The New Sudoku Players' Forum

[AnotherLife]

This puzzle is rated ER 9.3, and its solution seems to need dynamic forcing chains. Is it really so? As usual, human solutions are appreciated.

Code: Select all

|7.8|...|3..|
|...|2.1|...|
|5..|...|...|
|---+---+---|
|.4.|...|826|
|3..|.8.|...|
|...|1..|.93|
|---+---+---|
|.9.|6..|..4|
|...|.7.|5..|
|...|...|...|

7.8...3.....2.1...5.........4....8263...8.......1...93.9.6....4....7.5...........


[m_b_metcalf]

This puzzle is rated ER 9.3, and its solution seems to need dynamic forcing chains. Is it really so? As usual, human solutions are appreciated.

Well, it does have a backdoor. Does that count?

Regards,

Mike

Hidden Text: Show

7r6c6

[AnotherLife]

Well, it does have a backdoor. Does that count?

Hello, Mike,
Can you prove by logical means that r6c6=7 ?

[m_b_metcalf]

Hello, Mike,
Can you prove by logical means that r6c6=7 ?

Sorry, no.

Mike

[yzfwsf]

All the solution path only need ALS Chain.

Hidden Text: Show

Code: Select all

BT steps
2r789c1 = (2-8)r6c1 = (8-5)r6c2 = 5r9c2 =>r9c2<>2
9r2c1 = r4c1 - (9=5)r4c5 - (5=3469)r2c1235 => r2c79<>9
7r5c789 = r6c7 - (7=34695)r2c12357 -(5=9)r4c5 - (9=1457)r5c4789 =>r5c236<>7
BT steps
9r1c456 = (9-2)r1c9 = (2-1)r1c2 = (1-3)r3c2 = 3r3c5 =>r3c5<>9
(3=4697)r2c1237 - (7=125)r7c157 - (5=9)r4c5 - (9-1)r4c1 - (1=2)r7c1 -(2=1476)r2567c7 =>r2c2=3
BT steps
(5=4697)r2c1357 - (7=125)r7c157 -(5=9)r4c5 - (9-1)r4c1 - (1=2)r7c1 -(2=1476)r2567c7 -(6-495)r2c135 =>r2c5=5
BTE

[Cenoman]

In three krakenless steps:

Code: Select all

 +------------------------------+---------------------------+--------------------------+
 |  7       126       8         |  459     4569    4569     |  3       1456    1259    |
 |  469     36        3469      |  2      e34569   1        | c4679   d45678  d5789    |
 |  5       1236      123469    |  78      3469    78       |  12469   146     129     |
 +------------------------------+---------------------------+--------------------------+
 |  19      4         1579      |  3579   f59      3579     |  8       2       6       |
 |  3       26-7      269-7     | g479     8       2469-7   |gb147   ga1457  ga157     |
 |  268     25678     2567      |  1       2456    24567    | b47      9       3       |
 +------------------------------+---------------------------+--------------------------+
 |  128     9         12357     |  6       125     2358     |  127     1378    4       |
 |  12468   12368     12346     |  3489    7       23489    |  5       1368    1289    |
 |  12468   1235678   1234567   |  34589   12459   234589   |  12679   13678   12789   |
 +------------------------------+---------------------------+--------------------------+

1. (7)r5c89 = r56c7 - r2c7 = (78-5)r2c89 = r2c5 - (5=9)r4c5 - (9=1457)r5c4789 => -7 r5c236; HP(57)r69c2, 2 singles & ls

