The New Sudoku Players' Forum

[SCLT]

This puzzle solves with only X-Wings and basics... but can you find a one-stepper without the X-Wings?

Code: Select all

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


[SteveG48]

Code: Select all

 *------------------------------------------------------------------------------*
 | c134     9       5       | 6       12     c34      | 7      d2348   d238     |
 |  6       134     8       | 7       12      5       | 9       234    e23      |
 |  2       7       34      | 34      8       9       | 1       56      56      |
 *--------------------------+-------------------------+-------------------------|
 |  9       6      h134     | 134     5       8       | 2       7      e13      |
 |  13458   123458 h1234    | 1349    34-9    7       | 6       1389    1389    |
 | g138    g138     7       | 2       3-9     6       | 5      f1389    4       |
 *--------------------------+-------------------------+-------------------------|
 |bj134    b1234    6       | 5     aj349    j34      | 8      b12-9    7       |
 |  3578    2358    239     | 38-9    67      1       | 4       2569    2569    |
 |  14578   1458   i149     | 48-9    67      2       | 3       1569    1569    |
 *------------------------------------------------------------------------------*


9r7c5 = (291)r7c128 - (1=34)r1c16 - (3|4=82)r1c89 - (2=31)r24c9 - 1r6c8 = r6c12 - r45c3 = r9c3 - (1=349)r7c156 => - 9 r56c5,r7c8,r89c4 ; stte

[SpAce]

Code: Select all

.--------------------------.--------------------.-----------------.
| d134     9         5     |  6        12    34 | 7   2348   238  |
|  6      e1^34      8     |  7        12    5  | 9  e234   e23   |
|  2       7         34    |  34       8     9  | 1   56     56   |
:--------------------------+--------------------+-----------------:
|  9       6        g134   |  134      5     8  | 2   7     f13   |
| g13458  g123458  h(1)234 | a34[9]-1  349   7  | 6   1389   1389 |
| g138    g138       7     |  2        39    6  | 5   1389   4    |
:--------------------------+--------------------+-----------------:
| c1*34    1234      6     |  5       c349  c34 | 8   129    7    |
|  3578    2358      239   | b389      67    1  | 4   2569   2569 |
|  14578   1458      149   | b489      67    2  | 3   1569   1569 |
'--------------------------'--------------------'-----------------'


(9)r5c4 = r89c4 - (9=341*)r7c561 - r1c1 = (1^43)r2c289 - (3=1)r4c9 - b4p3*47^58 = (1)r5c3 => -1 r5c4; stte

As a kraken: Show

Code: Select all

Kraken Box (1)b4

(1)r5c3
||
(1)r4c3 - (1=32)r42c9 - (2=1)r2c5 - r2c2 = r1c1 - (1=349)r7c165 - r89c4 = (9)r5c4
||
(1)r56c1 - (1=349)r7c165 - r89c4 = (9)r5c4
||
(1)r56c2 - r2c2 = r1c1 - (1=349)r7c165 - r89c4 = (9)r5c4

=> -1 r5c4; stte

8x8 TM: Show

Code: Select all

 9r5c4 9r89c4
       9r7c5  34r7c56
              3|4r7c1 1r7c1
                      1r1c1  1r2c1
                             1r2c5  2r2c5
                                    2r2c9 3r2c9
                                          3r4c9 1r4c9
 1b4p6                1b4p47 1b4p58             1b4p3
-----------------------------------------------------
-1r5c4


[SpAce]

Hi Steve!

9r7c5 = (291)r7c128 - (1=34)r1c16 - (3|4=82)r1c89 - (2=31)r24c9 - 1r6c8 = r6c12 - r45c3 = r9c3 - (1=349)r7c156 => - 9 r56c5,r7c8,r89c4 ; stte

That's much nicer than mine! As written, the better conclusion is +9 r7c5, though. And, as usual, it indicates that simplifications could be made. How about something like:

(34=1)r7c61 - r1c1 = (12)r2c25 - (2=31)r24c9 - r6c8 = r6c12 - r45c3 = r9c3 - (1=34)r7c16 => -34 r7c25; stte

Still, the redundant end nodes indicate that further simplifications are available if we give up stte:

(1)r1c1 = (12)r2c25 - (2=31)r24c9 - r6c8 = r6c12 - r45c3 = (1)r9c3 => -1 r79c1; btte

[SteveG48]

Thanks, SpAce. I considered writing it as the +9 solution or, equivalently, -34r7c5 but I guess I'm in a rut.

