## I am stuck

pjgrun
New kid on the Grid
Posts: 2
Joined: Sat Jun 03, 2006 8:35 pm

### I am stuck

This puzzle is published in the sample section of "Solving Sudoku" document by Michael Mepham. It´s rated tough, but even with the "diabolical" in the same section I was luckier.

. . 1|9 . .|. . 8
6 . .|. 8 5|. 3 .
. . 7|. 6 .|1 . .
-----+-----+-----
. 3 4|. 9 .|. . .
. . .|5 . 4|. . .
. . .|. 1 .|4 2 .
-----+-----+-----
. . 5|. 7 .|9 . .
. 1 .|8 4 .|. . 7
7 . .|. . 9|2 . .

After using some basic techniques and finned x-wing I arrive to

.------------------.------------------.------------------.
| 2345 245 1 | 9 23 7 | 56 456 8 |
| 6 249 29 | 1 8 5 | 7 3 249 |
| 23589 2589 7 | 4 6 23 | 1 59 259 |
:------------------+------------------+------------------:
| 1258 3 4 | 267 9 268 | 568 1567 156 |
| 1289 26789 2689 | 5 23 4 | 368 1679 1369 |
| 589 56789 689 | 367 1 368 | 4 2 3569 |
:------------------+------------------+------------------:
| 248 2468 5 | 236 7 1 | 9 48 36 |
| 29 1 2369 | 8 4 236 | 356 56 7 |
| 7 468 368 | 36 5 9 | 2 148 14 |
'------------------'------------------'------------------'

Here I am stuck! Any ideas?
Ruud
Site Owner
Posts: 601
Joined: Fri Dec 30, 2005 10:21 pm
I can help you a little. When SudoCue reports a template check, I check for a Nishio style trick.

here it is:

Either R1C5 or C3C6 = 2.

When R1C5=2, R1C1 cannot be 2.
When R3C6=2, R7C4=2, R5C5=2, R4C1=2, R1C1 cannot be 2.
In both cases, R1C1 cannot be 2.

The next step must include a forcing chain or nice loop. I cannot find a simple one. Maybe one of our forum members can help us here.

Ruud
GreenLantern
Regular
Posts: 14
Joined: Tue May 30, 2006 8:07 pm

Code: Select all

``````+----------------------+----------------------+----------------------+
| 2345   245    1      | 9      23     7      | 56     456    8      |
| 6      249    29     | 1      8      5      | 7      3      249    |
| 23589  2589   7      | 4      6      23     | 1      59     259    |
+----------------------+----------------------+----------------------+
| 1258   3      4      | 267    9      268    | 568    1567   156    |
| 1289   26789  2689   | 5      23     4      | 368    1679   1369   |
| 589    56789  689    | 367    1      368    | 4      2      3569   |
+----------------------+----------------------+----------------------+
| 248    2468   5      | 236    7      1      | 9      48     36     |
| 29     1      2369   | 8      4      236    | 356    56     7      |
| 7      468    368    | 36     5      9      | 2      148    14     |
+----------------------+----------------------+----------------------+
``````
[r1c1]=3=[r1c5]=2=[r5c5]-2-[r5c123]=2=[r4c1]-2-[r1c1] => r1c1<>2
[r7c4]=3=[r7c9]-3-[r8c7]=3=[r5c7]-3-[r5c5]-2-[r4c4]=2=[r7c4] => r7c4=23
[r7c1]=4=[r1c1]=3=[r1c5]=2=[r5c5]-2-[r4c4]=2=[r7c4]-2-[r7c1] => r7c1<>2
XY-wing (236): r7c24,r9c4 => r9c23<>6
X-wing in 3's: r67c49 => r5c9<>3
Coloring in 2's: r1c25,r7c24,r4c4,r5c5 => r235c2<>2
Coloring in 2's: r1c25,r2c3,r5c5 => r5c3<>2

Code: Select all

``````+-------------------+-------------------+-------------------+
| 34    245   1     | 9     23    7     | 56    456   8     |
| 6     49    29    | 1     8     5     | 7     3     249   |
| 38    589   7     | 4     6     23    | 1     59    259   |
+-------------------+-------------------+-------------------+
| 12    3     4     | 27    9     68    | 568   1567  156   |
| 12    679   689   | 5     23    4     | 368   1679  169   |
| 5     679   689   | 37    1     68    | 4     2     369   |
+-------------------+-------------------+-------------------+
| 48    26    5     | 23    7     1     | 9     48    36    |
| 9     1     26    | 8     4     23    | 356   56    7     |
| 7     48    3     | 6     5     9     | 2     148   14    |
+-------------------+-------------------+-------------------+
``````
[r2c3]=2=[r2c9]-2-[r3c9]=2|8=[r3c2]-8-[r3c1]-3-[r1c1]-4-[r2c2]-9-[r2c3] => r2c3<>9 and the puzzle solves.