The New Sudoku Players' Forum

[shye]

Code: Select all

+-------+-------+-------+
| . 9 8 | . . . | . . . |
| 7 . . | . 6 5 | . . . |
| 6 . . | 4 . . | 3 . . |
+-------+-------+-------+
| . . 2 | . 5 . | . 4 . |
| . . . | 1 . 4 | . . . |
| . 1 . | . 2 . | 5 . . |
+-------+-------+-------+
| . . 3 | . . 1 | . . 8 |
| . . . | 2 8 . | . . 9 |
| . . . | . . . | 6 7 . |
+-------+-------+-------+
.98......7...65...6..4..3....2.5..4....1.4....1..2.5....3..1..8...28...9......67.

estimated rating: 8.9
i had an older puzzle with this name... but this one fits it much better my own path is many steps, but fun ones

[marek stefanik]

Code: Select all

.----------------------.-------------------.----------------------.
|#1245–3  9      8     | 37     137  237   | 1247   1256  #45–1267|
| 7       234    14    | 389    6    5     | 1289–4 1289   124    |
| 6       25     15    | 4      179  2789  | 3      1289–5 1257   |
:----------------------+-------------------+----------------------:
| 389     3678   2     | 36789  5    36789 | 1789   4      1367   |
| 3589    35678  5679  | 1      379  4     | 2789   23689  2367   |
| 3489    1      4679  | 36789  2    36789 | 5      3689   367    |
:----------------------+-------------------+----------------------:
| 2459    4567–2 3     | 5679   479  1     | 24     25     8      |
| 145     4567   4567–1| 2      8    367   | 14     135    9      |
|#12–4589 2458   1459  | 359    349  39    | 6      7     #1245–3 |
'----------------------'-------------------'----------------------'

Firework quad 1245r19c19 (12r9c1\b7 + 45r1c9\b3)

Code: Select all

.-------------.-------------------.-------------.
| 1   9   8   | 37     37   2     | 4    6   5  |
| 7   3   4   |#89     6    5     |#89   1   2  |
| 6   2   5   | 4      1    89    | 3   #89  7  |
:-------------+-------------------+-------------:
| 38 *67  2   | 36789  5    389–67| 789  4   1  |
| 38  5   679 | 1      379  4     | 789  2   36 |
| 4   1   679 | 367–89 2    36789 | 5   #89  36 |
:-------------+-------------------+-------------:
| 9  *67  3   | 67     4    1     | 2    5   8  |
| 5   4  *67  | 2      8   *67    | 1    3   9  |
| 2   8   1   | 5      39   39    | 6    7   4  |
'-------------'-------------------'-------------'

Two-string kites 67r8c2\r4c6b7, 89r2c8\r6c4b3; btte

Marek

[eleven]

Code: Select all

+-------------------------+-------------------------+--------------------------+
| 12345   9       8       | 37      137     237     |  1247    1256    124567  |
| 7     cb234   ca14      | 389     6       5       |  12489   1289    124     |
| 6     db25    da15      | 4       179     2789    |  3       12589   1257    |
+-------------------------+-------------------------+--------------------------+
| 389     3678    2       | 36789   5       36789   |  1789    4       1367    |
| 3589    35678   5679    | 1       379     4       |  2789    23689   2367    |
| 3489    1       4679    | 36789   2       36789   |  5       3689    367     |
+-------------------------+-------------------------+--------------------------+
| 2459    24567   3       | 5679    479     1       |cb24    db25      8       |
| 145     4567    14567   | 2       8       367     |ca14    da135     9       |
| 124589  2458    1459    | 359     349     39      |  6       7       12345   |
+-------------------------+-------------------------+--------------------------+

Haven't studied fireworks, so i see it this way:
If both r1c1/r9c9 are not 1, r9c1 must be 1 (by the locked candidates a in c3,r7)
If both r1c1/r9c9 are not 2, r9c1 must be 2 (lc b)
-> one of r1c1/r9c9 must be 1 or 2.
Same for 45 and r1c9 (lc c and d)
So at least one of r1c1/r9c9 must be 1 or 2, the other 4 or 5, r9c1 2 or 1, r1c9 5 or 4.

