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[ArkieTech]

Code: Select all

 *-----------*
 |...|5.4|...|
 |..2|.67|4.3|
 |...|...|.5.|
 |---+---+---|
 |2..|7.6|1..|
 |..1|.3.|6..|
 |..6|8.9|..4|
 |---+---+---|
 |.4.|...|...|
 |9.3|62.|5..|
 |...|3.1|...|
 *-----------*

...5.4.....2.674.3.......5.2..7.61....1.3.6....68.9..4.4.......9.362.5.....3.1...


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[Leren]

Code: Select all

*---------------------------------------*
| 13    136 79 | 5 89 4 | 278 1267 1267 |
|c58   b58  2  | 1 6  7 | 4   9    3    |
| 4     16  79 | 2 89 3 | 78  5    16   |
|--------------+--------+---------------|
| 2    a38  4  | 7 5  6 | 1   38   9    |
| 78    9   1  | 4 3  2 | 6   78   5    |
|d57-3  357 6  | 8 1  9 | 237 237  4    |
|--------------+--------+---------------|
| 16    4   8  | 9 7  5 | 23  1236 126  |
| 9     17  3  | 6 2  8 | 5   4    17   |
| 67    2   5  | 3 4  1 | 9   67   8    |
*---------------------------------------*

(3=8) r4c2 - r2c2 = (8-5) r2c1 = (5) r6c1 => - 3 r6c1; stte

Leren

[SpAce]

Code: Select all

.---------------.-----------.-------------------.
| 13   136  *79 | 5  *89  4 | *78+2  1267  1267 |
| 58   58    2  | 1   6   7 |  4     9     3    |
| 4    16   *79 | 2  *89  3 | *78    5     16   |
:---------------+-----------+-------------------:
| 2    38    4  | 7   5   6 |  1     38    9    |
| 78   9     1  | 4   3   2 |  6     78    5    |
| 357  357   6  | 8   1   9 |  237   237   4    |
:---------------+-----------+-------------------:
| 16   4     8  | 9   7   5 |  23    1236  126  |
| 9    17    3  | 6   2   8 |  5     4     17   |
| 67   2     5  | 3   4   1 |  9     67    8    |
'---------------'-----------'-------------------'

BUG-Lite+1 (789)r13c357: +2 r1c7; stte

[Ngisa]

Code: Select all

+------------------+--------------+---------------------+
| 13     136    79 | 5    89    4 | 278    1267    1267 |
|b58    c58     2  | 1    6     7 | 4      9       3    |
| 4      16     79 | 2    89    3 | 78     5       16   |
+------------------+--------------+---------------------+
| 2      38     4  | 7    5     6 | 1      38      9    |
|b78     9      1  | 4    3     2 | 6      78      5    |
| 357   d35-7   6  | 8    1     9 | 237    237     4    |
+------------------+--------------+---------------------+
| 16     4      8  | 9    7     5 | 23     1236    126  |
| 9     a17     3  | 6    2     8 | 5      4       17   |
|b67     2      5  | 3    4     1 | 9      67      8    |
+------------------+--------------+---------------------+


(7)r8c2 = (785)r952c1 - (5)r2c2 = (5)r6c2 => - 7r6c2; stte

Clement

[Cenoman]

(7)r8c2 = (785)r952c1 - (5)r2c2 = (5)r6c2 => - 7r6c2; stte

Hi Clement,
Nice ! (There are not so many interesting paths after Leren' and SpAce's)

Your first term (7s in box 7) could be omitted. Your solution would be shortened to (7=85)r52c1 - (5)r2c2 = (5)r6c2 => - 7r6c2; stte

[Cenoman]

As said above, not so many interesting paths after Leren', SpAce's and Clement's

Code: Select all

 +-------------------+-----------------+----------------------+
 |  13    136   79   |  5    89   4    |  278   1267   1267   |
 | d58   c58    2    |  1    6    7    |  4     9      3      |
 |  4     16    79   |  2    89   3    |  78    5      16     |
 +-------------------+-----------------+----------------------+
 |  2    c38    4    |  7    5    6    |  1    b38     9      |
 |  78    9     1    |  4    3    2    |  6     78     5      |
 | e57-3  357   6    |  8    1    9    | a237* a237*   4      |
 +-------------------+-----------------+----------------------+
 |  16    4     8    |  9    7    5    | a23*  a1236*  126    |
 |  9     17    3    |  6    2    8    |  5     4      17     |
 |  67    2     5    |  3    4    1    |  9     67     8      |
 +-------------------+-----------------+----------------------+

Almost X-wing
[(3)r6c7=r7c7 - r7c8=r6c8] = (3)r4c8 - (3=85)r24c2 - r6c2 = (5)r6c1 => -3 r6c1; ste

[SpAce]

Hi Cenoman,

(7)r8c2 = (785)r952c1 - (5)r2c2 = (5)r6c2 => - 7r6c2; stte

Nice ! Your first term (7s in box 7) could be omitted. Your solution would be shortened to (7=85)r52c1 - (5)r2c2 = (5)r6c2 => - 7r6c2; stte

Yes, a nice solution from Clement, and a good catch from you. The shortening would make it an H-Wing (fka H3-Wing). Leren's chain is an M3-Wing (fka H2-Wing). I use this opportunity to demonstrate why the latter was moved to the M-Wing family, and the numbering changed to match the logic in L-Wings (number of digits used):

(7=8)r5c1 - (8=5)r2c1 - r2c2 = (5)r6c2 : H-Wing (just one simple type left in that family, so no numbers needed)

(3=8)r4c2 - r2c2 = (8-5)r2c1 = (5)r6c1 : M3-Wing (3 digits)

(3=8)r4c2 - r2c2 = (8-3)r2c1 = (3)r6c1 : M2-Wing (2 digits), or just M-Wing as before

(The last one is just a hypothetical example to demonstrate the similarity. It doesn't obviously exist in this grid.)

[Mauriès Robert]

Hi Cenoman,
To echo an exchange with you about the previous puzzle (http://forum.enjoysudoku.com/post285654.html#p285654), here is how I find the results of Leren, Clément and you with TDP.
Leren : Anti-track P'(5r6c1) <=> -5r6c1 -> 5r6c2 -> 8r2c2 -> 3r4c2 => -3r6c1 (Th2 TDP part1)
Clement: Anti-track P'(5r6c2) <=> -5r6c2 -> 5r6c1 -> 8r2c1 -> 7r5c1 => -7r6c2 (Th2 TDP part1)
You: with two tracks P(3r7c78) <=> 3r7c78 -> 7r5c8 -> 8r5c1 -> 3r4c2 and P(3r4c8) <=> 3r4c8 -> 8r4c2 -> 5r2c2 -> 5r6c1 => -3r6c1 (Th3 TDP part 2)
Sincerely
Robert