Code: Select all

 +-------------------------+---------------------------+--------------------------+
 |  7      126    8        |  459     469-5   4569     |  3       1456    1259    |
 |  469    36     469      |  2      a34569   1        | c4679   b578-46 b578-9   |
 |  5      1236   2469     |  78      3469    78       |  12469   146     129     |
 +-------------------------+---------------------------+--------------------------+
 |  19     4      1579     |  3579    9-5     3579     |  8       2       6       |
 |  3      26     269      |  479     8       2469     |  14-7    1457    157     |
 |  8      57     2567     |  1       246-5   24567    |  4-7     9       3       |
 +-------------------------+---------------------------+--------------------------+
 | d12     9      357-1    |  6      d125     358-2    | d127     378-1   4       |
 |  1246   8      1346     |  349     7       2349     |  5       136     129     |
 |  1246   57     134567   |  34589   1249-5  234589   |  1269-7  13678   12789   |
 +-------------------------+---------------------------+--------------------------+

2. (5)r2c5 = (58-7)r2c89 = r2c7 - (7=125)r7c157 loop => -5 r1469c5, -46 r2c8, -9 r2c9, -7 r569c7, -1 r7c38, -2 r7c6; 23 placements & ls

Code: Select all

 +-------------------+------------------+-------------------+
 |  7    12    8     |  9    46   46    |  3    15    125   |
 |  9    3     4     |  2    5    1     |  6    78    78    |
 |  5    126   26    |  78   3    78    |  29   4     129   |
 +-------------------+------------------+-------------------+
 |  1    4     57*   |  57*  9    3     |  8    2     6     |
 |  3    26    9     |  4    8    26    |  1    57    57    |
 |  8    57    26    |  1    26   57    |  4    9     3     |
 +-------------------+------------------+-------------------+
 |  2    9     3-5   |  6    1    58    |  7    38    4     |
 |  4    8     1     |  3    7    29    |  5    6     29    |
 |  6    57*   357*  |  58*  24   249   |  29   138   18    |
 +-------------------+------------------+-------------------+

3. Finned X-Wing (5)r4c3 = r4c4 - r9c4 = r9c23 => -5 r7c3; ste

Note: in step 1, -7r5c2 and in step 2, -5r4c5 are the effective eliminations;

[AnotherLife]

Hi YZF,
Have you implemented ALS-nodes in your solver? I've been waiting for a long time.

Hi Cenoman,
Did you use YZF's hint (frankly)?

I have taken this example from Denis Berthier's book 'Pattern-Based Constraint Satisfaction and Logic Puzzles (Second Edition)', and Denis says on page 264, "This puzzle has moderate complexity (though it is on the high side of the fuzzy boundary of puzzles solvable by humans)..." As usual, Denis had solved it with whips, and I tried to find an alternative human solution. It is easy to see many almost locked sets in the resolution state after the basic steps, so it is natural to try ALS-based methods. This is my solution.

Code: Select all

.-------------------------.-----------------------.----------------------.
| 7      126      8       | 459    4569    4569   | 3      1456    1259  |
| c469   c36      c3469   | 2      c34569  1      | c4679  45678   5789  |
| 5      1236     123469  | 78     3469    78     | 12469  146     129   |
:-------------------------+-----------------------+----------------------:
| 19     4        1579    | 3579   b59     3579   | 8      2       6     |
| 3      26-7     269-7   | a479   8       2469-7 | ae147  ae1457  ae157 |
| 268    25678    2567    | 1      2456    24567  | d47    9       3     |
:-------------------------+-----------------------+----------------------:
| 128    9        12357   | 6      125     2358   | 127    1378    4     |
| 12468  12368    12346   | 3489   7       23489  | 5      1368    1289  |
| 12468  1235678  1234567 | 34589  12459   234589 | 12679  13678   12789 |
'-------------------------'-----------------------'----------------------'


1. AIC with a group and ALS's
(7=9)r5c4789 - (9=5)r4c5 - (5=7)r2c12357 - r6c7 = r5c789 => -7 r5c236; naked quad in c2 => 8r8c2, 8r6c1; lc

