The New Sudoku Players' Forum

[999_Springs]

I find 17-clue puzzles with no 9s in them annoying but not as annoying as this one.

Standard techniques take us to:

Code: Select all

4   8     7   3  12   12  56 9  56
59  359   39  6  48   48  2  7  1
1   2     6   57 9    57  3  8  4
7   34    5   89 348  489 1  6  2
69  13469 349 2  1346 57  8  34 57
28  1346  28  57 1346 14  57 34 9
58  45    1   48 7    6   9  2  3
3   67    89  1  28   289 4  5  67
269 4679  249 49 5    3   67 1  8

reached after SEVEN hidden pairs.

I then found a turbot fish

Code: Select all

4   8     7   3   12   12  56 9  56
59  359   39  6   48   48  2  7  1
1   2     6   57  9    57  3  8  4
7   34    5   89  348  489 1  6  2
69  13469 349 2   1346 57  8  34 57
28  1346  *28 57  1346 14  57 34 9
*58 45    1   *48 7    6   9  2  3
3   67    *89 1   28   289 4  5  67
269 4679  249 49  5    3   67 1  8

r6c4<>8


which made zero eliminations. Then I found an XYZ-wing

Code: Select all

4   8     7   3   12   12   56 9  56
59  359   39  6   48   *48  2  7  1
1   2     6   57  9    57   3  8  4
7   34    5   *89 348  *489 1  6  2
69  13469 349 2   1346 57   8  34 57
28  1346  28  57  1346 14   57 34 9
58  45    1   48  7    6    9  2  3
3   67    89  1   28   289  4  5  67
269 4679  249 49  5    3    67 1  8

r56c6<>8

which also made zero eliminations. Then I found another one:

Code: Select all

4   8     7    3  12   12  56 9  56
59  359   *39  6  48   48  2  7  1
1   2     6    57 9    57  3  8  4
7   *34   5    89 348  489 1  6  2
69  13469 *349 2  1346 57  8  34 57
28  1346  28   57 1346 14  57 34 9
58  45    1    48 7    6   9  2  3
3   67    89   1  28   289 4  5  67
269 4679  249  49 5    3   67 1  8

r46c3<>3


which also made zero eliminations. Then I found a Sue de Coq (which I hardly ever find in any puzzles at all)

Code: Select all

4    8      7    3   12   12  56 9  56
59   359    39   6   48   48  2  7  1
1    2      6    57  9    57  3  8  4
7    34     5    89  348  489 1  6  2
69   13469  349  2   1346 57  8  34 57
28   1346   28   57  1346 14  57 34 9
58   45     1    48  7    6   9  2  3
3    *67    89   1   28   289 4  5  67
*269 *4679  *249 *49 5    3   67 1  8

r7c123r8c13<>6,7
r9c56789<>4,9

which also makes zero eliminations. Add that up and you get an hour finding 0 eliminations. I cannot progress further than this.

This is by far the most frustrating puzzle I have ever attempted. Help!

[re'born]

Here is the original puzzle

48.3............71.2.......7.5....6....2..8.............1.76...3.....4......5....

From your point:

Code: Select all

 *--------------------------------------------------------------------*
 | 4      8      7      | 3      12     12     | 56     9      56     |
 | 59     359    39     | 6      48     48     | 2      7      1      |
 | 1      2      6      | 57     9      57     | 3      8      4      |
 |----------------------+----------------------+----------------------|
 | 7      34     5      | 89     348    489    | 1      6      2      |
 | 69     13469  349    | 2      1346   57     | 8      34     57     |
 | 28     1346   28     | 57     1346   14     | 57     34     9      |
 |----------------------+----------------------+----------------------|
 | 58     45     1      | 48     7      6      | 9      2      3      |
 | 3      67     89     | 1      28     289    | 4      5      67     |
 | 269    4679   249    | 49     5      3      | 67     1      8      |
 *--------------------------------------------------------------------*


there is a nice little chain that solves the puzzle:

[r9c3]-4-[r7c2]-5-[r7c1]-8-[r8c3]=8=[r6c3]=2=[r9c3], =>r9c3<>4.

