The New Sudoku Players' Forum

[jovi_al01]

this puzzle has a really lovely solve path, and one that i doubt any computer solvers know of. buckle up!

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

...........6..5..3..4..6.1....8...2.3...9......9..74...1...4..5..87..6...7......2

[m_b_metcalf]

this puzzle has a really lovely solve path, and one that i doubt any computer solvers know of. buckle up!

I doubt that backdoor value 3r7c8 is what you meant!

[denis_berthier]

.
As I have no idea which "paradigm shift" you are claiming, here is my solution in gW8.
Note that, without using g-whips but only whips, one needs much longer chains (the puzzle is in W18).

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 125789 23589  12357  ! 12349  123478 12389  ! 25789  456789 46789  !
   ! 12789  289    6      ! 1249   12478  5      ! 2789   4789   3      !
   ! 25789  23589  4      ! 239    2378   6      ! 25789  1      789    !
   +----------------------+----------------------+----------------------+
   ! 1457   456    157    ! 8      13456  13     ! 13579  2      1679   !
   ! 3      24568  1257   ! 12456  9      12     ! 1578   5678   1678   !
   ! 1258   2568   9      ! 12356  12356  7      ! 4      3568   168    !
   +----------------------+----------------------+----------------------+
   ! 269    1      23     ! 2369   2368   4      ! 3789   3789   5      !
   ! 2459   23459  8      ! 7      1235   1239   ! 6      349    149    !
   ! 4569   7      35     ! 13569  13568  1389   ! 1389   3489   2      !
   +----------------------+----------------------+----------------------+
249 candidates
254 g-candidates, 1593 csp-glinks and 921 non-csp glinks

