The New Sudoku Players' Forum

[jovi_al01]

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+-----------------------------------+
| 8   .   .   .   .   .   .   .   6 |
|                                   |
| .   .   .   .   2   .   .   .   . |
|                                   |
| .   .   2   5   .   4   1   .   . |
|                                   |
| .   .   1   .   6   .   3   .   . |
|                                   |
| .   4   .   .   .   .   .   1   . |
|                                   |
| .   .   3   .   .   .   5   .   . |
|                                   |
| .   .   5   4   .   1   2   .   . |
|                                   |
| .   .   .   .   3   .   .   .   . |
|                                   |
| 9   .   .   .   .   .   .   .   7 |
+-----------------------------------+
8.......6....2......25.41....1.6.3...4.....1...3...5....54.12......3....9.......7

[Leren]

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*---------------------------------------------------------*
| 8    5     4     |*379    1    *379    |*79    2    6   |
| 1    3    *79    |*6789   2    *6789   |*789   4    5   |
| 67   679   2     | 5      789   4      | 1     789  3   |
|------------------+---------------------+----------------|
| 257  789   1     |*2789   6    *25789  | 3     789  4   |
| 2567 4     678-9 |*23789 f5789 *235789 | 678-9 1    289 |
| 267  6789  3     | 1      4     2789   | 5     6789 289 |
|------------------+---------------------+----------------|
| 3    678   5     | 4      789   1      | 2     689  89  |
| 4    2     678   |*6789   3    *6789   |*689   5    1   |
| 9    1     68    | 268    58    2568   | 4     3    7   |
*---------------------------------------------------------*

Finned Franken Jellyfish in 9's r128b5 c3467 with a fin Cell r5c5 => - 9 r5c37; basics

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*------------------------------------------------------*
| 8     5     4   | 379    1     379    | 79  2    6   |
| 1     3     9   | 678    2     678    | 78  4    5   |
| 67    67    2   | 5      89    4      | 1   89   3   |
|-----------------+---------------------+--------------|
| 257   789   1   | 2789   6     25789  | 3   789  4   |
| 2567  4    a678 | 23789  589-7 235789 | 68  1    289 |
| 267   6789  3   | 1      4     2789   | 5   6789 289 |
|-----------------+---------------------+--------------|
| 3    c678   5   | 4     d789   1      | 2   689  89  |
| 4     2    b678 | 6789   3     6789   | 689 5    1   |
| 9     1     68  | 268    58    2568   | 4   3    7   |
*------------------------------------------------------*

Kite : (7) r5c3 = r8c3 - r7c2 = (7) r7c5 => - 7 r5c5; btte

[eleven]

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

7/9 in r5c5 lead to locked candidates in r8c46, 7/9 in r2c3 and lc in r1c46.
This kills all digits in c7.
8 in r5c5 leads to locked candidates in r2c46, 8r8c7 and lc in r9c46, killing all 8's in c3.
=> -789r5c5, stte
(maybe some named fish)

[Cenoman]

(maybe some named fish)

No new solution from me, just a follow up of eleven's note about named fish, in his nice solution.

Code: Select all

 +-----------------------+--------------------------+----------------------+
 |  8      5      4      |  379     1      379      |  79     2      6     |
 |  1      3      79     |  6789    2      6789     |  789    4      5     |
 |  67*    679*   2      |  5       789*   4        |  1      789*   3     |
 +-----------------------+--------------------------+----------------------+
 |  257*   789*   1      |  2789#   6      25789#   |  3      789*   4     |
 |  2567   4      6789   |  23789   5-789  235789   |  6789   1      289   |
 |  267*   6789*  3      |  1       4      2789#    |  5      6789*  289*  |
 +-----------------------+--------------------------+----------------------+
 |  3      678*   5      |  4       789*   1        |  2      689*   89*   |
 |  4      2      678    |  6789    3      6789     |  689    5      1     |
 |  9      1      68     |  268     58     2568     |  4      3      7     |
 +-----------------------+--------------------------+----------------------+

Without candidates in box 5, the four rows r3467 contain instances of each digit 7, 8, 9 (at least two) in four columns => these cells form three basic Jellyfishes. With 7b5p139, 8b5p139, 9b5p139 resp., they form finned Jellyfishes eliminating 7r5c5, 8r5c5, 9r5c5 resp.

