- A cell with exactly two candidates is a bi-value cell — the basis of many advanced techniques
- Never guess between the two options — there is always a logical way to determine the correct one
- Look for XY-Wing: a chain of three bi-value cells that forces one candidate out of a cell
- Look for Unique Rectangles: if both candidates would create a deadly pattern, one can be eliminated
- Use conjugate pair chains to trace consequences — one path will eventually lead to a contradiction
What It Means to Have Two Options
When a cell has exactly two candidates remaining — say 4 and 7 — neither has been eliminated by direct constraint from its row, column, or box. This bi-value state is not a dead end; it is an opportunity. Bi-value cells are the building blocks of virtually all advanced Sudoku techniques.
Technique 1: Look for an XY-Wing
If the bi-value cell has candidates XY, look for two other bi-value cells in its row, column, or box: one with candidates XZ and one with candidates YZ. If you find this triangle, any cell that sees both the XZ and YZ cells cannot hold Z — regardless of which option the XY cell takes. This is an XY-Wing elimination.
Technique 2: Check for a Unique Rectangle
If the bi-value cell and three other cells form a rectangle across two boxes, and all four cells contain the same two candidates, you have a potential Unique Rectangle. On a valid (single-solution) puzzle, this deadly pattern must be prevented — meaning the puzzle must have resolved one of those four cells in a specific way. Look at which cell has additional candidates to determine the resolution.
Technique 3: Conjugate Pair Tracing
If the two candidates in your cell form a conjugate pair (only two cells in some unit can hold that digit), trace what happens if one is true. Follow the logical chain: if this cell = 4, then that cell ≠ 4, then that other cell = 7… Continue until you either solve the chain cleanly or find a contradiction. The contradiction eliminates the assumed value.
When None of These Work Immediately
Check other parts of the grid first. Sometimes the two-option cell resolves itself after you apply techniques to a completely different area. The techniques library has a structured progression — work through it systematically before concluding that the bi-value cell is unresolvable by logic. If you're practicing this skill, the Expert puzzle page will give you plenty of real bi-value scenarios to work through.