The New Sudoku Players' Forum

[Mauriès Robert]

Hi all,

I propose you this puzzle of level 2 TDP, that is to say which can be solved with two successive T&E.

4..8....7.7..2..4...5..39.....2.4.3...3.....691.3.8.....2.7.6...6..3..8.3....1..2

puzzle: Show

resolution: Show

Two 9's of b9 can be eliminated with T&E, the third is a backdoor. But here is a step by step resolution.

(-4r8c9)->4r6c9->4r5c2->4r7c4->... => -4r8c4 => r7c4=4

(-8r2c3)->8r4c3->8r5c7->4r5c2->2r3c2->... => -8r3c2 => r3c2=2 => r5c1=2

(-1r7c8)->1r7c1->47r89c3->6r6c3->5r6c5->5r5c8->... => -1r5c8 => -1r4c5

(-5r2c9)->18r23c9->9r4c9->5r5c8->5r1c7->5r8c9->... => -5r6c9 => r6c9=4 and 2 placements

(-5r8c4)->9r8c4->9r4c9->5r5c8->... => -5r5c4 => -5r1c5

(-5r2c4)->5r8c4->9r8c9->9r5c8->9r2c4->... => -1r2c4 => r1c5=1 et r5c4=1

(-9r8c9)->9r8c4->5r2c4->5r8c9->... => -1r8c9

(-1r7c8)->1r8c7->1r4c9->9r8c9->... => -9r7c8

(-5r9c2)->9r9c2->9r8c9->5r2c9->5r8c4->... => -5r8c1

(-5r9c2)->9r9c2->9r8c9->1r4c9->1r8c7->5r7c8->... => -5r7c12 => r9c2=5 and stte

Robert

[P.O.]

Code: Select all

after singles and intersections:

4     3     169   8     159   569   125     1256   7             
168   7     1689  159   2     569   3       4     c(18)5     
1268  28    5     7     4     3     9       16    c(18)   
5678  58    678   2     1569  4     1578    3     d15+9           
258  a2±458 3     159   159   7    a1+458  e+159   6             
9     1     ×467  3     56    8     2457    257   b4+5             
158   ×4589 2     459   7     59    6      f(59)1  3             
157   6     147   459   3     2     1457    8      1459           
3     ×459 g+47   6     8     1    f(57)4  f(579)  2             

r5n4{c2 c7} - r6c9{n4 n5} - c9{r2r3}{n1n8} - r4n9{n1n5 n9} - r5c8{n5n9 n1} - b9{r7c8r9c7r9c8}{n5n7n9} - r9c3{n7 n4} => r6c3 r7c2 r9c2 <> 4
singles: ( r5c7b6 n8   r3c2b1 n2   r5c1b4 n2   r5c2b4 n4   r7c4b8 n4 )
intersection: r4n5{c1c2} => r5c5 r5c7 r5c9 <> 5
r4n9{c5 c9} - r8n9{c9 c4} - r5n9{c4 c5} => r5c4 <> 9
r7n1{c8 c1} - c3{r8r9}{n4n7} - c1n7{r8 r4} - r4c7{n7 n1} => r5c8 r8c7 <> 1

 4     3     169   8     159   569   125    1256  7             
 168   7     1689  159   2     569   3      4     158           
 168   2     5     7     4     3     9      16    18             
c56-78 58    678   2     169   4    b(17)   3    b(19)             
 2     4     3     1×5   159   7     8     b(9)5  6             
 9     1     67    3    a±56   8    a24*57 a2*57 a4*5             
 158   589   2     4     7     59    6      159   3             
c15+7  6     147  f+59   3     2    f4-57   8    f14-59           
 3     59   d+47   6     8     1    e4+57   579   2         

r6n5{c5 c7c8c9} - b6{r4c7r4c9r5c8}{n1n7n9} - c1n7{r4 r8} - r9c3{n7 n4} - r9c7{n4n7 n5} - r8n5{c7c9 c4} => r5c4 <> 5
ste.