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whip[6]: r4n9{c9 c7} - b6n3{r4c7 r6c8} - r8c8{n3 n4} - r9n4{c8 c1} - c1n6{r9 r7} - b7n9{r7c1 .} ==> r8c9≠9
g-whip[7]: c9n4{r1 r8} - r9n4{c8 c1} - c1n6{r9 r7} - b7n9{r7c1 r8c123} - r8c8{n9 n3} - c7n3{r9 r4} - r4n9{c7 .} ==> r1c9≠9
g-whip[7]: r8c9{n1 n4} - b7n4{r8c1 r9c1} - c1n6{r9 r7} - b7n9{r7c1 r8c123} - r8c8{n9 n3} - c7n3{r9 r4} - r4n9{c7 .} ==> r4c9≠1
g-whip[7]: r8c9{n1 n4} - b7n4{r8c1 r9c1} - c1n6{r9 r7} - b7n9{r7c1 r8c123} - r8c8{n9 n3} - c7n3{r9 r4} - r4c6{n3 .} ==> r8c6≠1
g-whip[6]: r8n1{c9 c5} - r8n5{c5 c123} - r9c3{n5 n3} - r7c3{n3 n2} - b8n2{r7c4 r8c6} - r5c6{n2 .} ==> r5c9≠1
whip[8]: c6n8{r1 r9} - c6n9{r9 r8} - c6n3{r8 r4} - r6n3{c5 c8} - r8c8{n3 n4} - r9n4{c8 c1} - c1n6{r9 r7} - b7n9{r7c1 .} ==> r1c6≠1
whip[8]: c6n8{r1 r9} - c6n9{r9 r8} - c6n3{r8 r4} - r6n3{c5 c8} - r8c8{n3 n4} - r9n4{c8 c1} - c1n6{r9 r7} - b7n9{r7c1 .} ==> r1c6≠2
whip[8]: c6n8{r9 r1} - c6n9{r1 r8} - c6n3{r8 r4} - r6n3{c5 c8} - r8c8{n3 n4} - r9n4{c8 c1} - c1n6{r9 r7} - b7n9{r7c1 .} ==> r9c6≠1
whip[1]: c6n1{r5 .} ==> r4c5≠1, r5c4≠1, r6c4≠1, r6c5≠1
finned-swordfish-in-rows: n1{r6 r8 r2}{c1 c9 c5} ==> r1c5≠1
t-whip[5]: r9c3{n3 n5} - r8n5{c2 c5} - r8n1{c5 c9} - r6n1{c9 c1} - b1n1{r1c1 .} ==> r1c3≠3
whip[1]: c3n3{r9 .} ==> r8c2≠3
t-whip[5]: r4c6{n1 n3} - r6n3{c5 c8} - r8n3{c8 c5} - r8n1{c5 c9} - r6n1{c9 .} ==> r4c1≠1, r4c3≠1
z-chain[5]: r6n1{c1 c9} - r8c9{n1 n4} - r9n4{c8 c1} - r4c1{n4 n7} - r4c3{n7 .} ==> r6c1≠5
whip[5]: r5c6{n2 n1} - b4n1{r5c3 r6c1} - r6n2{c1 c2} - b4n8{r6c2 r5c2} - r5n4{c2 .} ==> r5c4≠2
z-chain[6]: c8n5{r6 r1} - r1n6{c8 c9} - c9n4{r1 r8} - r9n4{c8 c1} - r4c1{n4 n7} - r4c3{n7 .} ==> r4c7≠5
t-whip[6]: r7c3{n2 n3} - r9c3{n3 n5} - r8n5{c2 c5} - r8n1{c5 c9} - r6n1{c9 c1} - b1n1{r1c1 .} ==> r1c3≠2
finned-x-wing-in-columns: n2{c3 c6}{r5 r7} ==> r7c5≠2, r7c4≠2
whip[1]: b8n2{r8c6 .} ==> r8c1≠2, r8c2≠2
biv-chain[4]: r4c6{n3 n1} - r5c6{n1 n2} - c3n2{r5 r7} - c3n3{r7 r9} ==> r9c6≠3
biv-chain[4]: r6n1{c1 c9} - r8n1{c9 c5} - r8n2{c5 c6} - r5c6{n2 n1} ==> r5c3≠1
singles ==> r6c1=1, r1c3=1, r8c9=1, r1c9=4, r1c8=6
whip[1]: c8n5{r6 .} ==> r5c7≠5
whip[1]: c3n7{r5 .} ==> r4c1≠7
whip[1]: b4n8{r6c2 .} ==> r1c2≠8, r2c2≠8, r3c2≠8
hidden-pairs-in-a-block: b2{n1 n4}{r2c4 r2c5} ==> r2c5≠8, r2c5≠7, r2c5≠2, r2c4≠9, r2c4≠2
finned-swordfish-in-columns: n5{c4 c8 c3}{r9 r5 r6} ==> r6c2≠5, r5c2≠5
g-whip[3]: b1n5{r3c2 r123c1} - r4c1{n5 n4} - b7n4{r8c1 .} ==> r8c2≠5
z-chain[3]: r8c2{n4 n9} - r8c1{n9 n5} - r4c1{n5 .} ==> r9c1≠4
hidden-single-in-a-row ==> r9c8=4
biv-chain[4]: c5n1{r9 r2} - c5n4{r2 r4} - c1n4{r4 r8} - r8n5{c1 c5} ==> r9c5≠5
z-chain[4]: c2n8{r5 r6} - r6c9{n8 n6} - r5n6{c9 c4} - r5n4{c4 .} ==> r5c2≠2
t-whip[4]: r8c8{n3 n9} - r8c2{n9 n4} - r8c1{n4 n5} - r9c3{n5 .} ==> r9c7≠3
naked-pairs-in-a-row: r9{c6 c7}{n8 n9} ==> r9c5≠8, r9c4≠9, r9c1≠9
biv-chain[4]: r5c6{n2 n1} - c7n1{r5 r4} - c7n3{r4 r7} - r7c3{n3 n2} ==> r5c3≠2
stte

[P.O.]