Also for each digit one of the marked cell pairs (a to d) must be locked.

[Cenoman]

1. The puzzle is automorphic with central symmetry and digit permutation [14][25][33][68][79] => +3 r5c5

Code: Select all

 +---------------------------+----------------------+----------------------------+
 |Hd1245-3   9       8       | A37   Ba17    237    | G1247  He256-1 HFe24567-1  |
 |  7        234     14      |  389    6     5      |  12489   1289    F124      |
 |  6        25     c15      |  4    Bb179   2789   |  3       12589    1257     |
 +---------------------------+----------------------+----------------------------+
 |  389      3678    2       |  6789   5     6789   |  1789    4        1367     |
 |  589      5678    5679    |  1      3     4      |  2789    2689     267      |
 |  3489     1       4679    |  6789   2     6789   |  5       3689     367      |
 +---------------------------+----------------------+----------------------------+
 |  2459     24567   3       |  5679  C479   1      |  24      25       8        |
 |  145      4567    14567   |  2      8     367    |  14      135      9        |
 |  12589-4  258-4   1459    |  359   D49    39     |  6       7       E1245-3   |
 +---------------------------+----------------------+----------------------------+

2. (1)r1c5 = r3c5 - (1=5)r3c3 - r1c1 = (56)r1c89 => -1 r1c89 (and by symmetry -4 r9c12)
3. (3=7)r1c4 - r13c5 = (7-4)r7c5 = r9c5 - r9c9 = r12c9 - r1c7 = (456)r1c189 => -3 r1c1 (and by symmetry -3 r9r9); 38 placements and ls

Code: Select all

 +------------------+---------------------+------------------+
 |  1    9    8     |  3      7    2      |  4     6    5    |
 |  7    3    4     |  89     6    5      |  89    1    2    |
 |  6    2    5     |  4      1    89     |  3     89   7    |
 +------------------+---------------------+------------------+
 |  3    67   2     |  6789   5    6789   |  789   4    1    |
 |  8    5    79    |  1      3    4      |  79    2    6    |
 |  4    1    679   |  6789   2    6789   |  5     89   3    |
 +------------------+---------------------+------------------+
 |  9    67   3     |  67     4    1      |  2     5    8    |
 |  5    4    67    |  2      8    67     |  1     3    9    |
 |  2    8    1     |  5      9    3      |  6     7    4    |
 +------------------+---------------------+------------------+

4. RP(67)r4c2, r8c6 (r7c2, r8c3) => -67 r4c6 (and by symmetry -89 r6c4); ste

@shye: Thank you for the puzzle !

[denis_berthier]

.

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 12345  9      8      ! 37     137    237    ! 1247   1256   124567 !
   ! 7      234    14     ! 389    6      5      ! 12489  1289   124    !
   ! 6      25     15     ! 4      179    2789   ! 3      12589  1257   !
   +----------------------+----------------------+----------------------+
   ! 389    3678   2      ! 36789  5      36789  ! 1789   4      1367   !
   ! 3589   35678  5679   ! 1      379    4      ! 2789   23689  2367   !
   ! 3489   1      4679   ! 36789  2      36789  ! 5      3689   367    !
   +----------------------+----------------------+----------------------+
   ! 2459   24567  3      ! 5679   479    1      ! 24     25     8      !
   ! 145    4567   14567  ! 2      8      367    ! 14     135    9      !
   ! 124589 2458   1459   ! 359    349    39     ! 6      7      12345  !
   +----------------------+----------------------+----------------------+
213 candidates.
SER = 8.8

Notice the very large number of remaining candidates.
There is no meaningful correlation between the rating (be it SER or W) and the number of givens or candidates at the start or after Singles or after Singles+Whips[1].
However, a large number of candidates is often an indication that it will be hard to find a path with few steps. Of course, this has exceptions, as almost every claim in Sudoku.

The best starting point is Cenoman's, using symmetry, but I'll forget about it here. Notice that using symmetry only at the start (i.e. setting r5c5=3) doesn't change the SER or the W rating.