In detail:
1. Finned Jellyfish (7)r3467\c1258 fb5p139 => -7 r5c5;
2. Finned Jellyfish (8)r3467\c2589 fb5p139 => -8 r5c5;
3. Finned Jellyfish (9)r3467\c2589 fb5p139 => -9 r5c5; ste

Count three steps or one step, up to you !

[jovi_al01]

wonderful solutions all! i wanted to share my line of thinking here

if you consider the structure of r37c37, with the corners of the grid, you could draw some parallels between this and SK loop.
with this line of thinking, you could note that r3c5, r5c3, r5c7, and r7c5 form a strange quadruple on 6789, all seeing r5c5.

of course, the finned fish work too, but this is a slightly fancier way of thinking, i think

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 8      5      4      ! 379    1      379    ! 79     2      6      !
   ! 1      3      79     ! 6789   2      6789   ! 789    4      5      !
   ! 67     679    2      ! 5      789    4      ! 1      789    3      !
   +----------------------+----------------------+----------------------+
   ! 257    789    1      ! 2789   6      25789  ! 3      789    4      !
   ! 2567   4      6789   ! 23789  5789   235789 ! 6789   1      289    !
   ! 267    6789   3      ! 1      4      2789   ! 5      6789   289    !
   +----------------------+----------------------+----------------------+
   ! 3      678    5      ! 4      789    1      ! 2      689    89     !
   ! 4      2      678    ! 6789   3      6789   ! 689    5      1      !
   ! 9      1      68     ! 268    58     2568   ! 4      3      7      !
   +----------------------+----------------------+----------------------+
134 candidates.

The simplest-first solution is in Z4.
There's no 1-step or 2-step solution with whips of reasonable length.

What's interesting with this puzzle is an illustration of the limitations of any steepest-descent algorithm - I'm thinking in particular of the fewer-steps algorithm.
On a first try, I found a solution in 4 non-W1 steps:

whip[4]: c2n9{r6 r3} - c5n9{r3 r7} - r8n9{c6 c7} - b3n9{r1c7 .} ==> r5c3≠9
hidden-single-in-a-column ==> r2c3=9
whip[1]: b1n7{r3c2 .} ==> r3c5≠7, r3c8≠7
whip[1]: c8n7{r6 .} ==> r5c7≠7
z-chain[3]: b7n7{r8c3 r7c2} - c5n7{r7 r5} - c3n7{r5 .} ==> r8c3≠6, r8c6≠7, r8c4≠7, r8c3≠8, r7c2≠7, r5c3≠7
with z-candidates = n7r8c3
naked-single ==> r8c3=7
hidden-single-in-a-row ==> r7c5=7
whip[1]: r7n9{c9 .} ==> r8c7≠9
biv-chain[2]: r3n9{c5 c8} - c7n9{r1 r5} ==> r5c5≠9
hidden-single-in-a-column ==> r3c5=9
naked-single ==> r3c8=8
naked-single ==> r2c7=7
naked-single ==> r1c7=9
biv-chain[4]: r9c3{n6 n8} - c5n8{r9 r5} - c7n8{r5 r8} - b9n6{r8c7 r7c8} ==> r7c2≠6
stte

Each of these steps has a high score (10, 12, 17, 35 final).
But if you consider Cenoman's solution in 3 steps, each of the first 2 steps has score only 1.
Conclusion: there's no chance of finding this with steepest descent (even if the descent is allowed to choose among candidates with score = best-score -1 or -2)

[DEFISE]

.
What's interesting with this puzzle is an illustration of the limitations of any steepest-descent algorithm - I'm thinking in particular of the fewer-steps algorithm.

Certainly, but this case is easily identifiable since we have a CSP-variable (r5c5) which contains a W1-backdoor (the 5) and of which all the other candidates (7,8,9) are the target of certain rules.
It is therefore sufficient to complete "fewer-steps" by searching for such CSP-variables, of minimum size.

