Unique Rectangles and the Deadly Pattern

The deadly pattern

Picture four cells that form a rectangle, sitting in two rows, two columns and spanning exactly two boxes. Now imagine all four cells hold only the same two candidates, say 3 and 7. If the finished puzzle really looked like that, you could swap the 3s and 7s around the rectangle and still satisfy every rule. That would give two solutions, which a proper puzzle never has. The pattern is called deadly for that reason.

Turning the pattern into a move

Because the deadly pattern cannot exist in a puzzle with one solution, something must break it. That knowledge lets you remove candidates. The simplest case is a Type 1 Unique Rectangle. Three of the four corners hold just the bare pair, and the fourth corner holds that pair plus one or more extra candidates. The extras are what save the puzzle, so the pair itself must be wrong in that fourth cell. You erase both pair values there, leaving only the extras.

How to spot one

1. Look for two rows and two columns whose four intersection cells all involve the same two candidates.
2. Check that the four cells span only two boxes. If they cross three boxes the argument does not hold.
3. If three corners are exactly the bare pair and one has extra candidates, you have a Type 1.
4. Delete both pair values from the corner that carries the extras.

Use it with care

Unique Rectangles only work when the puzzle is guaranteed to have a single solution. Every board in Shapedoku is validated for a unique solution before it is served, so the logic is safe here. If you ever solve a puzzle from an untrusted source, be aware that uniqueness tricks can misfire on an improper grid.