Sue de Coq
Short answer: take the open cells where a box crosses a row or column, add a cell or two from the rest of that box and a cell or two from the rest of that line, and count. If the group holds exactly as many shapes as it has cells, and the box helpers and the line helpers share no shape, every shape in the group is used up inside it — so each one is struck from the rest of whichever unit it is trapped in.
What a Sue de Coq looks like
The two or three cells where a box crosses a line are the only cells in the grid that belong to both units at once, which is why so many techniques start there. Box/line reduction uses them to move one shape between the two units. Sue de Coq uses them to move a whole handful, by treating the intersection and one helper set in each unit as a single group that has to swallow its entire pool of shapes.
Count it through. Four cells, four shapes, and no shape outside that pool anywhere in the four — so each cell takes a different one and all four shapes are spent. Two of the four hold only the diamond and the star, so the plus and the ring have to go to the other two cells, and both of those sit in the column. The column has therefore already placed its plus and its ring, and every other cell in it loses them.
How to use Sue de Coq
- Pick a busy intersection. Find a box and a row or column that cross in two or three still-open cells. List every shape those cells can hold — that pool is what the rest of the pattern has to account for. If the pool has fewer than two more shapes than there are intersection cells, move on.
- Fill the box side. Look in the rest of the box for one or two cells whose candidates all come from the pool. These are your box helpers, and whatever shapes they take are shapes the box has now used up.
- Fill the line side. Do the same in the rest of the line, with one rule added: the line helpers must share no shape with the box helpers. If they overlap, the two sides could take the same shape and the counting collapses.
- Check the count, then strike. The intersection cells and both helper sets must total exactly as many cells as the pool has shapes. When they do, remove every pool shape the line helpers cannot hold from the rest of the box, and every pool shape the box helpers cannot hold from the rest of the line.
Both halves fire at once, which is what makes the pattern worth the effort — but only one half produces anything on most grids, as in the figure above. Check both anyway: the elimination you were not looking for is usually the one that unblocks the puzzle.
Sue de Coq vs box/line reduction
They start in the same place and stop at very different depths. Box/line reduction asks one question about one shape: is it confined to the intersection? Sue de Coq asks about every shape in the intersection at once, and answers by finding cells elsewhere in each unit that mop up the leftovers. That is why it can strike shapes in both units from one pattern, and why it is worth reaching for only once the single-shape questions have all been asked.
Find Sue de Coq in your own grid
Paste a puzzle and this page will look for Sue de Coq in it — the same pattern shown above, in your grid instead of ours. Nothing is uploaded; it runs in your browser.
Frequently asked questions
Where does the name come from?
From the forum handle of the person who first described it, on the Sudoku Programmers forum in 2005. It is a name, not a description — which is why every language keeps it as it is. Solvers that dislike naming techniques after people call it "two-sector disjoint subsets", which says exactly what it does and nobody remembers.
Why do the two helper sets have to be disjoint?
Because a cell in the box helpers and a cell in the line helpers do not see each other — they share no row, column or box. Every other pair of cells in the pattern does. If both helper sets could take the same shape, that shape might be used twice inside the group, the cell count would no longer force one shape each, and the whole argument goes.
What if one of the helper sets is empty?
Then it is not a Sue de Coq. With no line helpers the group sits entirely inside the box and is just a naked subset there; with no box helpers it is a naked subset in the line. Both are worth spotting, but you learned them several tiers ago and neither needs the intersection.
Is this really an almost locked set technique?
Yes — it is two almost locked sets doubly linked through the intersection, and solvers that implement ALS chains often find it without a separate rule. It is taught on its own here because the geometry is fixed: a box, a line and the cells where they cross is something you can scan for by eye, while a general pair of almost locked sets is not.
How often is it actually available?
Rarely, and less often than it looks: many grids that contain one also let something easier reach the same eliminations. The board above is deliberately not one of those — none of the twenty-two easier techniques form9 knows can strike the plus from that cell. If you want the check done for you, the sudoku solver walks a grid one technique at a time and names each move.