I found this by 3D coloring. It can be split up into two moves, an xy-wing and an xy-chain. It is only after the fact that I put it together into one move.

Edit: There is also a uniqueness based move that will solve the puzzle. Using the potential deadly pattern in r24c56<48>, we get:

[r8c6]-9-[r4c6]=9|3=[r4c5]-3-[r4c2]-4-[r7c2]=4=[r7c4]-4-[r9c4]-9-[r8c6], => r8c6<>9.

Edit 2: Okay, here is one more pleasing (at least to me) solution. I think this is some sort of BUG-lite, but I could use some clarification on that point.

Code: Select all

 *--------------------------------------------------------------------*
 | 4      8      7      | 3      12     12     | 56*    9      56*    |
 | 59     359    39     | 6      48     48     | 2      7      1      |
 | 1      2      6      | 57*    9      57*    | 3      8      4      |
 |----------------------+----------------------+----------------------|
 | 7      34     5      | 89     348    489    | 1      6      2      |
 | 69     13469  349    | 2      1346   57*    | 8      34     57*    |
 | 28     1346   28     | 57*    1346   14     | 57*    34     9      |
 |----------------------+----------------------+----------------------|
 | 58     45     1      | 48     7      6      | 9      2      3      |
 | 3      67*    89     | 1      28     289    | 4      5      67*    |
 | 269    67+49  249    | 49     5      3      | 67*    1      8      |
 *--------------------------------------------------------------------*


To avoid a deadly pattern, we must have r9c2<>6,7, solving the puzzle.

[udosuk]

You've both missed to spot/mention a relatively basic SSTS move (XY-wing) from that position:

Code: Select all

 *--------------------------------------------------------------------*
 | 4      8      7      | 3      12     12     | 56     9      56     |
 |*59     359   -39     | 6      48     48     | 2      7      1      |
 | 1      2      6      | 57     9      57     | 3      8      4      |
 |----------------------+----------------------+----------------------|
 | 7      34     5      | 89     348    489    | 1      6      2      |
 | 69     13469  349    | 2      1346   57     | 8      34     57     |
 | 28     1346   28     | 57     1346   14     | 57     34     9      |
 |----------------------+----------------------+----------------------|
 |*58     45     1      | 48     7      6      | 9      2      3      |
 | 3      67    *89     | 1      28     289    | 4      5      67     |
 |-269    4679   249    | 49     5      3      | 67     1      8      |
 *--------------------------------------------------------------------*

XY-wing:
r7c1=5|8 => one or both of r2c1,r8c3 must be 9
=> r2c3<>9, r9c1<>9

However, it isn't needed. Here is a simple ALS-xz to complement re'born's nice uniqueness/chain moves:

Code: Select all

 *--------------------------------------------------------------------*
 | 4      8      7      | 3      12     12     | 56     9      56     |
 | 59     359   A39     | 6      48     48     | 2      7      1      |
 | 1      2      6      | 57     9      57     | 3      8      4      |
 |----------------------+----------------------+----------------------|
 | 7     -34     5      | 89     348    489    | 1      6      2      |
 | 69    -13469 A349    | 2      1346   57     | 8      34     57     |
 | 28    -1346   28     | 57     1346   14     | 57     34     9      |
 |----------------------+----------------------+----------------------|
 |B58    B45     1      | 48     7      6      | 9      2      3      |
 | 3      67    A89     | 1      28     289    | 4      5      67     |
 | 269    4679  -249    | 49     5      3      | 67     1      8      |
 *--------------------------------------------------------------------*

ALS-xz:
ALS A: r258c3={3489}
ALS B: r7c12={458}
restricted common: x=8
common: z=4

Therefore r456c2<>4 & r9c3<>4, and the puzzle is solved.

[re'born]

You've both missed to spot/mention a relatively basic SSTS move (XY-wing) from that position:

Au contraire!

I found this by 3D coloring. It can be split up into two moves, an xy-wing and an xy-chain. It is only after the fact that I put it together into one move.

[udosuk]

Au contraire!

Désolé!

[Steve R]

As it happens, the puzzle also responds to an observation George Woods made recently.

