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[Yogi]

....163..54.......7..3......86..3......4...5................6.14..5.........2....

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+---+---+---+
|...|.16|3..|
|54.|...|...|
|7..|3..|...|
+---+---+---+
|.86|..3|...|
|...|4..|.5.|
|...|...|...|
+---+---+---+
|...|...|6.1|
|4..|5..|...|
|...|.2.|...|
+---+---+---+


Not just another 17er. See what happens when you ‘Solve Singles.’
After that it’s all in the eye of the beholder. Is it easy to solve, hard, or just interesting?
Hmm . . . No 9s, only one 2 and one 8 solved, and no (28) cells, until you make some.
Can the Chain Gang find a single-stepper or something like it?

[pjb]

Ugly! A memory chain and a simple chain. Surely something better

Code: Select all

 289     29      289    | 7      1      6      | 3      4      5     
 5       4       3      | 289    89     289    | 1      6      7     
 7       6       1      | 3      4      5      |d29    e289    289   
------------------------+----------------------+---------------------
 1       8       6      |a29     5      3      | 4      7    b29     
 3       29      7      | 4      89     1      |c289    5      6     
h29      5       4      | 6      7      89-2   |c289    1      3     
------------------------+----------------------+---------------------
g289     7       5      | 89*    3      4      | 6     f289    1     
 4       1       289    | 5      6      89     | 7      3      289   
 6       3       89     | 1      2      7      | 5      89     4     


(2=9)r4c4 - (9=2)r4c9 - (2)r56c7 = (2)r3c7 - (2)r3c8 = (2-9)r7c8*4 = (9)r7c1 - (9=2)r6c1 => -2 r6c6
Then
(2=9)r5c2 - (9=8)r5c5 - (8=9)r6c6 - (9)r8c6 = (9-2)r8c3 = (2)r1c3 => -2 r1c2; stte

Phil

[jco]

I found a solution related to Phil's findings. Also two steps.

After basics

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.----------------------------------------------------.
|a(2)89 29   289  | 7    1    6    |  3    4    5    |
|  5    4    3    | 289  89   289  |  1    6    7    |
|  7    6    1    | 3    4    5    | g9-2 A289  289  |
|-----------------+----------------+-----------------|
|  1    8    6    |d29   5    3    |  4    7   e29   |
|  3   E29   7    | 4    89   1    |fF289  5    6    |
| D29   5    4    | 6    7    289  |f 289  1    3    |
|-----------------+----------------+-----------------|
|bC289  7    5    |c89   3    4    |  6   B289  1    |
|  4    1    289  | 5    6    89   |  7    3    289  |
|  6    3    89   | 1    2    7    |  5    89   4    |
'----------------------------------------------------'

1. Almost X-Chain

(2*-8)r1c1 = (8)r7c1 - (8=9)r7c4 - (9)r4c4 = (9)r4c9 - (9)r56c7 = (9)r3c7 [tags a...g]
||
(2): r3c8 = r7c8 - r7c1 =* r6c1 - r5c2 = r4c7 [tags A...F]

=> -2 r4c7 [4 placements]
----

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.--------------------------------------------------.
| 289  9-2 a289  | 7    1    6    | 3    4    5    |
| 5    4    3    | 89   89   2    | 1    6    7    |
| 7    6    1    | 3    4    5    | 9    28   28   |
|----------------+----------------+----------------|
| 1    8    6    | 2    5    3    | 4    7    9    |
| 3   f29   7    | 4   e89   1    | 28   5    6    |
| 29   5    4    | 6    7   d89   | 28   1    3    |
|----------------+----------------+----------------|
| 289  7    5    | 89   3    4    | 6    289  1    |
| 4    1   b289  | 5    6   c89   | 7    3    28   |
| 6    3    89   | 1    2    7    | 5    89   4    |
'--------------------------------------------------'

2. Extended M-wing

(2)r1c3 = (2-9)r8c3 = (9)r8c6 - (9)r6c6 = (9)r5c5 - (9=2)r5c2 => -2 r1c2; ste

Thanks for the puzzle!

[denis_berthier]

....163..54.......7..3......86..3......4...5................6.14..5.........2....
Is it easy to solve, hard, or just interesting?
Can the Chain Gang find a single-stepper or something like it?

SER = 7.1; W = 3; BC = 3
It's a good example of the absurdity of trying to find 1-step or 2-step solutions at any cost.

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Resolution state after Singles and whips[1]:
   +-------------+-------------+-------------+
   ! 289 29  289 ! 7   1   6   ! 3   4   5   !
   ! 5   4   3   ! 289 89  289 ! 1   6   7   !
   ! 7   6   1   ! 3   4   5   ! 29  289 289 !
   +-------------+-------------+-------------+
   ! 1   8   6   ! 29  5   3   ! 4   7   29  !
   ! 3   29  7   ! 4   89  1   ! 289 5   6   !
   ! 29  5   4   ! 6   7   289 ! 289 1   3   !
   +-------------+-------------+-------------+
   ! 289 7   5   ! 89  3   4   ! 6   289 1   !
   ! 4   1   289 ! 5   6   89  ! 7   3   289 !
   ! 6   3   89  ! 1   2   7   ! 5   89  4   !
   +-------------+-------------+-------------+
63 candidates