Code: Select all

.--------------------.-----------------------.-----------------------.
| 7     126   8      | 459    469-5   4569   | 3       1456    1259  |
| a469  a36   a469   | 2      a34569  1      | a4679   578-46  578-9 |
| 5     1236  2469   | 78     3469    78     | 12469   146     129   |
:--------------------+-----------------------+-----------------------:
| 19    4     1579   | 3579   9-5     3579   | 8       2       6     |
| 3     26    2679   | 479    8       24679  | 14-7    1457    157   |
| 8     57    2567   | 1      246-5   24567  | 4-7     9       3     |
:--------------------+-----------------------+-----------------------:
| b12   9     357-1  | 6      b125    358-2  | b127    378-1   4     |
| 1246  8     1346   | 349    7       2349   | 5       136     129   |
| 1246  57    134567 | 34589  1249-5  234589 | 1269-7  13678   12789 |
'--------------------'-----------------------'-----------------------'


2. Doubly Linked ALS-XZ (note that the first ALS is the same as in step 1)
(5=7)r2c12357 - (7=5)r7c157 - (5=7)r2c12357 => -5 r1469c5, -7 r569c7, -46 r2c8, -9 r2c9, -1 r7c38, -2 r7c6; singles and lc

Code: Select all

.-------------.--------------.--------------.
| 7  12   8   | 9   46  46   | 3   15   125 |
| 9  3    4   | 2   5   1    | 6   78   78  |
| 5  126  26  | 78  3   78   | 29  4    129 |
:-------------+--------------+--------------:
| 1  4    7-5 | 57  9   3    | 8   2    6   |
| 3  26   9   | 4   8   26   | 1   57   57  |
| 8  *57  26  | 1   26  *57  | 4   9    3   |
:-------------+--------------+--------------:
| 2  9    *35 | 6   1   *58  | 7   38   4   |
| 4  8    1   | 3   7   29   | 5   6    29  |
| 6  7-5  357 | 58  24  249  | 29  138  18  |
'-------------'--------------'--------------'


3. There are many ways to continue, and this one seems the simplest:
Skyscraper (5) r67 => -5 r4c3, r9c2; ste

And again, this puzzle proves to be of ALSC-class, but without the appendix 'long', as it is solvable in three steps. I think that its complexity is comparable to this one. I was greatly surprised that Andrew Stuart's Solver was unable to solve this puzzle, and I got the message, "Run out of known strategies."

P.S. Denis, thanks for the puzzle.

[yzfwsf]

Hi YZF,
Have you implemented ALS-nodes in your solver? I've been waiting for a long time.

Yes, I am going to include the ALS node in AIC, and I am debugging the code. The biggest problem now is that I have not thought of a good way to include the ALS node in the dynamic chain, so I am not in a hurry to launch a new version.

[eleven]

1. AIC with a group and ALS's
(7=9)r5c4789 - (9=5)r4c5 - (5=7)r2c12357 - r6c7 = r5c789 => -7 r5c236

Note that such a chain is much easier to spot for manual solvers with hidden sets:

Code: Select all

  +-----------+-----------+-----------+
  | *7  . *8  |  .  .  .  |  3  .  .  |
  |  .  .  .  | '2  x  1  |  x  -  -  |
  | *5  .  .  |  .  .  .  |  .  .  .  |
  +-----------+-----------+-----------+
  |  .  4  .  |  .  59 .  | *8 '2 '6  |
  |  3  y  y  |  - *8  y  |  .  .  .  |
  |  .  .  .  |  1  .  .  |  . '9  3  |
  +-----------+-----------+-----------+
  |  . '9  .  | '6  .  .  |  .  .  4  |
  |  .  .  .  |  . *7  .  | *5  .  .  |
  |  .  .  .  |  .  .  .  |  .  .  .  |
  +-----------+-----------+-----------+

The almost hidden triple 578 in r2 gives the link 5r2c5 = 7r2c7
The almost hidden triple 269 in r5 gives the link 9r5c4 = 269r5c236
5r4c5 == 7r2c7 - r56c7 = 7r5c89
||
9r4c5 - 9r5c4 == 269r5c236
=> -7r5c236, hidden triple 578 in r689c2

[Added:] corrected typo, thx to jco

The 2nd chain then can be reduced to
5r2c5 == 7r2c7 - (7=125)r7c175, loop => -5r1469c5, -7r3569

[AnotherLife]

Note that such a chain is much easier to spot for manual solvers with hidden sets...
...
=> -7r5c236, hidden triple 578 in r689c2...

