The New Sudoku Players' Forum

[mith]

Code: Select all

+-------+-------+-------+
| . . . | . . . | . . 1 |
| . . 2 | . . 1 | . 3 . |
| . 3 . | . 4 5 | . 2 6 |
+-------+-------+-------+
| . . . | . . 2 | 3 6 . |
| . . . | . 6 . | . 5 . |
| 2 . . | . 5 3 | 1 . 4 |
+-------+-------+-------+
| . 7 8 | . . . | . 1 5 |
| 5 . 9 | . . . | . . . |
| 6 2 . | 5 . 4 | . . . |
+-------+-------+-------+
........1..2..1.3..3..45.26.....236.....6..5.2...531.4.78....155.9......62.5.4...

[marek stefanik]

Code: Select all

.---------------------.---------------------.-------------------.
| 4789    45689  4567 | 23      23   a#6789 | 45789A#4789  1    |
|c4789   c45689  2    |b6789   #789    1    |c45789  3    #789  |
| 1789    3      17   |#789     4      5    |#789    2     6    |
:---------------------+---------------------+-------------------:
| 14789   14589  1457 | 14789 α#1789   2    | 3      6    #789  |
| 134789  1489   1347 | 14789   6     #789  |Ω#2789  5    Ψ2789 |
| 2       689    67   |#789     5      3    | 1     #789   4    |
:---------------------+---------------------+-------------------:
|d34      7      8    | 2369    239    69   | 2469   1     5    |
| 5       14     9    | 123678  12378  678  | 24678 B478  Χ2378 |
| 6       2     γ1–3  | 5      β13789  4    |B789   B789 BΧ3789 |
'---------------------'---------------------'-------------------'
TH 789b2356
| 6r1c6 – 6r2c4 = 456r2c127 – (4=3)r7c1
| 4r1c8 – (4=3789)b9p5789
| 1r4c5 – 1r9c5 = 1r9c3
| 2r5c7 – 2r5c9 = 23r89c9
=> –3r9c3

Code: Select all

.-------------.------------------.---------------.
| 89   689  5 | 23    23    689–7|#789  4    1   |
| 4    689  2 | 6789  789   1    | 5    3    789 |
| 1    3    7 | 89    4     5    | 89   2    6   |
:-------------+------------------+---------------:
| 789  5    4 | 1789  1789  2    | 3    6    789 |
| 789  1    3 | 4     6     789  | 2    5    789 |
| 2    89   6 | 789   5     3    | 1    789  4   |
:-------------+------------------+---------------:
| 3    7    8 | 269   29    69   | 4    1    5   |
| 5    4    9 | 13    13   #78   | 6   #78   2   |
| 6    2    1 | 5     78    4    |#789  789  3   |
'-------------'------------------'---------------'

7r8c7\r1c6b9 => -7r1c6, btte

Marek

[mith]

Perfect

I thought of the chains slightly differently (but amounting to the same thing):

Code: Select all

TO 789 b2356
| 6r1c6 – (6=4789)r2c1459 – (4=3)r7c1
| 4r1c8 – r8c8 = 4r8c2
| 1r4c5 – 1r9c5 = 1r9c3
| 2r5c7 – (2=3789)r2459c9 - (3=1)r9c3
=> +3,4,1b7p159

Just cool that the guardians are hitting all three cells in b7 (which is of course the only box where 789 appear as givens).

[denis_berthier]

.
Now that I have ORk-Forcing-Whips based on anti-tridagons, let me try the old puzzles.

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------------+----------------------+----------------------+
   ! 4789   45689  4567   ! 236789 23789  6789   ! 45789  4789   1      !
   ! 4789   45689  2      ! 6789   789    1      ! 45789  3      789    !
   ! 1789   3      17     ! 789    4      5      ! 789    2      6      !
   +----------------------+----------------------+----------------------+
   ! 14789  14589  1457   ! 14789  1789   2      ! 3      6      789    !
   ! 134789 1489   1347   ! 14789  6      789    ! 2789   5      2789   !
   ! 2      689    67     ! 789    5      3      ! 1      789    4      !
   +----------------------+----------------------+----------------------+
   ! 34     7      8      ! 2369   239    69     ! 2469   1      5      !
   ! 5      14     9      ! 123678 12378  678    ! 24678  478    2378   !
   ! 6      2      13     ! 5      13789  4      ! 789    789    3789   !
   +----------------------+----------------------+----------------------+
200 candidates.

