Sudoku techniques · Extreme
Sue de Coq in Sudoku
Sue de Coq looks at the cells a box and a line share. When those cells hold two more distinct candidates than there are cells, and two bivalue helpers, one elsewhere in the line, one elsewhere in the box, draw disjoint pairs from the same pool, every number in that pool is placed exactly once across the crossing and the helpers. That pins down eliminations in both the line and the box.
Also known as: Two-Sector Disjoint Subsets.
Why it works
When cells at a box-line crossing collectively have two more distinct candidates than cells, a bivalue helper outside the box in the line and another outside the line in the box can draw disjoint pairs from that pool. Every pool digit must then be placed exactly once among the crossing cells and helpers. The line helper's digits can be removed from the line outside the crossing cells and that helper; the box helper's digits can be removed from the box outside the crossing cells and that helper. Any pool digits in neither helper are confined to the crossing cells and can be removed from both the line and the box outside those cells.
How to spot it
One of the least intuitive patterns in Sudoku, and among the most productive when it lands.
- Start at a box-line crossing with two or three unsolved cells and count their distinct candidates. You want cells + 2.
- Find a bivalue cell in the line outside the crossing and another in the box outside the line, whose candidate pairs come from the pool and do not overlap.
- Eliminations land in the line and the box separately, which is why it is called a two-sector pattern.
Builds on
Worked example
These are the app's own lesson boards. Step through them the same way a hint does.
PatternAnswerContextBlockerElimination
26
38
2368
236
Step 1 of 3
- 1
These 2 cells sit where the outlined box crosses a column. Together they hold 4 different candidates, two more than the number of cells, so every digit that lands in them must come from that small pool.
- 2
Two more helper cells take their candidates from the same pool, and each of them has only two candidates left. One helper is in the same column and its two candidates are 2, 6. The other is in the same box and its two candidates are 3, 8. The two pairs have no candidate in common. So there are now 4 cells and 4 digits: the crossing cells and the two helpers each take a different digit from the pool, and every pool digit is used exactly once.
- 3
However the digits fall, 2, 6 can only be in the crossing cells or in the column helper, and 3, 8 can only be in the crossing cells or in the box helper. So we can remove 2, 6 from all the remaining cells of the column, and 3, 8 from all the remaining cells of the box.