Code: Select all

a computer solution but nothing lovely in it:

intersection:
((((6 0) (7 1 7) (2 6 9)) ((6 0) (9 1 7) (4 5 6 9))))

349r8c8 => r1c6 r4c5 r5c4 r6c45 r8c6 r9c6 <> 1 
 r8c8=3 - b6n3{r6c8 r4c7} - r4c6{n3 n1}
 r8c8=4 - 2359b7p3459 - r8c9{n49 n1} - 123r458c6
 r8c8=9 - 2345b7p3459 - r8c9{n49 n1} - 123r458c6
 
349r8c8 => r8c9 <> 4,9
 r8c8=3 - b6n3{r6c8 r4c7} - 129r458c6 - 2345b7p3459 - r8c9{n49 n1}
 r8c8=4 - 2359b7p3459 - r8c9{n49 n1}
 r8c8=9 - 2345b7p3459 - r8c9{n49 n1}
 
( n1r8c9  n1r6c1  n4r1c9  n6r1c8  n1r1c3 )
intersections:
((((8 0) (5 2 4) (2 4 5 6 8)) ((8 0) (6 2 4) (2 5 6 8)))
 (((7 0) (4 3 4) (5 7)) ((7 0) (5 3 4) (2 5 7)))
 (((5 0) (5 8 6) (5 7 8)) ((5 0) (6 8 6) (3 5 8)))
 (((3 0) (7 3 7) (2 3)) ((3 0) (9 3 7) (3 5))))
QUAD ROW: ((2 1 1) (2 7 8 9)) ((2 2 1) (2 9)) ((2 7 3) (2 7 8 9)) ((2 8 3) (7 8 9))
(((2 4 2) (1 2 4 9)) ((2 5 2) (1 2 4 7 8)))

1r5c67 => r4c12 r5c2 r6c2 r9c3 <> 5
 r5c6=1 - r4c6{n1 n3} - b6n3{r4c7 r6c8} - r8n3{c8 c5} - b8n5{r8c5 r9c45} - c3n5{r9 r45}
 r5c7=1 - r5c6{n1 n2} - 57r45c3
 
ste.


[jovi_al01]

i suppose it's time for me to explain my solution!

Code: Select all

.----------------------.----------------------.----------------------.
| 125789  23589 ST12357| 12349  123478  12389 | 25789  456789  46789 |
| 12789   289   S6     | 1249   12478   5     | 2789   4789    3     |
| 25789   23589 S4     | 239    2378    6     | 25789  1       789   |
:----------------------+----------------------+----------------------:
| 1457    456   S157   | 8      13456  B13    | 13579  2       1679  |
| 3       24568 S1257  | 12456  9      B12    | 1578   5678    1678  |
|S1258   S2568  SS9    |S12356 S12356  S7     |S4     S3568   S168   |
:----------------------+----------------------+----------------------:
| 269     1     S23    | 2369   2368    4     | 3789   3789    5     |
|S2459   S23459 SS8    |S7    ST1235   S1239  |S6     S349    S149   |
| 4569    7     S35    | 13569  13568   1389  | 1389   3489    2     |
'----------------------'----------------------'----------------------'

Mutant Exocet:

Base cells: r4c6, r5c6
Cross lines: r6, r8, c3
Cover houses: b4, b7, c8, c9
Target cells: r1c3, r8c5
-57r1c3, -5r8c5

(edit: it has been pointed out to me by marek that -1r4c1 is also an elimination.)

After some basics:

Code: Select all

.------------------.--------------------.----------------------.
| 25789  23589 T1  | 2349   23478  2389 | 25789  456789  46789 |
| 2789   289    6  | 1249   12478  5    | 2789   4789    3     |
| 25789  23589  4  | 239    2378   6    | 25789  1       789   |
:------------------+--------------------+----------------------:
| 14     46     57 | 8      13456 B13   | 13579  2       1679  |
| 3      2468   57 | 12456  9     B12   | 1578   5678    1678  |
| 128    268    9  | 12356  12356  7    | 4      3568    168   |
:------------------+--------------------+----------------------:
| 69     1      2  | 369    368    4    | 3789   3789    5     |
| 459    459    8  | 7     T123    1239 | 6      349     149   |
| 469    7      3  | 1569   1568   189  | 189    489     2     |
'------------------'--------------------'----------------------'

by virtue of 1 having been placed in a target cell:
-1r8c5
Claiming/pointing set: 1r45c6

stte