The New Sudoku Players' Forum

[noggi]

Hi. I've got this tiny puzzle here, that I can't seem to solve without trial and error. Can anyone see the natural way out? Thanks.

x12 x5x
3x5 1x2

xx1 xxx
xxx 2xx

1x3 5x6
x5x 3xx

[Sue De Coq]

I wouldn't go so far as to call the following natural but hopefully it will be of help. It's the simplest solution I could coax out of my solver:

Code: Select all

1. The cell r1c6 is the only candidate for the value 3 in Row 1.
2. Consider the chain r2c5-4-r2c2~4~r5c2-4-r5c5.
The cell r5c5 must contain the value 4 if the cell r2c5 doesn't.
Therefore, these two cells are the only candidates for the value 4 in Column 5.
- The moves r3c5:=4, r4c5:=4 and r6c5:=4 have been eliminated.
Consider the chain r2c2-4-r2c5-4-r5c5-4-r5c2.
The cell r5c2 must contain the value 4 if the cell r2c2 doesn't.
Therefore, these two cells are the only candidates for the value 4 in Column 2.
- The moves r3c2:=4 and r4c2:=4 have been eliminated.
Consider the chain r3c2~6~r2c2-6-r1c1-6-r1c4-6-r3c4.
When the cell r3c2 contains the value 6, so does the cell r3c4 - a contradiction.
Therefore, the cell r3c2 cannot contain the value 6.

- The move r3c2:=6 has been eliminated.
Consider the chain r3c1-2-r6c1-6-r6c3-4-r4c3~4~r3c1.
When the cell r3c1 contains the value 4, it likewise contains the value 2 - a contradiction.
Therefore, the cell r3c1 cannot contain the value 4.
- The move r3c1:=4 has been eliminated.
The value 4 in Box 4 must lie in Row 3.
- The move r4c6:=4 has been eliminated.
Consider the chain r6c1-2-r3c1-5-r3c6-4-r6c6~4~r6c1.
When the cell r6c1 contains the value 4, it likewise contains the value 2 - a contradiction.
Therefore, the cell r6c1 cannot contain the value 4.
- The move r6c1:=4 has been eliminated.
Consider the chain r2c2-4-r5c2-2-r6c1~6~r1c1-4-r2c2.
When the cell r2c2 contains the value 4, the chain is self-contradicting.
 Therefore, the cell r2c2 cannot contain the value 4.
- The move r2c2:=4 has been eliminated.
The value 6 is the only candidate for the cell r2c2.


[noggi]

Thanks. I thought some sort of chain was needed.

[tso]

I don't have a solver -- here's a paper based solution. This is a good example of why these 6x6 puzzles are so good to work on. More complex tactics are much easier to spot, especially when solving on paper, than in a 9x9.

Code: Select all

+------------------+------------------+
|  .     1     2   |   .     5     .  |
|  3     .     5   |   1     .     2  |
+------------------+------------------+
|  .     .     1   |   .     .     .  |
|  .     .     .   |   2     .     .  |
+------------------+------------------+
|  1     .     3   |   5     .     6  |
|  .     5     .   |   3     .     .  |
+------------------+------------------+

Tactics in the order I found them:

(1) Filling in r1c6=3 (single) and the candidate lists:

Code: Select all

+------------------+------------------+
|  46     1     2  |  46     5     3  |
|   3    46     5  |   1    46     2  |
+------------------+------------------+
|2456  2346     1  |  46   346    45  |
| 456   346    46  |   2  1346   145  |
+------------------+------------------+
|   1    24     3  |   5    24     6  |
| 246     5    46  |   3   124    14  |
+------------------+------------------+

(2) Coloring 6s eliminates the candidate 6 from r3c2:

Code: Select all

+------------------+------------------+
| +46     1     2  | -46     5     3  |
|   3   -46     5  |   1    46     2  |
+------------------+------------------+
|2456  234x     1  | +46   346    45  |
| 456   346    46  |   2  1346   145  |
+------------------+------------------+
|   1    24     3  |   5    24     6  |
| 246     5    46  |   3   124    14  |
+------------------+------------------+

(3) X-wing in 4s, rows 2 and 5, eliminates candidates 4 from r34c25:

Code: Select all

+------------------+------------------+
|  46     1     2  |  46     5     3  |
|   3   +46     5  |   1   +46     2  |
+------------------+------------------+
|2456   23x     1  |  46   3x6    45  |
| 456   3x6    46  |   2  13x6   145  |
+------------------+------------------+
|   1   +24     3  |   5   +24     6  |
| 246     5    46  |   3   124    14  |
+------------------+------------------+

(4) No xy-wing exists. There is at least one forcing chain in the five marked (+) cells:

Code: Select all

+------------------+------------------+
|  46     1     2  |  46     5     3  |
|   3    46     5  |   1   +46     2  |
+------------------+------------------+
|2456   +23     1  |  46   +36    45  |
| 456    36    46  |   2   136   145  |
+------------------+------------------+
|   1   +24     3  |   5   +24     6  |
| 246     5    46  |   3   124    14  |
+------------------+------------------+

+------------------+------------------+
|   .     .     .  |   .     .     .  |
|   .     .     .  |   .    46     .  |
+------------------+------------------+
|   .    23     .  |   .    36     .  |
|   .     .     .  |   .     .     .  |
+------------------+------------------+
|   .    24     .  |   .    24     .  |
|   .     .     .  |   .     .     .  |
+------------------+------------------+

Either value for r2c3 leads to r5c2=4.

The rest is relatively simple.