There is a totally trivial solution:

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biv-chain[2]: r4n9{c9 c4} - b8n9{r7c4 r8c6} ==> r8c9≠9
whip[1]: b9n9{r9c8 .} ==> r3c8≠9
biv-chain[3]: r2c5{n9 n8} - b5n8{r5c5 r6c6} - c6n2{r6 r2} ==> r2c6≠9
biv-chain[3]: c6n9{r8 r6} - r6c1{n9 n2} - b7n2{r7c1 r8c3} ==> r8c3≠9
singles ==> r8c6=9, r7c4=8, r1c1=8
finned-swordfish-in-rows: n2{r1 r8 r5}{c2 c3 c9} ==> r4c9≠2
(This is also a bivalue-chain[3]: biv-chain[3]: r5n2{c7 c2} - r1n2{c2 c3} - r8n2{c3 c9} ==> r4c9≠2)
stte

There's no 1-step solution with g-braids of any length.

The simplest 2-step solution requires a z-chain[5]:

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z-chain[5]: b5n2{r4c4 r6c6} - r6c1{n2 n9} - r7n9{c1 c8} - b9n2{r7c8 r8c9} - r4c9{n2 .} ==> r4c4≠9
singles ==> r4c4=2, r4c9=9, r3c7=9, r2c6=2
biv-chain[3]: b7n2{r7c1 r8c3} - r8n9{c3 c6} - r6n9{c6 c1} ==> r6c1≠2, r7c1≠9
stte

Remember that complexity of chains increases exponentially with their length.

[DEFISE]

A lot of singles.
Box/Line: 8b6c7 => -8r3c7
whip[5]: r4c4{n2 n9}- r4c9{n9 n2}- b9n2{r8c9 r7c8}- r7n9{c8 c1}- r6c1{n9 .} => -2r6c6
Single(s): 2r2c6, 2r4c4, 9r4c9, 9r3c7
whip[3]: c6n9{r8 r6}- r6c1{n9 n2}- b7n2{r7c1 .} => -9r8c3
STTE

[denis_berthier]

A lot of singles.
Box/Line: 8b6c7 => -8r3c7
whip[5]: r4c4{n2 n9}- r4c9{n9 n2}- b9n2{r8c9 r7c8}- r7n9{c8 c1}- r6c1{n9 .} => -2r6c6
Single(s): 2r2c6, 2r4c4, 9r4c9, 9r3c7
whip[3]: c6n9{r8 r6}- r6c1{n9 n2}- b7n2{r7c1 .} => -9r8c3
STTE

It seems I had failed to see some of SudoRules results. I've corrected my post.

[P.O.]

a POM solution:

Hidden Text: Show

Code: Select all

templates after initialization + singles:
....1..........1....1......1.............1..........1.........1.1..........1.....

..2...........2..........2....2......2.............2..2................2....2....
.2............2...........2...2...........2..2...............2...2..........2....
2.............2...........2...2......2.............2.........2...2..........2....
2...........2...........2..........2.2............2..........2...2..........2....

......3....3.........3..........3...3................3....3...........3..3.......

.......4..4...........4..........4.....4.......4...........4...4................4

........55.............5.......5...........5..5.........5.........5...........5..

.....6..........6..6.........6..............6...6...........6......6....6........

...7.............77...............7...7..........7.....7.............7.......7...

..8.........8.............8.8...........8..........8..8.............8..........8.
8.............8...........8.8...........8..........8.....8.......8.............8.
8.............8..........8..8...........8..........8.....8.............8..8......
8............8............8.8.............8.......8......8.......8.............8.
8............8...........8..8.............8.......8......8.............8..8......
8...........8.............8.8...........8..........8.........8......8.....8......

..9..........9............9...9......9.............9..9.............9..........9.
.9............9.........9..........9....9....9...........9.......9.............9.
.9...........9............9...9...........9..9...............9......9.....9......
.9..........9...........9..........9....9....9...............9......9.....9......
9............9............9...9......9.............9.........9......9.....9......
9............9..........9..........9.9............9......9.......9.............9.


testing for compatibility between (2 8) (2 9) and (8 9) gives only one possibility in each case:
..2...........2..........2....2......2.............2..2................2....2....
8............8............8.8.............8.......8......8.......8.............8.

..2...........2..........2....2......2.............2..2................2....2....
.9..........9...........9..........9....9....9...............9......9.....9......

8............8............8.8.............8.......8......8.......8.............8.
.9..........9...........9..........9....9....9...............9......9.....9......


ans so only one possibility for (2 8 9)
..2...........2..........2....2......2.............2..2................2....2....
8............8............8.8.............8.......8......8.......8.............8.
.9..........9...........9..........9....9....9...............9......9.....9......


solution:
....1..........1....1......1.............1..........1.........1.1..........1.....
..2...........2..........2....2......2.............2..2................2....2....
......3....3.........3..........3...3................3....3...........3..3.......
.......4..4...........4..........4.....4.......4...........4...4................4
........55.............5.......5...........5..5.........5.........5...........5..
.....6..........6..6.........6..............6...6...........6......6....6........
...7.............77...............7...7..........7.....7.............7.......7...
8............8............8.8.............8.......8......8.......8.............8.
.9..........9...........9..........9....9....9...............9......9.....9......