Hidden Single in a Box
Cross-hatching
Pick a digit and a box, cast rays from the copies of that digit, and find the only cell still able to take it.
Rule
In a box, digit d has only one cell no ray reaches → that cell is d.
Pick a box and a digit
Look at digit 4 in box 4. The box has no 4 yet and 6 empty cells. Every 4 already on the board is shaded green.
The idea
Switch the question from "which digit goes in this cell?" to "where does the 5 of this box go?". Every box must contain a 5, and every 5 already on the board blocks its whole row and column. We call that a ray.
Cast rays from every 5 onto the box you are studying. Empty cells on a ray are out, and so are cells that already hold a digit. If only one cell is left, the box's 5 must be there — even if, viewed on its own, that cell still has several options.
This is the technique players use most, and usually the fastest way to find digits early in a puzzle.
How to spot it
- Start with the digit that appears most often on the board: it casts the most rays.
- Scan by band: three boxes side by side share three rows. If two of them already have digit d, the third has only one row left for d.
- Boxes with few empty cells tend to give quick results.
Common mistakes
- Forgetting that cells which already hold a digit cannot take d either.
- Scanning only rows and forgetting columns, or the other way round.
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Related techniques
References
The examples on this page are generated from random puzzles, not taken from these sources.