Here is the simplest-first solution, in W5 (consistent with SER = 8.5): Show

z-chain[4]: r1n6{c8 c9} - r1n5{c9 c1} - r3c3{n5 n1} - c5n1{r3 .} ==> r1c8≠1
z-chain[4]: r1n6{c8 c9} - r1n5{c9 c1} - b1n3{r1c1 r2c2} - r2n2{c2 .} ==> r1c8≠2
z-chain[4]: r1n6{c9 c8} - r1n5{c8 c1} - r3c3{n5 n1} - c5n1{r3 .} ==> r1c9≠1
z-chain[4]: r1n6{c9 c8} - r1n5{c8 c1} - b1n3{r1c1 r2c2} - r2n2{c2 .} ==> r1c9≠2
z-chain[4]: r9n8{c1 c2} - r9n2{c2 c9} - r7c7{n2 n4} - c5n4{r7 .} ==> r9c1≠4
z-chain[4]: r9n8{c1 c2} - r9n2{c2 c9} - b9n3{r9c9 r8c8} - r8n5{c8 .} ==> r9c1≠5
z-chain[4]: r9n8{c2 c1} - r9n2{c1 c9} - r7c7{n2 n4} - c5n4{r7 .} ==> r9c2≠4
z-chain[4]: r9n8{c2 c1} - r9n2{c1 c9} - b9n3{r9c9 r8c8} - r8n5{c8 .} ==> r9c2≠5
z-chain[4]: c6n2{r1 r3} - b2n8{r3c6 r2c4} - r2n3{c4 c2} - r2n2{c2 .} ==> r1c7≠2
z-chain[4]: c4n5{r9 r7} - b8n6{r7c4 r8c6} - r8n3{c6 c8} - r8n5{c8 .} ==> r9c3≠5
t-whip[4]: r8n5{c3 c8} - r8n3{c8 c6} - r9c6{n3 n9} - r7n9{c5 .} ==> r7c1≠5
t-whip[4]: r2n2{c9 c2} - r2n3{c2 c4} - r1c4{n3 n7} - r3n7{c6 .} ==> r3c9≠2
whip[5]: c2n4{r8 r2} - c9n4{r2 r1} - r1n6{c9 c8} - r1n5{c8 c1} - b1n3{r1c1 .} ==> r9c3≠4
t-whip[4]: r9c6{n3 n9} - r9c3{n9 n1} - b1n1{r2c3 r1c1} - r1n2{c1 .} ==> r1c6≠3
z-chain[5]: c8n1{r3 r8} - r8n3{c8 c6} - r9c6{n3 n9} - r9c3{n9 n1} - r2n1{c3 .} ==> r3c9≠1, r1c7≠1
t-whip[3]: r1c7{n4 n7} - r3c9{n7 n5} - b1n5{r3c2 .} ==> r1c1≠4
whip[1]: r1n4{c9 .} ==> r2c7≠4, r2c9≠4
biv-chain[3]: b1n3{r1c1 r2c2} - r2n4{c2 c3} - b4n4{r6c3 r6c1} ==> r6c1≠3
biv-chain[3]: c9n4{r9 r1} - r1c7{n4 n7} - r3c9{n7 n5} ==> r9c9≠5
hidden-single-in-a-row ==> r9c4=5
whip[1]: c9n5{r3 .} ==> r1c8≠5, r3c8≠5
naked-single ==> r1c8=6
t-whip[3]: r2c9{n2 n1} - c8n1{r3 r8} - b9n3{r8c8 .} ==> r9c9≠2
whip[1]: r9n2{c2 .} ==> r7c1≠2, r7c2≠2
hidden-pairs-in-a-block: b7{n2 n8}{r9c1 r9c2} ==> r9c1≠9, r9c1≠1
biv-chain[3]: r7c1{n4 n9} - r9c3{n9 n1} - r2c3{n1 n4} ==> r8c3≠4
biv-chain[3]: c1n1{r8 r1} - r2c3{n1 n4} - b4n4{r6c3 r6c1} ==> r8c1≠4
biv-chain[3]: r8c1{n5 n1} - r9n1{c3 c9} - b9n3{r9c9 r8c8} ==> r8c8≠5
singles ==> r7c8=5, r7c7=2
biv-chain[4]: r2c3{n1 n4} - b4n4{r6c3 r6c1} - r7c1{n4 n9} - r9c3{n9 n1} ==> r3c3≠1, r8c3≠1
24 Singles
finned-x-wing-in-columns: n6{c2 c4}{r7 r4} ==> r4c6≠6
x-wing-in-rows: n6{r4 r7}{c2 c4} ==> r6c4≠6
finned-x-wing-in-rows: n8{r3 r6}{c8 c6} ==> r4c6≠8
x-wing-in-columns: n8{c6 c8}{r3 r6} ==> r6c4≠8
hidden-pairs-in-a-block: b5{n6 n8}{r4c4 r6c6} ==> r6c6≠9, r6c6≠7, r6c6≠3, r4c4≠9, r4c4≠7, r4c4≠3
finned-x-wing-in-columns: n9{c4 c7}{r2 r6} ==> r6c8≠9
stte

