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[ArkieTech]

Code: Select all

 *-----------*
 |.5.|.84|...|
 |.6.|.39|.15|
 |9..|...|...|
 |---+---+---|
 |...|1.5|3..|
 |52.|...|.64|
 |..3|8.6|...|
 |---+---+---|
 |...|...|..9|
 |81.|96.|.4.|
 |...|41.|.2.|
 *-----------*


Play/Print this puzzle online

[Leren]

Code: Select all

*---------------------------------------------------*
| 1     5   27   | 267  8   4    | 2679  379   2367 |
| 247   6   8    | 27   3   9    | 247   1     5    |
| 9     3   247  | 2567 57  1    | 2467  78    2678 |
|----------------+---------------+------------------|
| 467   8   4679 | 1    24  5    | 3     79    27   |
| 5     2   1    | 37   9   37   | 8     6     4    |
| 47    479 3    | 8    24  6    | 279   5     1    |
|----------------+---------------+------------------|
| 23467 47  2467 | 357  57 c2378 | 1    d78-3  9    |
| 8     1   257  | 9    6  b237  | 57    4    a37   |
| 37    79  579  | 4    1   378  | 567   2     3678 |
*---------------------------------------------------*

L3 Wing: (3) r8c9 = (3-2) r8c6 = (2-8) r7c6 = (8) r7c8 => - 3 r7c8; stte

Leren

[Ngisa]

Code: Select all

+----------------------+--------------------+---------------------+
| 1        5      27   | 267     8     4    | 2679    379    2367 |
| 247      6      8    | 27      3     9    | 247     1      5    |
| 9        3      247  | 2567    57    1    | 2467   c78     2678 |
+----------------------+--------------------+---------------------+
| 467      8     d4679 | 1       24    5    | 3      c79     27   |
| 5        2      1    | 37      9    a37   | 8       6      4    |
| 47       479    3    | 8       24    6    | 279     5      1    |
+----------------------+--------------------+---------------------+
| 23467    47     2467 | 357     57    2378 | 1      c378    9    |
| 8        1     f57-2 | 9       6    a237  | 57      4      37   |
| 37       79    e579  | 4       1    a378  | 567     2     b3678 |
+----------------------+--------------------+---------------------+


(2=378)r589c6 - (8)r9c9 = (879)r347c8 - (9)r4c3 = (9-5)r9c3 = (5)r8c3 => - 2r8c3; stte

Clement

[SteveG48]

Code: Select all

 *--------------------------------------------------------------------*
 | 1      5      27     | 267    8      4      | 2679   379    2367   |
 | 247    6      8      | 27     3      9      | 247    1      5      |
 | 9      3      247    | 2567   57     1      | 2467   78     2678   |
 *----------------------+----------------------+----------------------|
 | 467    8      4679   | 1      24     5      | 3      79     27     |
 | 5      2      1      | 37     9     c37     | 8      6      4      |
 | 47     479    3      | 8      24     6      | 279    5      1      |
 *----------------------+----------------------+----------------------|
 | 23467  47     2467   | 357    57     2378   | 1     a78-3   9      |
 | 8      1     d257    | 9      6     c237    |d57     4     d37     |
 | 37     79     579    | 4      1     c378    | 567    2     b3678   |
 *--------------------------------------------------------------------*


8r7c8 = r9c9 - (8=237)r489c6 - (2=357)r8c369 => -3 r7c8 ; stte

Hmm. Well at least it's not exactly the same as Leren's.

[SpAce]

Code: Select all

.----------------------.--------------------.----------------------.
|   1       5     27   |  267      8   4    |  2679   b379    2367 |
|   247     6     8    |  27       3   9    |  247     1      5    |
|   9       3     247  |  2567    g57  1    |  2467   f78    f2678 |
:----------------------+--------------------+----------------------:
|   467     8    c4679 |  1        24  5    |  3      b79     27   |
|   5       2     1    |  37       9   37   |  8       6      4    |
|   47      479   3    |  8        24  6    |  279     5      1    |
:----------------------+--------------------+----------------------:
|   2467-3  47    2467 | h(5)7-3  h57  2378 |  1     a[3]78   9    |
|   8       1     257  |  9        6   237  |  57      4      37   |
| d(3)7    d79   d579  |  4        1   378  | e567     2     e3678 |
'----------------------'--------------------'----------------------'

(3)r7c8 = (39)r14c8 - r4c3 = @(973-5)r9c321 = (56-8)r9c79 = (87)r3c98 - r3c5 = (75)r7c54 => -3 r7c14; stte

Edit: corrected a typo in the end node (r7c5 -> r7c54).

