Sue de Coq
A box/line intersection splits its digits between the line and box.
The Sue de Coq sudoku technique — sometimes labelled a two-sector disjoint subset — works on the small cluster of cells where a box overlaps a row or column. You gather the candidates sitting in that intersection, then ask whether they split cleanly into one group finished off by a subset elsewhere in the line and a separate, non-overlapping group finished off by a subset elsewhere in the box. When they divide that way, the line-part digits are locked out of the rest of the line and the box-part digits out of the rest of the box, both in a single move.
Worked example
On this grid box 7 meets row 7 at R7C1={3,4,5} and R7C3={4,5,9}, so the intersection between them carries the four digits {3,4,5,9}. Elsewhere in row 7 the bivalue R7C7={4,5} accounts for the 4 and 5, while elsewhere in box 7 the bivalue R8C3={3,9} accounts for the 3 and 9 — a clean, disjoint split of those four digits. That confines {4,5} to the row-7 sector, so R7C5={4,7} loses its 4; and it confines {3,9} to the box-7 sector, so R9C2={3,8} loses its 3.
When to use it
Reach for it late in a solve, once singles, pointing pairs and naked subsets have stalled on a grid dense with box/line interactions. Scan the two or three cells where a box crosses a row or column, total their combined candidates, then hunt for a bivalue in the rest of the line and a bivalue in the rest of the box that between them cover every one of those digits with no overlap. A perfect, non-overlapping match earns you eliminations in both houses at once.
How to use it
- Find the intersection pair. Find two cells where a box and a line (row or column) overlap that together hold exactly four candidates.
- Split with two bivalue cells. Find a two-candidate cell in the line (outside the box) holding two of the four digits, and a two-candidate cell in the box (outside the line) holding the other two.
- Clear each pair from its house. The four cells use the four digits between them, so the line pair leaves the rest of the line and the box pair leaves the rest of the box.
Frequently asked questions
What is a Sue de Coq in Sudoku?
It is a box/line intersection pattern, also known as a two-sector disjoint subset. The candidates in the cells where a box overlaps a row or column divide into two disjoint groups: one completed by a subset in the rest of the line, the other by a subset in the rest of the box. That split forces eliminations in both houses simultaneously — in the worked example {4,5} clears from the rest of row 7 while {3,9} clears from the rest of box 7.
How do I spot a Sue de Coq?
Start at the two or three cells where a box overlaps a line and tally their combined candidates — here {3,4,5,9} across R7C1 and R7C3. Then look for one bivalue in the rest of the line and one in the rest of the box that together cover exactly those digits with nothing shared: R7C7={4,5} and R8C3={3,9} do it. When the two subsets partition the intersection's digits perfectly, with no overlap, you have a Sue de Coq.
How is a Sue de Coq related to naked subsets and ALS?
It is essentially two almost-locked sets that share the intersection cells — a naked-subset argument stretched across a box and a line at the same time. The line subset locks its digits into the line just as a naked pair would, and the box subset does the same within the box. Reading R7C7={4,5} and R8C3={3,9} as the two ALS sharing R7C1 and R7C3 makes the double elimination fall out naturally.