Code: Select all

hidden-pairs-in-a-row: r1{n2 n3}{c4 c5} ==> r1c5≠9, r1c5≠8, r1c5≠7, r1c4≠9, r1c4≠8, r1c4≠7, r1c4≠6
finned-x-wing-in-rows: n4{r7 r2}{c7 c1} ==> r1c1≠4
biv-chain[3]: r3n1{c1 c3} - r9c3{n1 n3} - b4n3{r5c3 r5c1} ==> r5c1≠1
z-chain[3]: b7n4{r7c1 r8c2} - c8n4{r8 r1} - c3n4{r1 .} ==> r4c1≠4, r5c1≠4
z-chain[4]: r7n4{c7 c1} - b7n3{r7c1 r9c3} - r9n1{c3 c5} - r9n9{c5 .} ==> r7c7≠9
whip[1]: b9n9{r9c9 .} ==> r9c5≠9
z-chain[5]: c7n6{r8 r7} - b9n2{r7c7 r8c9} - c9n3{r8 r9} - b7n3{r9c3 r7c1} - r7n4{c1 .} ==> r8c7≠4
z-chain[5]: c7n6{r8 r7} - b9n4{r7c7 r8c8} - r8c2{n4 n1} - r9n1{c3 c5} - r9n7{c5 .} ==> r8c7≠7
z-chain[5]: c7n6{r8 r7} - b9n4{r7c7 r8c8} - r8c2{n4 n1} - r9n1{c3 c5} - r9n8{c5 .} ==> r8c7≠8
t-whip[5]: r8c2{n1 n4} - r7c1{n4 n3} - c3n3{r9 r5} - r5n4{c3 c4} - r5n1{c4 .} ==> r4c2≠1
t-whip[5]: c9n3{r8 r9} - b7n3{r9c3 r7c1} - r7n4{c1 c7} - c7n6{r7 r8} - b9n2{r8c7 .} ==> r8c9≠7, r8c9≠8
t-whip[5]: r7n3{c5 c1} - r7n4{c1 c7} - c7n6{r7 r8} - b9n2{r8c7 r8c9} - c9n3{r8 .} ==> r9c5≠3
t-whip[5]: r2n6{c4 c2} - r2n5{c2 c7} - r2n4{c7 c1} - r7n4{c1 c7} - c7n6{r7 .} ==> r8c4≠6
whip[5]: r3c3{n7 n1} - r9c3{n1 n3} - c1n3{r7 r5} - c1n7{r5 r4} - c1n1{r4 .} ==> r1c3≠7
whip[6]: r2n5{c7 c2} - r2n4{c2 c1} - r7c1{n4 n3} - c3n3{r9 r5} - c3n4{r5 r4} - r4n5{c3 .} ==> r2c7≠7
whip[6]: r2n5{c7 c2} - r2n4{c2 c1} - r7c1{n4 n3} - c3n3{r9 r5} - c3n4{r5 r4} - r4n5{c3 .} ==> r2c7≠8
whip[6]: r2n5{c7 c2} - r2n4{c2 c1} - r7c1{n4 n3} - c3n3{r9 r5} - c3n4{r5 r4} - r4n5{c3 .} ==> r2c7≠9
whip[6]: c4n4{r5 r4} - b5n1{r4c4 r4c5} - r9n1{c5 c3} - c3n3{r9 r5} - r5n1{c3 c2} - r5n4{c2 .} ==> r5c4≠7
whip[6]: c4n4{r5 r4} - b5n1{r4c4 r4c5} - r9n1{c5 c3} - c3n3{r9 r5} - r5n1{c3 c2} - r5n4{c2 .} ==> r5c4≠8
whip[6]: c4n4{r5 r4} - b5n1{r4c4 r4c5} - r9n1{c5 c3} - c3n3{r9 r5} - r5n1{c3 c2} - r5n4{c2 .} ==> r5c4≠9
   +-------------------+-------------------+-------------------+
   ! 789   45689 456   ! 23    23    6789  ! 45789 4789  1     !
   ! 4789  45689 2     ! 6789  789   1     ! 45    3     789   !
   ! 1789  3     17    ! 789   4     5     ! 789   2     6     !
   +-------------------+-------------------+-------------------+
   ! 1789  4589  1457  ! 14789 1789  2     ! 3     6     789   !
   ! 3789  1489  1347  ! 14    6     789   ! 2789  5     2789  !
   ! 2     689   67    ! 789   5     3     ! 1     789   4     !
   +-------------------+-------------------+-------------------+
   ! 34    7     8     ! 2369  239   69    ! 246   1     5     !
   ! 5     14    9     ! 12378 12378 678   ! 26    478   23    !
   ! 6     2     13    ! 5     178   4     ! 789   789   3789  !
   +-------------------+-------------------+-------------------+