After the xy-wing we have:

Code: Select all

 *------------------------------------------------------------------*
 | 4      8      7    | 3      12     12     | 56     9      56     |
 | 59     359    3    | 6      48     48     | 2      7      1      |
 | 1      2      6    | 57     9      57     | 3      8      4      |
 |--------------------+----------------------+----------------------|
 | 7      34     5    | 89     348    489    | 1      6      2      |
 | 69     13469  49   | 2      1346   57     | 8      34     57     |
 | 28     1346   28   | 57     1346   14     | 57     34     9      |
 |--------------------+----------------------+----------------------|
 |B58     45     1    | 48     7      6      | 9      2      3      |
 | 3      67     89   | 1      28     289    | 4      5      67     |
 | 269    4679   249  | 49     5      3      | 67     1      8      |
 *------------------------------------------------------------------*

r5c3 and r9c4 contain the same two candidates (49). The cells are linked by the conjugates for 9 in the eighth row, so one must contain a 4. Thus 4 may be eliminated from r9c3 and the puzzle is again solved.

Of course the argument is equivalent to a short nice loop. However, as the base cells contain the same two candidates, the pattern (a w-wing?) is particularly easy to spot.

Steve

[re'born]

Ah, nicely spotted Steve. I'm disappointed I didn't see it as we had been discussing that pattern a couple of months ago.

[udosuk]

Of course the argument is equivalent to a short nice loop. However, as the base cells contain the same two candidates, the pattern (a w-wing?) is particularly easy to spot.

Yes, very good spotting Steve. I think this move is called "Y-wing" officially (check re'born's link).

I think your XY-wing+Y-wing route is more elegant than my ALS-xz route.

[999_Springs]

r5c3 and r9c4 contain the same two candidates (49). The cells are linked by the conjugates for 9 in the eighth row, so one must contain a 4. Thus 4 may be eliminated from r9c3 and the puzzle is again solved.

I spotted the one in 2 and 8 with cells r6c1 and r8c5, linked by the strong link in r7. I didn't spot that one.

Is it just my very bad luck that I find all of these techiques, none of which solve the puzzle?

[Mike Barker]

If it makes you feel any better one reason I started developing my solver was for the same feeling of wasting time looking for something that wasn't there or wouldn't help. I would probably be a better manual solver if I spent more time learning to quickly recognize patterns and spent less time on my solver. By quickly spotting the patterns the frustration of not being able to use them will be reduced. It sounds as if you've already come a long way in this direction.

A couple of recommendations which you may already know.

I honestly wouldn't look for Turbot Fish, but focus on the strong links. The advantage is the strong links are pretty easy to see, but more importantly you can cover a lot more ground. I've already pointed out that a skyscraper (one of the three types of "Turbot Fish" in Havard's aquarium) is the same as a sashimi X-wing so search for both together. Grouped skyscrapers are equivalent to finned X-wings and there are a lot more finned fish in the tank then unfinned.

The second type of "Turbot Fish" is, for lack of a better name, a "turbot fish" and consists of strong links in a box and in a line. This is equivalent to an Empty Rectangle, so search for both together again including the "finned/grouped" variety. FYI it's also a franken fish, but I'm not sure that that fact will lead to more eliminations.

The third type is a kite which is a mutant fish (kind of cool that the three types of Turbot Fish map the the three types of Ultimate Fish!). This probably doesn't extend well to additional replacements, however, by focusing on the strong links they are pretty easy to find. Again look for the grouped variety. Interestingly a question about a grouped Turbot Fish is what brought me to this forum in the first place.

You can do a similar thing with XY-wings. You found an XYZ-wing which wasn't much help, but a WXYZ-wing would have solved the puzzle following the XY-wing. By focusing on all three you have a better chance of finding an elimination. The only difference is the size of the ALS which, because it can be contained in a box, is a little more palatable then general ALS. Also note that in the method hierarchy WXYZ-wings are about twice as effective as XYZ-wings for solving puzzles.

The hierarchy also suggests a lot of bang for the buck with short XY-chains and nice loops. Focusing on these might (and I do mean might because I haven't tried it) lead to more satisfying eliminations.