Hi Eleven,
You see, I have some problems with hidden sets, and I do not always spot even a hidden pair. I understand that it is very hard for most solvers to find an ALS of 6 elements, but it is possible after some training (maybe hard). When I started to solve this puzzle, I knew a priori only that it was solvable by ALS-based methods, and I worked out my own solution. Firstly I spotted that the set (3469)r2c123 was almost locked, then (34569)r2c1235 was almost locked, then (345679)r2c12357 also was. The same was true of the sets (1457)r5c789 and (14579)r5c4789. By the way, another succession of almost locked sets could be found in c2: (1236)r123c2, (12367)r1235c2, (123678)r12358c2. After that, I tried to combine these 'atomic' patterns into chains, and I got my solution.

[Cenoman]

Hi Cenoman,
Did you use YZF's hint (frankly)?

Hi Bogdan,
Your suspicious question is a bit disappointing.
The answer is "of course, I didn't"
If you look at my past messages you could see that I quite always aknowledge my borrowings.

Anyhow, for the present puzzle, I do not need help of any external solver. My own does the job rather well.

The first technique used is precisely your favourite: AIC's with (potentially) ALS nodes (or equivalent AHS nodes). If this technique is not enough, then I use three (or four, even five) way logic (simple krakens) and if this is not yet enough, then I use multikrakens (giving nets).
Now, for puzzles as this recent one, if the solution with AIC's only is aburdly long, I try to lower the number of steps with krakens.
For puzzles at ratings such the present one, don't ask me to solve them manually: it's too much time consuming.

[AnotherLife]

Ok, Cenoman, let me explain myself.

All the solution path only need ALS Chain.

You had posted your solution in 26 minutes after YZF's post, and I thought that they were somehow connected. Sorry if I was wrong. I did not mean that you had used YZF_Solver.

For puzzles at ratings such the present one, don't ask me to solve them manually: it's too much time consuming.

Actually, a high ER is not always informative, and I will continue to prove it in the future. I agree that solving extreme puzzles takes much time. Frankly speaking, I solved the current puzzle in several sessions, and I postponed it when I got stuck, but as it was a challenge for me to solve it manually, I had to find the solution.
P.S. I see no reason to quarrel with you.

[Cenoman]

Ok, Cenoman, let me explain myself.
...
Actually, a high ER is not always informative, and I will continue to prove it in the future. I agree that solving extreme puzzles takes much time.
...
P.S. I see no reason to quarrel with you.

I see no reason to quarrel with you, either !

As regards ER ratings, I definitely will not quarrel with you, nor with anybody else: I'm not interested at all with rating discussions.
As regards the puzzles that you qualify "extreme puzzles", if you have in mind the examples treated in the last weeks, I'd would not qualify any of them as extreme. To me, extreme puzzles are rated at ER > 10.5 (i.e. puzzles posted by David Filmer on Sudokuwiki.org or puzzles gathered in the "Hardest Database") And in the interval, there is a kind of grey zone, with puzzles having long and tedious solutions (sometimes called "puzzles for masochists")

I welcome your contributions to the forum. Please keep on posting them.

[AnotherLife]

As regards the puzzles that you qualify "extreme puzzles", if you have in mind the examples treated in the last weeks, I'd would not qualify any of them as extreme. To me, extreme puzzles are rated at ER > 10.5 ...

I think your point of view is unconventional in this case. As to the current puzzle (and many other puzzles I posted recently), HoDoKu and YZF_Solver rate it as 'extreme', and Andrew Stuart's Solver not only cannot rate it but cannot solve it. As to puzzles rated ER 10-11, YZF_Solver rates them as 'insane' (I am not sure if this a conventional approach).