I knew about the btte solution, but naturally didn't want to give up the singles solution.

It's interesting that we both used a hidden triple with unique placement of the candidates as one of our nodes.

[SpAce]

I knew about the btte solution, but naturally didn't want to give up the singles solution.

Of course not! I just mentioned it because the possibility revealed itself with the alternate writing. It's embedded in the original too, but it didn't jump out to me from that.

It's interesting that we both used a hidden triple with unique placement of the candidates as one of our nodes.

Yeah, it's sometimes an easy workaround to avoid those nasty commas or anded terms when exact placements are needed. The price is that it's not always as intuitive as the alternative. For example, I actually saw mine as (12,3)r2c259 but wrote it (143)r2c289 to drop the comma. The latter is a bit harder to see in the grid, I think. Then again, your solution made me ask myself why I didn't write: (12)r2c25 - (2=31)r24c9.

[RSW]

My solver came up with a 5-fish, then 4-fish, then 3-fish, in that order. (I've still got the search order set up to search for fish in order of decreasing size, just to see how big a fish it can catch.)

Code: Select all

  1     2      3      4    5   6    7 8    9     
+-------------------+-------------+-------------+
| 134   9      5    | 6    12  34 | 7 2348 238  |
| 6     134    8    | 7    12  5  | 9 234  23   |
| 2     7      34   | 34   8   9  | 1 56   56   |
+-------------------+-------------+-------------+
| 9     6      134  | 134  5   8  | 2 7    13   |
| 13458 123458 1234 | 1349 349 7  | 6 1389 1389 |
| 138   138    7    | 2    39  6  | 5 1389 4    |
+-------------------+-------------+-------------+
| 134   1234   6    | 5    349 34 | 8 129  7    |
| 3578  2358   239  | 389  67  1  | 4 2569 2569 |
| 14578 1458   149  | 489  67  2  | 3 1569 1569 |
+-------------------+-------------+-------------+


5-Fish (aka Starfish, Squirmbag): In columns 1 2 5 6 & 8, digit 4 must go in rows 1 2 5 7 & 9
Therefore candidate 4 can be removed from all other cells in rows 1 2 5 7 & 9
Removing candidate 4 from r5c3 r5c4 r9c3 r9c4.

4-Fish (aka Jellyfish): In rows 1 2 6 & 7, digit 1 must go in columns 1 2 5 & 8
Therefore candidate 1 can be removed from all other cells in columns 1 2 5 & 8
Removing candidate 1 from r5c1 r9c1 r5c2 r9c2 r5c8 r9c8.

3-Fish (aka Swordfish): In columns 3 4 & 9, digit 9 must go in rows 5 8 & 9
Therefore candidate 9 can be removed from all other cells in rows 5 8 & 9
Removing candidate 9 from r5c5 r5c8 r8c8 r9c8.

Then basics to end.

(And yes, I realize this wasn't a one stepper, but I thought it was an interesting way to avoid x-wings, by going for bigger fish.)

[SCLT]

For what it's worth, here's the solution I found:

Code: Select all

+-------------------------+-----------------+------------------+
|  c134    9       5      |  6     12  c34  |  7 c2348  c238   |
|   6      134     8      |  7     12   5   |  9  234   d23    |
|   2      7       34     |  34    8    9   |  1  56     56    |
+-------------------------+-----------------+------------------+
|   9      6       34-1   |  134   5    8   |  2  7     d13    |
|   3458-1 23458-1 234-1  |  1349  349  7   |  6  1389   1389  |
| af138  af138     7      |  2    a39   6   |  5 e389-1  4     |
+-------------------------+-----------------+------------------+
|  b134    1234    6      |  5    b349 b34  |  8  129    7     |
|   3578   2358    239    |  389   67   1   |  4  2569   2569  |
|   14578  1458    149    |  489   67   2   |  3  1569   1569  |
+-------------------------+-----------------+------------------+


