.

[ravel]

You need more than x-wing for this puzzle. Here is a possible solution:

You missed a hidden 34-pair in column 5, but it does not help much.
There is also a turbot fish to eliminate 1 from r9c6 (either r9c1=1 or r3c1=1 => r2c3<>1 => r2c6=1), which also does not help much.
But then you can eliminate 6 from r9c7 with an error chain:
r9c7=6 => r9c9=8 => r1c9<>8 => r1c4=8 => r1c5=3 => r1c6=4 => r9c6=6.

This brings you some steps further.

Code: Select all

 *-----------------------------------------------------------------------------*
 | 57      6       59      | 389     34      49      | 2       1       578     |
 | 8       23      123     | 5       7       12      | 6       4       9       |
 | 1257    279     4       | 12689   1689    1269    | 578     57      3       |
 |-------------------------+-------------------------+-------------------------|
 | 457     34789   358     | 12789   1589    12579   | 13579   23      6       |
 | 2567    1       256     | 4       569     3       | 579     8       57      |
 | 9       3478    3568    | 12678   1568    12567   | 1357    2357    4       |
 |-------------------------+-------------------------+-------------------------|
 | 3       28      128     | 1679    1569    15679   | 4       6       27      |
 | 46      49      69      | 37      2       8       | 357     357     1       |
 | 12      5       7       | 136     34      46      | 38      9       28      |
 *-----------------------------------------------------------------------------*


An error net eliminates 5 from r1c9:
r1c9=5 => r1c13<>5 => r3c1=5
r1c9=5 => r9c9=8 => r9c1=2 => r3c1=1

Code: Select all

 *-----------------------------------------------------------------------------*
 | 57      6       59      | 389     34      49      | 2       1       78      |
 | 8       23      123     | 5       7       12      | 6       4       9       |
 | 127     279     4       | 12689   1689    1269    | 578     57      3       |
 |-------------------------+-------------------------+-------------------------|
 | 457     34789   358     | 12789   1589    12579   | 13579   23      6       |
 | 267     1       26      | 4       569     3       | 579     8       5       |
 | 9       3478    3568    | 12678   1568    12567   | 1357    2357    4       |
 |-------------------------+-------------------------+-------------------------|
 | 3       28      128     | 1679    1569    15679   | 4       6       27      |
 | 46      49      69      | 37      2       8       | 357     357     1       |
 | 12      5       7       | 136     34      46      | 38      9       28      |
 *-----------------------------------------------------------------------------*


Then you can eliminate 5 from r1c3:
r1c3=5 => r8c3=9 => r8c1=6 => r4c1=4 => r1c1=5

This solves it.

[Len]

How did you get r6c9=4?

[ravel]

Hi Len,

you are right, r4c8=23457, when one gets stuck with basic methods. I copied the grid from kiyoshige and did not notice it, because it had no influence to the solution.

After elimination of 6 in r9c7 you get r2c7=6 => r2c8=4 => r2c9=9 => r6c9=4.

[Len]

Thanks. In your post about the hidden 34-pair, this find is necessary for your error chain argument. I don't see your turbot fish idea though because r9c1=1 => r7c3<>1 => r2c3=1.

[ravel]

Hm, since either r9c1=1 or (r3c1=1 => r2c3<>1 =>) r2c6=1 must be true, r9c6, which sees both cells, cannot be 1.
If you have 2 strong links for a number in cells A-B and C-D and B and C share a unit, you can eliminate the number from all cells, which see both A and D. See this thread for more.

[daj95376]

Code: Select all

.6....21.8..57......4.....3........6.1.4.3.8.9........3.....4......28..1.57....9.

r2  b3  -  469   Naked  Triple (row and box)
r8  b7  -  469   Naked  Triple (row and box)
    b2  -  3     Locked Candidate (1)
    b7  -  8     Locked Candidate (1)
    b8  -  5     Locked Candidate (1)
  c5    -  34    Hidden Pair

At this point, you can skip the Coloring/Turbot Fish and go straight to

Code: Select all

[r8c1]=6,[r8c3]=9,[r1c3]=5,[r1c1]=7,[r1c9]=8,[r9c9]=2,[r7c9]=7,[r7c8]=6,[r2c8]=4,[r2c9]=9,[r5c9]=5 => [c1]=INVALID

Thus, [r8c1]=4 and this cracks the puzzle.