The New Sudoku Players' Forum

[m_b_metcalf]

Code: Select all

 1 . . 2 3 . . . .
 . . 4 . . 5 . . .
 . 5 . . . . 6 . .
 6 . . . . 3 . 7 .
 8 . . . 1 . . . 3
 . 2 . 5 . . . 8 .
 . . 9 . . . 1 . .
 . . . 7 . 4 . . .
 . . . . 6 . . . 2   one backdoor + singles

1..23......4..5....5....6..6....3.7.8...1...3.2.5...8...9...1.....7.4.......6...2

Thanks for the solutions so far, but I still have no idea to what extent P&P solvers can spot these backdoors

[denis_berthier]

Thanks for the solutions so far, but I still have no idea to what extent P&P solvers can spot these backdoors

Hi Mike.
This is the 1 million dollar question and you'll get no answer.

This puzzle has a single Singles-backdoor: n6r7c8

Let me first discard the often suggested idea that one should "focus on the bivalue cells". It doesn't work for finding candidates that can be eliminated and it doesn't work here either.

After initialisation, the resolution state is as follows, in each of the 4 views, where I've marked with a * the place of candidate n6r7c8:

Code: Select all

standard rc-view:
Physical rows are rows, physical columns are columns. Data are digits.
   1         6789      678       2         3         6789      45789     459       45789     
   2379      36789     4         1689      789       5         23789     1239      1789     
   2379      5         2378      1489      4789      1789      6         12349     14789     
   6         149       15        489       2489      3         2459      7         1459     
   8         479       57        469       1         2679      2459      24569     3         
   3479      2         137       5         479       679       49        8         1469     
   23457     34678     9         38        258       28        1         3456*     45678     
   235       1368      123568    7         2589      4         3589      3569      5689     
   3457      13478     13578     1389      6         189       345789    3459      2         

The following representations, first introduced in the "Hidden Logic of Sudoku"  (HLS, 2007),
may be used e.g. to more easily spot:
rn-, cn- or bn- bivalue pairs (also named bilocal pairs),
mono-typed-chains (the 2D-chains of HLS),
Hidden Subsets and Fishes (which will appear as Naked Subsets in the proper space).

rn-view:
Physical rows are rows, physical columns are digits. Data are columns.
   1         4         5         789       789       236       23679     23679     26789     
   489       178       1278      3         6         24        12579     24579     1245789   
   4689      138       138       4589      2         7         13569     34569     145689   
   239       57        6         24579     379       1         8         45        24579     
   5         678       9         2478      378       468       236       1         24678     
   39        2         13        1579      4         69        1356      8         15679     
   7         156       1248      1289      1589      289*      129       24569     3         
   23        135       12378     6         135789    2389      4         23579     5789     
   2346      9         123478    1278      1378      5         1237      23467     4678     

cn-view:
Physical rows are columns, physical columns are digits. Data are rows.
   1         2378      236789    679       789       4         23679     5         236       
   489       6         2789      4579      3         1278      12579     12789     1245     
   4689      38        3689      2         4589      18        13569     1389      7         
   239       1         79        345       6         25        8         23479     23459     
   5         478       1         346       78        9         236       23478     23468     
   39        57        4         8         2         156       1356      1379      13569     
   7         245       289       14569     14589     3         129       1289      1245689   
   23        235       23789     13579     15789     578*      4         6         123589   
   2346      9         5         13467     1478      678       1237      12378     123468   

bn-view:
Physical rows are blocks, physical columns are digits. Data are positions in a block.
   1         479       4579      6         8         235       234579    2359      2457     
   479       1         2         78        6         34        3589      345789    345789   
   5689      458       458       12389     123       7         13469     13469     12345689 
   239       8         79        257       36        1         5679      4         257       
   5         26        3         1248      7         469       689       12        124689   
   39        145       6         134579    1345      59        2         8         134579   
   5689      146       12456789  1278      14679     256       12789     25689     3         
   79        235       17        6         25        8         4         123579    579       
   1         9         24578     2378      2345678   2356*     37        3467      45678     

As you can see, candidate n6r7c8 is not in a bivalue cell, in any of the four spaces.
.

[denis_berthier]

.
Now, let's compare your problem with the much more frequently encountered one: find an anti-backdoor. The two problems are formally very similar (add a decided value vs delete a candidate).

The latter problem has been appearing on this forum for decades, under the question: find a single-step solution. (I know the two problems are not equivalent when a single rule can eliminate several candidates, but they are sufficiently close to illustrate my point.)
My point is, all along these decades, you have seen thousands of 1-step solutions to particular puzzles, but have you ever seen any answer to the question: how do you find a 1-step solution (other than "try all the candidates")?

The general problem is, the effects of adding a decided value or eliminating a candidate are unpredictable. You have to try it and check the results.

Talking about adding a decided value, there are very few resolution rules that add a value, but the (relatively) recent case of the simplest case of tridagons (i.e. with a single guardian) is a very good example. After you add the value decided by the tridagon rule, what you are left with may be as simple as a puzzle in BC3 (e.g. the famous Loki puzzle) or may still be in T&E(2).
.

[m_b_metcalf]

Thanks for the solutions so far, but I still have no idea to what extent P&P solvers can spot these backdoors

Hi Mike.
This is the 1 million dollar question and you'll get no answer.

Denis,
Thanks for your thorough analysis. My project is hereby abandoned.

This puzzle has a single Singles-backdoor: n6r7c8

I find also 6r1c2.

Regars,

Mike