Code: Select all

OR4-anti-tridagon[12] (type antidiag) for digits 7, 8 and 9 in blocks:
        b2, with cells: r1c6, r2c5, r3c4
        b3, with cells: r1c8, r2c9, r3c7
        b5, with cells: r5c6, r4c5, r6c4
        b6, with cells: r5c7, r4c9, r6c8
with 4 guardians: n6r1c6 n4r1c8 n1r4c5 n2r5c7

OR4-forcing-whip-elim[7] based on OR4-anti-tridagon[12] for n2r5c7, n4r1c8, n6r1c6 and  n1r4c5:
   || n2r5c7 - partial-whip[1]: r8c7{n2 n6} -
   || n4r1c8 - partial-whip[1]: b9n4{r8c8 r7c7} -
   || n6r1c6 - partial-whip[1]: b8n6{r8c6 r7c4} -
   || n1r4c5 - partial-whip[3]: r9n1{c5 c3} - b7n3{r9c3 r7c1} - r7n4{c1 c7} -
 ==> r7c7≠6

hidden-single-in-a-block ==> r8c7=6

OR4-forcing-whip-elim[7] based on OR4-anti-tridagon[12] for n4r1c8, n6r1c6, n1r4c5 and  n2r5c7:
   || n4r1c8 - partial-whip[1]: r8n4{c8 c2} -
   || n6r1c6 - partial-whip[1]: r2n6{c4 c2} -
   || n1r4c5 - partial-whip[2]: c4n1{r5 r8} - r8c2{n1 n4} -
   || n2r5c7 - partial-whip[2]: r7c7{n2 n4} - b7n4{r7c1 r8c2} -
 ==> r2c2≠4

x-wing-in-rows: n4{r2 r7}{c1 c7} ==> r1c7≠4
biv-chain[5]: b4n5{r4c3 r4c2} - r2n5{c2 c7} - b3n4{r2c7 r1c8} - r8n4{c8 c2} - c2n1{r8 r5} ==> r4c3≠1
biv-chain[6]: r4n5{c3 c2} - r2n5{c2 c7} - r2n4{c7 c1} - b7n4{r7c1 r8c2} - b7n1{r8c2 r9c3} - r3c3{n1 n7} ==> r4c3≠7
t-whip[6]: r2n5{c2 c7} - r2n4{c7 c1} - r7c1{n4 n3} - r5n3{c1 c3} - c3n4{r5 r4} - r4n5{c3 .} ==> r1c2≠5

OR4-forcing-whip-elim[7] based on OR4-anti-tridagon[12] for n4r1c8, n2r5c7, n1r4c5 and  n6r1c6:
   || n4r1c8 -
   || n2r5c7 - partial-whip[1]: r7c7{n2 n4} -
   || n1r4c5 - partial-whip[2]: c4n1{r5 r8} - r8c2{n1 n4} -
   || n6r1c6 - partial-whip[3]: r2n6{c4 c2} - r2n5{c2 c7} - b3n4{r2c7 r1c8} -
 ==> r8c8≠4

singles ==> r7c7=4, r2c7=5, r7c1=3, r9c3=1, r3c3=7, r6c3=6, r8c2=4, r3c1=1, r5c2=1, r5c4=4, r5c3=3, r4c3=4, r1c3=5, r2c1=4, r1c8=4, r4c2=5, r9c9=3, r8c9=2, r5c7=2
naked-pairs-in-a-block: b8{r8c6 r9c5}{n7 n8} ==> r8c5≠8, r8c5≠7, r8c4≠8, r8c4≠7
finned-x-wing-in-rows: n7{r8 r6}{c8 c6} ==> r5c6≠7
finned-x-wing-in-columns: n7{c6 c7}{r1 r8} ==> r8c8≠7
stte