(1=389)r6c125 - (9=341)r7c156 - (1=3482)r1c1689 - (2=31)r24c9 - 1r6c8 = r6c12 => -1 r4c3, r5c123, r6c8 ; stte

[eleven]

Code: Select all

 *--------------------------------------------------------------------*
 | f134     9        5      |  6     e12    34    |  7  2348   238    |
 |  6       134      8      |  7     d12     5    |  9  234   d23     |
 |  2       7        34     |  34     8      9    |  1  56     56     |
 |--------------------------+---------------------+-------------------|
 |  9       6       c134    |  134    5      8    |  2  7     c13     |
 |  13458   123458  c1234   |  1349   349    7    |  6  1389   1389   |
 |  138     138      7      |  2      39     6    |  5  1389   4      |
 |--------------------------+---------------------+-------------------|
 |ga134    a1234     6      |  5      9-34 ga34   |  8  129    7      |
 |  3578    2358    b239    |  389    67     1    |  4  2569   2569   |
 |  14578   1458    b149    |  489    67     2    |  3  1569   1569   |
 *--------------------------------------------------------------------*

(34=12)r7c126 - r89c3 = hp12r45c3 - (1=3)r4c9 - (3=1)r2c59 - r1c5 = r1c1 - (1=34)r7c16 => -34r7c5, stte

[SpAce]

5-Fish (aka Starfish, Squirmbag): In columns 1 2 5 6 & 8, digit 4 must go in rows 1 2 5 7 & 9
Therefore candidate 4 can be removed from all other cells in rows 1 2 5 7 & 9
Removing candidate 4 from r5c3 r5c4 r9c3 r9c4.

I would advice against using '&' there. It adds no value but makes it harder to read. This would be much easier on the eyes:

In columns 1 2 5 6 8, digit 4 must go in rows 1 2 5 7 9

Personally I'd find this even faster to read:

In c12568, digit 4 must go in r12579

Of course, all three quoted lines could be replaced with this compact statement:

(4)c12568\r12579 => -4 r5c34, r9c34

And then everyone would easily see that it's a basic, finless 5-fish -- which makes no practical sense at all, because there must be a smaller fish around.

[SpAce]

hp12r45c3

Here I thought we'd got rid of those ugly and unnecessary "hp" prefixes Why not simply write it: (21)r45c3? That would make the following weak link easier to read too, with the logical digit order (linking digit 1).

[eleven]

Why not simply write it: (21)r45c3?

Maybe, and maybe better 21r54c3.
But i would never write something like (9)r5c4 = r89c4 - (9=341*)r7c561 - r1c1 = (1^43)r2c289 - (3=1)r4c9 - b4p3*47^58 = (1)r5c3 => -1 r5c4;

[SpAce]

Why not simply write it: (21)r45c3?

Maybe, and maybe better 21r54c3.

Well, it's better than the original for sure. Personally I just don't like that style, especially with multiple digits, because I find it uglier and less readable than standard Eureka with all n-digits bracketed. Many, including you, seem to prefer that style, but I don't really understand why. A different sense of aesthetics, I guess. (I use that style in matrices where it takes less space and can be used consistently, but I see no real benefit in chains.)

But i would never write something like (9)r5c4 = r89c4 - (9=341*)r7c561 - r1c1 = (1^43)r2c289 - (3=1)r4c9 - b4p3*47^58 = (1)r5c3 => -1 r5c4;

Unless you have something specific to criticize or an improved version to show, I think that comment is pretty pointless. Personally I can't really see a better way to write that piece of logic as a chain, but I'm looking forward to getting enlightened by you! Fully realizing how ugly it was, I did provide kraken and matrix POVs as well, didn't I? I just happen to prefer chains when possible, especially when the kraken has so much redundancy as here. Normally I would also prefer a non-memory chain, but it wouldn't make much sense in this case. Sometimes memory is the simplest option.

PS. Here's one version without memory:

(1)r5c123 = b4p378 - r4c9&r6c28&r2c2 = (3)r4c9|(1)r61c1 - (341)r2c982&(1)r579c1 = r16c1 - (1=349)r7c165 - r89c4 = (9)r5c4 => -1 r5c4

Better?