The New Sudoku Players' Forum

[200e200w]

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


200e200w

[Leren]

Hodoku and I tied on 12 non-basic moves each to solve this one. Leren

[SteveG48]

Hodoku and I tied on 12 non-basic moves each to solve this one. Leren

Well, that lightens the load. If we take the first 10 non-basic Hodoku moves, we get:

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 *----------------------------------------------------*
 |af345 af34   7    |f126 f126 e168  | 9   f25   8-3  |
 |  2     6    35   | 7    9    48   | 1    45   38   |
 |  8     9    1    | 24   5    3    | 6    24   7    |
 *------------------+----------------+----------------|
 |  7     23   236  | 26   8    9    | 4    1    5    |
 |  14    124  8    | 5    12   7    | 3    9    6    |
 | b59    15  c69   | 3    4   d16   | 7    8    2    |
 *------------------+----------------+----------------|
 |  6     125  25   | 9    7    145  | 8    3    14   |
 |  13    7    4    | 8    13   2    | 5    6    9    |
 | b359   8    39   | 14  c36  d56   | 2    7    14   |
 *----------------------------------------------------*


Then

(3=45)r1c12 - (5=39)r69c1 - (9|3=6)(r6c3&r9c5) - r69c6 = r1c6 - (6=12345)r1c12458 => -3 r1c9 ; stte
Hodoku -1.

Seriously, well done, Leren. This one is a bear.

[Cenoman]

A long path, made of simple steps:

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 +-----------------------+------------------------+------------------+
 | D345-8  B348Z-5 7     |  1246-8 b126   1468    |  9    245  C38   |
 |  2       6      35    |  7       9     48      |  1    45    38   |
 |  48*     9      1     |  248*    5     3       |  6    24    7    |
 +-----------------------+------------------------+------------------+
 |  7       23     236   | d26      8     9       |  4    1     5    |
 |  14X     124Y   8     |  5      c12    7       |  3    9     6    |
 |  159     15yW   569   |  3       4     16      |  7    8     2    |
 +-----------------------+------------------------+------------------+
 |  6       125z   25z   |  9       7     145     |  8    3     14   |
 | E138*    7      4     |  18*     13    2       |  5    6     9    |
 | E1359-8 A18-35  359   |  14-68  a136   14568   |  2    7     14   |
 +-----------------------+------------------------+------------------+

1. X-wing (8*)r38c14 => -8 r19c14
2. (6)r9c5 = (6-2)r1c5 = r5c5 - (2=6)r4c4 => -6 r9c4 (a,b,c,d)
3. (8)r9c2 = r1c2 - (8=3)r1c9 - r1c1 = (3)r89c1 => -3 r9c2 (A,B,C,D,E)
4. (5=1)r6c2 - (1=25)r7c23 => -5 r9c2; 3 placements (y,z)
5. (5=1)r6c2 - (1=4)r5c1 - r5c2 = (4)r1c2 => -5 r1c2 (W,X,Y,Z)

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 +--------------------+--------------------+-----------------+
 |  345u  34    7     |  126   126   168   |  9    25v  38   |
 |  2     6     35    |  7     9     48x   |  1    45w  38   |
 |  8     9     1     | b24    5     3     |  6    24   7    |
 +--------------------+--------------------+-----------------+
 |  7     23    236   | b26    8     9     |  4    1    5    |
 |  14    124   8     |  5     12    7     |  3    9    6    |
 |  159   15   C569   |  3     4   aB16    |  7    8    2    |
 +--------------------+--------------------+-----------------+
 |  6     125z  25z   |  9     7     145y  |  8    3    14   |
 |  13    7     4     |  8     13    2     |  5    6    9    |
 |  39-5  8    D39-5  | b14    36   A56    |  2    7    14   |
 +--------------------+--------------------+-----------------+

6. (1=6)r6c6 - (6=241)r349c4 => -1 r7c6 (a,b)
7. (5=6)r9c6 - r6c6 = (6-9)r6c3 = (9)r9c3 => -5 r9c3 (A,B,C,D)
8. (5)r1c1 = r1c8 - (5=4)r2c8 - r2c6 = (4-5)r7c6 = (5)r7c23 => -5 r9c1; stte (u,v,w,x,y,z)

[SteveG48]

Nice, Cenoman.

