The New Sudoku Players' Forum

[jco]

(...)
I did not like specially step 4 (long chain). I may have missed a much simpler path.
(...)

After a night sleep, and looking back at it, although it was a long chain in step 4,
it was the most important move and the one that took me longer to find
(and for this reason, it was very nice when it was found while searching
for ways to continue the chain based on an initial conviction that it should work in some way).
So, I take back the "I did not like specially step 4".
**I did like everything!**, but would be interested to know in case there is some nice idea that would produce (in the chosen framework) a shorter solution.

[jco]

Solution withdrawn: incorrect. My apologies.

Edit: I found a correction shown in my last post in this thread.

[denis_berthier]

would be interested to know in case there is some nice idea that would produce (in the chosen framework) a shorter solution

Apart from
- the starting point:

Code: Select all

Resolution state after Singles and whips[1]:
   +-------------------+-------------------+-------------------+
   ! 689   1     2     ! 469   7     4689  ! 3     5     89    !
   ! 3     589   569   ! 2     69    1     ! 4     89    7     !
   ! 4     789   79    ! 5     3     89    ! 2     1     6     !
   +-------------------+-------------------+-------------------+
   ! 2     59    359   ! 3469  169   4569  ! 589   7     1589  !
   ! 1     6     3579  ! 379   8     579   ! 59    4     2     !
   ! 579   4     8     ! 79    129   2579  ! 6     3     159   !
   +-------------------+-------------------+-------------------+
   ! 5679  3     1     ! 8     269   2679  ! 579   69    4     !
   ! 6789  2     4     ! 1     5     679   ! 789   689   3     !
   ! 56789 5789  5679  ! 679   4     3     ! 1     2     589   !
   +-------------------+-------------------+-------------------+

- the maximum length of chains (8)
- giving up eleven's replacement technique (useless in this case)

I can't see anything special in the "chosen framework".

Yesterday, I didn't try hard to find fewer steps with chains of max length 8, but it appears it's not so difficult (actually, each of the five more tries gave 4 steps; it seems my first two tries were unlucky). Here's the first 4-step solution I found:

Code: Select all

=====> STEP #1
whip[8]: c1n7{r9 r6} - r6c4{n7 n9} - r9c4{n9 n6} - c3n6{r9 r2} - r1n6{c1 c6} - c6n8{r1 r3} - c2n8{r3 r2} - r2n5{c2 .} ==> r9c2≠7
singles ==> r3c2=7, r3c3=9, r3c6=8
=====> STEP #2
whip[6]: c2n9{r4 r9} - c1n9{r9 r6} - r6c4{n9 n7} - r9c4{n7 n6} - c3n6{r9 r2} - r2n5{c3 .} ==> r4c2≠5
naked-single ==> r4c2=9
=====> STEP #3
whip[5]: r2c5{n6 n9} - r2c8{n9 n8} - c2n8{r2 r9} - c9n8{r9 r4} - r4n1{c9 .} ==> r4c5≠6
singles ==> r4c5=1, r6c9=1, r5c7=9
whip[1]: b6n5{r4c9 .} ==> r4c3≠5, r4c6≠5
singles ==> r4c3=3, r5c4=3
=====> STEP #4
whip[7]: r2n8{c2 c8} - r8n8{c8 c7} - r4c7{n8 n5} - r7n5{c7 c1} - r6c1{n5 n7} - r5n7{c3 c6} - r8n7{c6 .} ==> r1c1≠8
stte

Whether there could be a solution with 3 steps (still with chains-max-length equal to 8) is a question I'll leave open as I have little interest in allowing so long chains for a puzzle solvable with max-length 4. I prefer my original solution with 5 steps of length ≤ 6.

[DEFISE]

Whether there could be a solution with 3 steps (still with chains-max-length equal to 8) is a question I'll leave open as I have little interest in allowing so long chains for a puzzle solvable with max-length 4. I prefer my original solution with 5 steps of length ≤ 6.

After modifying my initial algo a bit, I found some solutions in W8 in 3 steps, with 15 tries.
Here is one :

Code: Select all

Resolution state after 7 singles:
   +-------------------+-------------------+-------------------+
   ! 689   1     2     ! 469   7     4689  ! 3     5     89    !
   ! 3     589   569   ! 2     69    1     ! 4     89    7     !
   ! 4     789   79    ! 5     3     89    ! 2     1     6     !
   +-------------------+-------------------+-------------------+
   ! 2     59    359   ! 3469  169   4569  ! 589   7     1589  !
   ! 1     6     3579  ! 379   8     579   ! 59    4     2     !
   ! 579   4     8     ! 79    129   2579  ! 6     3     159   !
   +-------------------+-------------------+-------------------+
   ! 5679  3     1     ! 8     269   2679  ! 579   69    4     !
   ! 6789  2     4     ! 1     5     679   ! 789   689   3     !
   ! 56789 5789  5679  ! 679   4     3     ! 1     2     589   !
   +-------------------+-------------------+-------------------+

whip[8]: c1n7{r7 r6}- r6c4{n7 n9}- r9c4{n9 n6}- c3n6{r9 r2}- r2c5{n6 n9}- r2c8{n9 n8}- c2n8{r2 r3}- r3c6{n8 .}
=> -7r9c2
Singles: 7r3c2, 9r3c3, 8r3c6

whip[6]: r2c3{n5 n6}- r1c1{n6 n8}- b3n8{r1c9 r2c8}- r8n8{c8 c7}- r4c7{n8 n9}- r4c2{n9 .}
=> -5r4c3
Singles: 3r4c3, 3r5c4

whip[8]: r1c1{n6 n8}- b3n8{r1c9 r2c8}- r8n8{c8 c7}- c7n7{r8 r7}- r7n5{c7 c1}- r9c3{n5 n7}- r5n7{c3 c6}- c4n7{r6 .} => -6r2c3
STTE
 

[jco]

This is my last post in this thread.
I found an elementary mistake in both previously posted solutions. The mistake is in the long chain:
"-(9)r2c23=(9-6)r2c5" is incorrect. There is a y in r2c8 (first solution) and a (89) in r2c8 (second solution)
that makes the claim for that strong link invalid.
I removed both solutions. A corrected solution follows (Edit part). Apologies for the previous posts.