N.B: I believe this case was already produced in some other puzzles, but since this was a 3-candidate CSP-variable (producing a 2-step solution) you didn't need "fewer-steps" since you have another program that systematically searches for all 2-step solutions.

1. Finned Jellyfish (7)r3467\c1258 fb5p139 => -7 r5c5;
2. Finned Jellyfish (8)r3467\c2589 fb5p139 => -8 r5c5;
3. Finned Jellyfish (9)r3467\c2589 fb5p139 => -9 r5c5; ste

I have not implemented the finned- (Xwing, Swordfish, Jellyfish) because I have found very often that they could be replaced by a whip of the same size. This is the case here: 7r5c5, 8r5c5, 9r5c5 are each the target of a
whip [4].

[denis_berthier]

.
What's interesting with this puzzle is an illustration of the limitations of any steepest-descent algorithm - I'm thinking in particular of the fewer-steps algorithm.

Certainly, but this case is easily identifiable since we have a CSP-variable (r5c5) which contains a W1-backdoor (the 5) and of which all the other candidates (7,8,9) are the target of certain rules.
It is therefore sufficient to complete "fewer-steps" by searching for such CSP-variables, of minimum size.

Right, but fewer-steps (and any systematic method for reducing the number of steps) is based on T&E-ish techniques (first "step" is finding anti-backdoors, anti-backdoor-pairs or finding and evaluating all the erasable candidates...). Having first to look for the backdoors would add one more T&E-ish step at the start (with no guarantee that the selected cell would lead to a solution).

Such a T&E-ish technique isn't a problem for a program, but I doubt any manual solver could do this. We'll probably never know, because there are not many participants in this section of the forum claiming to be manual solvers (and, from all the over-complicated solutions that are proposed here, it's obvious there are still fewer that really are).

Anyway, the situation in this puzzle, with a backdoor in an rc-cell and 3 similar patterns having other candidates in the same rc-cell as their targets, is extremely rare. Due credit for it goes to the puzzle designer. Manual solvers expect something special in the puzzles proposed here, and they look for improbable patterns. The game is thus totally biased. I don't think it worth to base any general technique on this example.

The only purpose of my remark was to underline an extreme example where steepest-descent doesn't work. It looks like the following mountain, where you start at x. Steepest descent takes you to the left side; you'll need many steps to reach the base. But, if you had delayed steepest-descent by 2 steps, you'd find the really shortest path.

Code: Select all

 1 bar (—, / or \) is one step)

                                 X
                                 ———
                               /     \
                        ——————        \
                      /                \
               ——————                   \
             /                           \
      ——————                               —————————————


Not only is steepest-descent not guaranteed to find the shortest path, it's also guaranteed not to find it in some easy to imagine cases.

[DEFISE]

I don't think it worth to base any general technique on this example.

With my graphical interface, I can visualize simultaneously T-backdoors and targets of whips[<=n].
So for me the work is already done, at least in semi-automatic mode.

The only purpose of my remark was to underline an extreme example where steepest-descent doesn't work. It looks like the following mountain, where you start at x. Steepest descent takes you to the left side; you'll need many steps to reach the base. But, if you had delayed steepest-descent by 2 steps, you'd find the really shortest path.
...
Not only is steepest-descent not guaranteed to find the shortest path, it's also guaranteed not to find it in some easy to imagine cases.

I have observed this as well and, to reduce this problem a little, I improved my algorithm.
First of all, I remind you my goal is to reduce the number of whips[>=2] (which are patterns with a single target). So that's less general than your “Fewer-steps” algorithm.
In summary, instead of choosing a best score target of a whip[<=n] at each step, my improvement consists in choosing a best score pair of targets.
The score (S) of a pair of targets (t1,t2) is defined as
S = 2 + number of candidates that would be deleted with basics if t1 and t2 were deleted. This, considering that t1 and t2 exist simultaneously as targets in the current resolution state (for version V2A).
But there is a second version (V2b) that allows me to also search for pairs (t1,t2) where t2 only appears as a target after removing t1 and executing basics. In this case I will call (t1,t2) a pair of consecutive targets.
Obviously V2b is much more expensive in execution time than V2a.
Finally I have 3 versions:
V1: For each step, deletion of a best score target. (initial version).
V2a: For each step, deletion of a best score pair of simultaneous targets.
V2b: For each step, deletion of a best score pair of targets (consecutive or simultaneous).