We all know how programs like Hodoku work. The programmer programs a set of logical moves for the computer to follow. Then he, or the user, puts them in order (somewhat subjectively) from most basic to most advanced. The computer goes through the possible moves from basic to advanced until it finds an elimination. Then it goes back to the beginning and goes through the list again and again until the puzzle is solved. Human solvers generally follow a similar plan.

You appear to not be strictly following that plan here, since at various stages in your solution somewhat more basic moves are available that you chose not to take. Could you enlighten us about how you approached this thing?

[Cenoman]

Nice, Cenoman.

Thanks, Steve !

We all know how programs like Hodoku work. The programmer programs a set of logical moves for the computer to follow. Then he, or the user, puts them in order (somewhat subjectively) from most basic to most advanced. The computer goes through the possible moves from basic to advanced until it finds an elimination. Then it goes back to the beginning and goes through the list again and again until the puzzle is solved. Human solvers generally follow a similar plan.

In recent exchanges related to 200e200w's Nightmare#16 (here) I made no secrecy about using my solver. This one is my own programming, based on champagne's "Full tagging method"(here). Fundamentally, it calculates comprehensively all AIC's (embedding ANS's and/or AHS's). At the first level, these AIC's find eliminations. The second level is the search of additional eliminations from krakens. More complex eliminations from multi-krakens are the third level (finding nets).

You appear to not be strictly following that plan here, since at various stages in your solution somewhat more basic moves are available that you chose not to take. Could you enlighten us about how you approached this thing?

For the present puzzle, the first run of the first level does not solve the puzzle. No solving single step is found at the second neither third level. In such a case, I run again the first level starting from the puzzle status after the first run. Here, the puzzle is solved. I sort the efficient eliminations in this second run, and then, back to the first run, I sort eliminations that are required by the chosen steps in the second run. These choices are human-made and subjective (very often, other choices are possible, with a lot of combinations). It happened sometimes that I missed the benefits of a first run elimination that looked rather inefficient.

As there is no hierarchy within my first level, some simple moves may be discarded as far as they don't contribute to the solution. Anyhow, there is a large part of human intervention in such a sorting process. I just ask the computer to help me in tedious calculations of derived weak and strong links.

[SteveG48]

Thanks, Cenoman!

[SpAce]

Here's my pure p&p (pencil and paper) solution:

1. Kraken Cell r4c3 (236) => [(5)r9c6 | (8)r2c6 | (8)r8c4] * => -8 r9c6
2. AIC: (6=2)r4c4 - r5c5 = (2-6)r1c5=(6)r9c5 => -6 r9c4
3. AIC: (3=5)r2c3 - (5=4)r2c8 - r2c6 = (4-5)r7c6 = (5-6)r9c6 = (6-3)r9c5 = (3-1)r8c5 = r8c1 - (1=4)r5c1 - r1c1 = (4)r1c2 => -3 r1c2
4. AIC: (5=2)r7c3 - (2=6)r4c3 - r4c4 = r6c6 - (6=5)r9c6 => -5 r7c6, r9c13
5. AIC: (2)r1c5 = (2-1)r5c5 = r6c6 - (1=4)r7c6 - r9c4 = (4)r3c4 => -2 r3c4; stte

* Step 1:

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(2)r4c3 - (2=5)r7c3 - r7c6 = (5)r9c6
 ||
(3)r4c3 - r2c3 = (3-8)r2c9 = (8)r2c6
 ||
(6)r4c3 - (6=2)r4c4 - r5c5 = (2-4)r5c2 = r5c1 - (4=8)r3c1 - r8c1 = (8)r8c4

=> -8 r9c6

Notes:

1) My original first step was the obvious X-Wing (8 r38/c14) but the Kraken made it moot, so I didn't list it here.
2) Step 5 would be simpler as an XYZ-Wing, but I wrote it here it as I saw it.
3) Step 2 could be rewritten as a WXYZ-Wing(?) or an ALS-XZ, I guess. Again, that's not what I originally saw.