[re'born]

If it makes you feel any better one reason I started developing my solver was for the same feeling of wasting time looking for something that wasn't there or wouldn't help. I would probably be a better manual solver if I spent more time learning to quickly recognize patterns and spent less time on my solver. By quickly spotting the patterns the frustration of not being able to use them will be reduced. It sounds as if you've already come a long way in this direction.

A couple of recommendations which you may already know.

I honestly wouldn't look for Turbot Fish, but focus on the strong links. The advantage is the strong links are pretty easy to see, but more importantly you can cover a lot more ground. I've already pointed out that a skyscraper (one of the three types of "Turbot Fish" in Havard's aquarium) is the same as a sashimi X-wing so search for both together. Grouped skyscrapers are equivalent to finned X-wings and there are a lot more finned fish in the tank then unfinned.

The second type of "Turbot Fish" is, for lack of a better name, a "turbot fish" and consists of strong links in a box and in a line. This is equivalent to an Empty Rectangle, so search for both together again including the "finned/grouped" variety. FYI it's also a franken fish, but I'm not sure that that fact will lead to more eliminations.

The third type is a kite which is a mutant fish (kind of cool that the three types of Turbot Fish map the the three types of Ultimate Fish!). This probably doesn't extend well to additional replacements, however, by focusing on the strong links they are pretty easy to find. Again look for the grouped variety. Interestingly a question about a grouped Turbot Fish is what brought me to this forum in the first place.

You can do a similar thing with XY-wings. You found an XYZ-wing which wasn't much help, but a WXYZ-wing would have solved the puzzle following the XY-wing. By focusing on all three you have a better chance of finding an elimination. The only difference is the size of the ALS which, because it can be contained in a box, is a little more palatable then general ALS. Also note that in the method hierarchy WXYZ-wings are about twice as effective as XYZ-wings for solving puzzles.

The hierarchy also suggests a lot of bang for the buck with short XY-chains and nice loops. Focusing on these might (and I do mean might because I haven't tried it) lead to more satisfying eliminations.

Very interesting and informative post Mike (as usual). I have a question about the WXYZ-wing. Typically, I think of a WXYZ-wing as having 4 candidates in the pivot cell, but I don't see any nice opportunities for one in this grid. Does one also allow for a WXYZ-wing with only 3 candidates in the pivot cell such as:

Code: Select all

 *--------------------------------------------------------------------*
 | 4      8      7      | 3      12     12     | 56     9      56     |
 | 59     359    39     | 6      48     48     | 2      7      1      |
 | 1      2      6      | 57     9      57     | 3      8      4      |
 |----------------------+----------------------+----------------------|
 | 7      34     5      | 89     348    489    | 1      6      2      |
 | 69     13469  349    | 2      1346   57     | 8      34     57     |
 | 28     1346   28%    | 57     1346   14     | 57     34     9      |
 |----------------------+----------------------+----------------------|
 | 58     45     1      | 48     7      6      | 9      2      3      |
 | 3      67     89%    | 1      28     289    | 4      5      67     |
 | 269-   4679-  249*   | 49%    5      3      | 67     1      8      |
 *--------------------------------------------------------------------*


(where r9c3 is the pivot cell and r68c3,r9c4 are the wings). The upshot of this elimination is that it can be done before the xy-wing and still give the same eliminations. Is this the elimination your solver found, or is there another in the grid?

[Mike Barker]

There was some interesting discusion of what should and shouldn't be an WXYZ wing here. Discussion ranged from it must have a 4 candidate pivot cell to what you are showing which is also an ALS xz-rule with a bivalue cell and a 4 candidate ALS. My belief was that restricting them to 4-candidate pivots was overly restrictive since such structures don't occur often (kind of like only searching for X-wings when there are so many more finned X-wings out there). On the other hand, the technique should be a stepping stone to ALS xz-rule. I compromised by requiring the ALS to be in a box, but this is not necessary. What you show is a valid generalized WXYZ-wing. This just further underscores the idea of looking for eliminations based on identifying groups of techniques. How large the group is is a function of experience.