Application to this puzzle (Cornered)
With version V1: in W4 15 tries all gave a path with 3 whips + 1 naked pairs. Here is one:

Hidden Text: Show

20 singles.
Box/Line: 6r3b1 => -6r2c3
whip[4]: b1n9{r2c3 r3c2}- c5n9{r3 r7}- b9n9{r7c8 r8c7}- b3n9{r1c7 .} => -9r5c3
Single: 9r2c3
Box/Line: 7b1r3 => -7r3c5 -7r3c8
Box/Line: 7c8b6 => -7r5c7
whip[2]: r7n7{c5 c2}- c3n7{r8 .} => -7r5c5
Singles: 7r7c5, 7r8c3
Box/Line: 9r7b9 => -9r8c7
whip[2]: c5n9{r3 r5}- c7n9{r5 .} => -9r3c8
Singles: 8r3c8, 7r2c7, 9r1c7, 9r3c5
Naked pairs: 68r5c37 => -6r5c1 -8r5c4 -8r5c5 -8r5c6 -8r5c9
STTE.

With version V2a: in W4 one try gave this path with 2 whips + 2 naked pairs:

Hidden Text: Show

20 singles
Box/Line: 6r3b1 => -6r2c3
whip[4]: r7n7{c5 c2}- c3n7{r8 r2}- r3n7{c1 c8}- c7n7{r1 .} => -7r5c5
whip[4]: c3n9{r5 r2}- r3n9{c2 c8}- r7n9{c8 c9}- b6n9{r5c9 .} => -9r5c5
Naked pairs: 58c5r59 => -8r3c5 -8r7c5
Single: 8r3c8
Box/Line: 7c8b6 => -7r5c7
Box/Line: 9b3c7 => -9r5c7 -9r8c7
Box/Line: 9r8b8 => -9r7c5
Singles: 7r7c5, 9r3c5, 9r1c7, 7r2c7, 9r2c3, 7r8c3
Naked pairs: 68r5c37 => -6r5c1 -8r5c4 -8r5c5 -8r5c6 -8r5c9
STTE

With version V2b: in W4 one try gave the same path.

[jovi_al01]

Such a T&E-ish technique isn't a problem for a program, but I doubt any manual solver could do this. We'll probably never know, because there are not many participants in this section of the forum claiming to be manual solvers (and, from all the over-complicated solutions that are proposed here, it's obvious there are still fewer that really are)... Due credit for it goes to the puzzle designer. Manual solvers expect something special in the puzzles proposed here, and they look for improbable patterns.

i felt the urge to respond to this saying that i am both a manual puzzle solver and puzzle creator, so you're definitely right in saying that there is typically "something special" to be expected in the puzzles i post here

[shye]

.
similar approach to others, different method

Code: Select all

+-------+---------+-------+
|a8a. . | .  .  . | .a.a6 |
|a.a. . | .  2  . | .a.a. |
| . .b2 |b5 b. b4 |b1 . . |
+-------+---------+-------+
| . .b1 | .  6  . |b3 . . |
| . 4b. | .-789 . |b. 1 . |
| . .b3 | .  .  . |b5 . . |
+-------+---------+-------+
| . .b5 |b4 b. b1 |b2 . . |
|a.a. . | .  3  . | .a.a. |
|a9a. . | .  .  . | .a.a7 |
+-------+---------+-------+

the cells marked with 'a' and the cells marked with 'b' contain the same set of digits via SET (b1379 in set a, r37 & c37 in set b)
7, 8 and 9 need to appear in the b cells, and each position points at r5c5
=> -789r5c5 stte

solve enough modern variant sudokus and you will recognise this partition instantly
nice puzzle!