This is a long path (30 non-W1 steps).

By allowing longer chains, one can find an 8-step path in W8:
whip[7]: b1n3{r2c2 r1c1} - b1n4{r1c1 r2c3} - r2c9{n4 n1} - c8n1{r3 r8} - c1n1{r8 r9} - r9n2{c1 c9} - b9n3{r9c9 .} ==> r2c2≠2
whip[1]: r2n2{c9 .} ==> r1c7≠2, r1c8≠2, r1c9≠2, r3c8≠2, r3c9≠2
whip[8]: r7c7{n2 n4} - r8c7{n4 n1} - r1c7{n1 n7} - r1c4{n7 n3} - r1c6{n3 n2} - c1n2{r1 r9} - c1n1{r9 r1} - r1c5{n1 .} ==> r7c8≠2
singles ==> r7c8=5, r9c4=5
whip[8]: r3c3{n5 n1} - r2c3{n1 n4} - r6n4{c3 c1} - r8c1{n4 n1} - r9c3{n1 n9} - r7c1{n9 n2} - r9n2{c2 c9} - r9n1{c9 .} ==> r1c1≠5
singles ==> r1c9=5, r1c8=6
whip[5]: r9c6{n3 n9} - r9c5{n9 n4} - c9n4{r9 r2} - r2c3{n4 n1} - r9c3{n1 .} ==> r9c9≠3
hidden-single-in-a-block ==> r8c8=3
whip[1]: c8n1{r3 .} ==> r1c7≠1, r2c7≠1, r2c9≠1, r3c9≠1
singles ==> r3c9=7, r1c7=4, r2c9=2, r7c7=2, r8c7=1, r9c9=4, r7c5=4, r7c1=9, r9c3=1, r2c3=4, r2c2=3, r3c3=5, r3c2=2, r1c1=1, r9c2=8, r9c1=2, r3c5=1, r2c8=1, r1c6=2, r8c2=4, r8c1=5, r5c2=5, r6c1=4, r4c9=1, r5c8=2
whip[6]: r5n6{c9 c3} - r4c2{n6 n7} - r7n7{c2 c4} - c6n7{r8 r6} - r6n3{c6 c4} - r1c4{n3 .} ==> r5c9≠3
singles ==> r5c9=6, r6c9=3
whip[6]: r5n8{c1 c7} - r6c8{n8 n9} - r3n9{c8 c6} - c4n9{r2 r4} - r4n3{c4 c6} - r9c6{n3 .} ==> r4c1≠8
singles ==> r4c1=3, r5c1=8, r5c5=3, r1c5=7, r1c4=3, r9c5=9, r9c6=3
finned-x-wing-in-columns: n6{c3 c6}{r8 r6} ==> r6c4≠6
whip[6]: r6c8{n8 n9} - c7n9{r5 r2} - r2c4{n9 n8} - r6c4{n8 n7} - r4n7{c6 c2} - r7n7{c2 .} ==> r4c7≠8
stte

[jovi_al01]

same path as marek's! enjoyed thoroughly. i appreciate you taking time to look at this specific technique :]