PIsaacson wrote:Shouldn't the wiki be corrected to state that the A/B sets are N cells with N+1 candidates?

I think you are right (after all, if it was N cells with N candidates we would have two locked sets, no need for an SDC). But even with that change, it won't cover all cases. Look at the following example (posted by ronk a while back). It has 6 candidates in 4 cells in r8:

- Code: Select all
`.---------------.--------------------.------------------------------.`

| 19 3 256 | 24579 24789 4579 | 4568 -4-5678 1678 |

| 8 7 25 | 6 24 1 | 9 C45 3 |

| 19 4 56 | 3579 3789 3579 | 568 2 1678 |

:---------------+--------------------+------------------------------:

| 2 15 1347 | 8 379 6 | 345 A4579 B79 |

| 357 68 9 | 2347 2347 347 | 1 A45678 B678 |

| 37 68 347 | 1 5 3479 | 234-6-8 A46789 2-6-7-8-9 |

:---------------+--------------------+------------------------------:

| 4 19 137 | 37 367 2 | 68 689 5 |

| 357 59 37 | 347 3467 8 | 26 1 269 |

| 6 2 8 | 59 1 59 | 7 3 4 |

'---------------'--------------------'------------------------------'

Sue de Coq: r456c8 - {456789} (r2c8 - {45}, r45c9 - {6789}) => r1c8<>45, r6c7<>68, r6c9<>6789

Although I just got corrected by DonM in another thread I still refer to the original definition (plus the additions made in the "Sue de Co revisited" thread):

Sue de Coq wrote:Consider the set of unfilled cells C that lies at the intersection of Box B and Row (or Column) R. Suppose |C|>=2. Let V be the set of candidate values to occur in C. Suppose |V|>= |C|+2. The pattern requires that we find |V|-|C| cells in B and R, with at least one cell in each, with candidates drawn entirely from V. Label the sets of cells CB and CR and their candidates VB and VR. Crucially, no candidate is allowed to appear in VB and VR. Then C must contain V\(VB U VR) [possibly empty], |VB|-|CB| elements of VB and |VR|-|CR| elements of VR. The construction allows us to eliminate the candidates V\VR from B\(C U CB) and the candidates V\VB from R\(C U CR).