Multisector Locked Set
When the maximum counts of each digit across cells in multiple rows and columns sum to the number of cells, every maximum must be reached, eliminating conflicting candidates.
All candidates have been entered in the empty cells.
The 8 cells in A have no candidates other than 1, 2, 3 and 4.
| Digit | Positions and limits within A | Maximum |
|---|---|---|
| 1 | At most one in each of row B, row C | 2 |
| 2 | At most one in each of row C, row D | 2 |
| 3 | At most one in each of column E, column F | 2 |
| 4 | At most one in each of column F, column G | 2 |
Suppose 1 is placed outside A in row C. No cell of A in row C can then contain 1. In A, 1 can now appear only in row B, so its maximum drops to 1. A can then contain at most 1 + 2 + 2 + 2 = 7 digits, which cannot fill its 8 cells. Remove candidate 1 marked × outside A in row C.