[denis_berthier]

.
SER = 7.8

Code: Select all

Resolution state after Singles and whips[1]:
   +----------------+----------------+----------------+
   ! 4    3    169  ! 8    159  569  ! 125  1256 7    !
   ! 168  7    1689 ! 159  2    569  ! 3    4    158  !
   ! 1268 28   5    ! 7    4    3    ! 9    16   18   !
   +----------------+----------------+----------------+
   ! 5678 58   678  ! 2    1569 4    ! 1578 3    159  !
   ! 258  2458 3    ! 159  159  7    ! 1458 159  6    !
   ! 9    1    467  ! 3    56   8    ! 2457 257  45   !
   +----------------+----------------+----------------+
   ! 158  4589 2    ! 459  7    59   ! 6    159  3    !
   ! 157  6    147  ! 459  3    2    ! 1457 8    1459 !
   ! 3    459  47   ! 6    8    1    ! 457  579  2    !
   +----------------+----------------+----------------+
139 candidates

No need of "two steps on T&E".
One step of Forcing-T&E is enough.
FORCING[3]-T&E(W1) applied to trivalue candidates n6r4c1, n6r4c3 and n6r4c5 :
===> 16 values decided in the three cases: n6r3c8 n7r8c1 n4r9c3 n1r8c3 n1r7c8 n4r7c4 n4r8c7 n4r6c9 n1r5c4 n6r1c6 n9r1c3 n1r1c5 n8r5c7 n2r3c2 n4r5c2 n2r5c1
===> 63 candidates eliminated in the three cases: n1r1c3 n6r1c3 n5r1c5 n9r1c5 n5r1c6 n9r1c6 n1r1c7 n1r1c8 n5r1c8 n6r1c8 n8r2c1 n1r2c3 n9r2c3 n1r2c4 n6r2c6 n2r3c1 n6r3c1 n8r3c2 n1r3c8 n1r3c9 n7r4c1 n1r4c5 n5r4c5 n5r4c7 n8r4c7 n5r4c9 n5r5c1 n8r5c1 n2r5c2 n5r5c2 n8r5c2 n5r5c4 n9r5c4 n1r5c5 n1r5c7 n4r5c7 n5r5c7 n1r5c8 n4r6c3 n4r6c7 n5r6c7 n7r6c7 n5r6c9 n1r7c1 n4r7c2 n5r7c4 n9r7c4 n5r7c8 n9r7c8 n1r8c1 n5r8c1 n4r8c3 n7r8c3 n4r8c4 n1r8c7 n5r8c7 n7r8c7 n1r8c9 n4r8c9 n4r9c2 n7r9c3 n4r9c7 n5r9c8
stte

Of course, this is absurd for a puzzle that can be solved in Z4.

[DEFISE]

Here is a short solution in W5:

Single(s): 7r3c4, 4r3c5, 3r7c9, 3r2c7, 3r1c2, 2r8c6, 8r9c5, 6r9c4, 7r5c6
Box/Line: 2r1b3 => -2r3c8
Box/Line: 2r6b6 => -2r5c7 -2r5c8
Box/Line: 9c2b7 => -9r8c3 -9r9c3
Box/Line: 6c6b2 => -6r1c5
Box/Line: 8c7b6 => -8r4c9
Naked triplets: 159r5c458 => -5r5c1 -5r5c2 -1r5c7 -5r5c7
Box/Line: 5b4r4 => -5r4c5 -5r4c7 -5r4c9

Code: Select all

|--------------------------------------------------|
| 4    3    169  | 8    159  569  | 125  1256 7    |
| 168  7    1689 | 159  2    569  | 3    4    158  |
| 1268 28   5    | 7    4    3    | 9    16   18   |
|--------------------------------------------------|
| 5678 58   678  | 2    169  4    | 178  3    19   |
| 28   248  3    | 159  159  7    | 48   159  6    |
| 9    1    467  | 3    56   8    | 2457 257  45   |
|--------------------------------------------------|
| 158  4589 2    | 459  7    59   | 6    159  3    |
| 157  6    147  | 459  3    2    | 1457 8    1459 |
| 3    459  47   | 6    8    1    | 457  579  2    |
|--------------------------------------------------|

whip[2]: r4n9{c5 c9}- r8n9{c9 .} => -9r5c4
Box/Line: 9b5c5 => -9r1c5

whip[5]: c9n4{r6 r8}- c9n9{r8 r4}- r5n9{c8 c5}- c5n5{r5 r1}- r2n5{c4 .} => -5r6c9
Single(s): 4r6c9, 8r5c7, 2r5c1, 4r5c2, 2r3c2, 4r7c4

whip[3]: r8n4{c7 c3}- r9c3{n4 n7}- r8n7{c3 .} => -1r8c7

whip[5]: b2n1{r1c5 r2c4}- c3n1{r2 r8}- c9n1{r8 r4}- c9n9{r4 r8}- c4n9{r8 .} => -1r1c7
STTE