[SteveG48]

Interesting. Good clean fun. Both eliminations are needed for the singles solution. How did you come up with that?

I gather that the @ indicates the beginning of the chain within the chain?

[SpAce]

Interesting. Good clean fun. Both eliminations are needed for the singles solution. How did you come up with that?

Hi Steve! Glad you liked it. It was found via my usual coloring method (a variant of GEM). I typically pick the largest Simple Coloring cluster as my starting point and then enlarge it with 3D Medusa and finally with GEM extensions if need be. In this case it was the 9s (eight conjugates). That proved to a bit frustrating choice, as it didn't yield easy stte-eliminations or contradictions (which would have been stte). Starting with the 8s -- the second largest cluster with six conjugates -- would have yielded Leren's solution or its derivatives almost immediately (but there was no way to know that, of course). However, I kept going with my original choice because it still yielded tons of pincer eliminations, though most of them were useless. The two 3s happened to yield some placements, and while ineffective by themselves I noticed that together they were stte. So, I ended up using them because I didn't want to start over with a different cluster to look for a shorter chain.

I gather that the @ indicates the beginning of the chain within the chain?

I'd rather call it the end of the embedded chain if read from left to right. I use the @ to mark additional end-points in relatively simple cases, and then the main start node should be assumed as the other end-point. If there were more embedded chains perhaps using both main end-points, I'd mark it more explicitly this way (the letters corresponding with the grid diagram):

a:(3)r7c8 = (39)r14c8 - r4c3 = d:(973-5)r9c321 = (56-8)r9c79 = (87)r3c98 - r3c5 = h:(75)r7c54 => -3 r7c1 (a-d), -3 r7c4 (a-h); stte

Either way it should provide this derived strong link and conclusion: (3)r7c8 == (973)r9c321&(75)r7c54 => -3 r7c14

With no indications of the multi-headed nature I wouldn't accept the conclusion. In general I try to avoid multi-headers if there's an easy way to turn it into a split-node chain with all end-points clearly at both ends. They just tend to be longer and possibly harder to read.

PS. Here's what GEM coloring taken to the extremes (or a bit over) would yield here:

Code: Select all

.--------------------------.-----------------------.---------------------------.
|  1          5    '7:2    |  26:7    8     4      |  269-7   †9‡3-7  †3:2-67  |
| '2:47       6     8      | '7:2     3     9      |  24-7     1       5       |
|  9          3    '4:2-7  |  256-7  +5-7   1      |  26.7:4  †8‡7     2.6:8-7 |
:--------------------------+-----------------------+---------------------------:
|  67:4       8    †9:467  |  1      '4:2   5      |  3       †7‡9    '2:7     |
|  5          2     1      | +3-7     9    +7-3    |  8        6       4       |
|  47        ‡9.47  3      |  8      '2:4   6      | †9:27     5       1       |
:--------------------------+-----------------------+---------------------------:
|  6.4:2-37  +4-7   26.4-7 | +5-37   +7-5  :23-7†8 |  1       †3‡8-7   9       |
|  8          1    †2‡5-7  |  9       6    "2.3-7  | †5‡7      4      '7:3     |
| +3-7       †9‡7  †5‡9-7  |  4       1   +‡8-37   | †6‡5-7    2     +‡6-37†8  |
'--------------------------'-----------------------'---------------------------'

All of those zillion eliminations are pincer eliminations, i.e. they see par or super candidates of both parities (or proven placements). Only at the very end a contradiction was found too, as the †-parity would empty r7c6 -- so we could immediately place all ‡-candidates and "-candidates, as well as eliminate all †-candidates and .-candidates and the already found trap eliminations. (Btw, I switched from David's postfix notation to prefix notation, along with some other changes. I'd also like to find replacements for the par markers because they're not found on the keyboard.)