Edit 1: Improved the text and most importantly, I found a correction to Step 2, but had to change other steps and added one step.

Solution in 5 steps. After basics:

Code: Select all

.----------------------------------------------------------.
|  689    1     2    |  469   7     4689 |  3    5    89   |
|  3      589   569  |  2     69    1    |  4    89   7    |
|  4      789   79   |  5     3     89   |  2    1    6    |
|--------------------+-------------------+-----------------|
|  2      59    359  |  3469  169   4569 |  589  7    1589 |
|  1      6     3579 |  379   8     59-7 |  59   4    2    |
| *579    4     8    | #79    129  *2579 |  6    3    159  |
|--------------------+-------------------+-----------------|
| *5679   3     1    |  8     269  *2679 | *579  69   4    |
| *6789   2     4    |  1     5    *679  | *789  689  3    |
|  56789  5789  5679 |  679   4     3    |  1    2    589  |
'----------------------------------------------------------'

1. Finned Swordfish (7) r678 \ c167 fin: r6c4 => -7 r5c6

NP: (59)r5c67 => -5 r5c3, -9 r5c34

Code: Select all

.---------------------------------------------------------.
| 689    1      2    |  469    7    4689 | 3    5    89   |
| 3      58-9  b56-9 |  2     a69   1    | 4    89   7    |
| 4      789   g79   |  5      3    8-9  | 2    1    6    |
|--------------------+-------------------+----------------|
| 2      59     359  |  3469   169  4569 | 589  7    1589 |
| 1      6     f37   | e37     8    59   | 59   4    2    |
| 579    4      8    | d79     129  2579 | 6    3    159  |
|--------------------+-------------------+----------------|
| 5679   3      1    |  8      269  2679 | 579  69   4    |
| 6789   2      4    |  1      5    679  | 789  689  3    |
| 56789  5789  c5679 | d679    4    3    | 1    2    589  |
'---------------------------------------------------------'

2. (9=6)r2c5-r2c3=r9c3-(6=97)r69c4-r5c4=r5c3-(7=9)r3c3 => -9 r2c23, r3c6

[& 1 placement, LC: (9)r3c23 => -9 r1c1]

Code: Select all

.--------------------------------------------------------.
| 68      1     2    | 469   7    469  | 3     5    89   |
| 3      b58    56   | 2     69   1    | 4    c89   7    |
| 4       79    79   | 5     3    8    | 2     1    6    |
|--------------------+-----------------+-----------------|
| 2       59    359  | 3469  169  4569 | 589   7    1589 |
| 1       6     37   | 37    8    59   | 59    4    2    |
| 579     4     8    | 79    129  2579 | 6     3    159  |
|--------------------+-----------------+-----------------|
| 5679    3     1    | 8     269  2679 | 579   69   4    |
| 679-8   2     4    | 1     5    679  | 789  d689  3    |
| 56789  a5789  5679 | 679   4    3    | 1     2    59-8 |
'--------------------------------------------------------'

3. Skyscraper (8)r9c2=r2c2-r2c8=(8)r8c8 => -8 r8c1,r9c9

Code: Select all

.------------------------------------------------------.
| 68     1     2    | 469   7    469  | 3    5    89   |
| 3      58    56   | 2     69   1    | 4    89   7    |
| 4      79    79   | 5     3    8    | 2    1    6    |
|-------------------+-----------------+----------------|
| 2     d59   d359  | 3469  169  4569 | 89-5 7    1589 |
| 1      6     37   | 37    8    59   | 59   4    2    |
|c579    4     8    | 79    129  2579 | 6    3    159  |
|-------------------+-----------------+----------------|
|b5679   3     1    | 8     269  2679 |a579  69   4    |
| 679    2     4    | 1     5    679  | 789  689  3    |
| 56789  5789  5679 | 679   4    3    | 1    2    59   |
'------------------------------------------------------'

4. ER (5)r7c7=r7c1-r6c1=(5)r4c23 => -5 r4c7

Code: Select all

.-----------------------------------------------------------.
| 68      1     2    | 469   7    469  |  3     5    a89    |
| 3      c58    56   | 2     69   1    |  4    b89    7     |
| 4       79    79   | 5     3    8    |  2     1     6     |
|--------------------+-----------------+--------------------|
| 2      c59    359  | 3469  169  4569 | e89    7     159-8 |
| 1       6     37   | 37    8    59   |  59    4     2     |
| 579     4     8    | 79    129  2579 |  6     3     159   |
|--------------------+-----------------+--------------------|
| 5679    3     1    | 8     269  2679 |  579   69    4     |
| 679     2     4    | 1     5    679  |  789   689   3     |
| 56789   5789  5679 | 679   4    3    |  1     2     59    |
'-----------------------------------------------------------'

5. (8)r1c9=r2c8-(8=59)r24c2-(9=8)r4c7 => -8 r4c9; ste

Edit 2: Removed conclusions (from this Edit 2).