The what-if technique says: suppose a square is kept unshaded (or shaded), and follow what the chain forces. If a rule breaks, the square goes the other way. It’s the technique for when nothing simpler works anywhere.
This is the last of the Hitori techniques.
The rule
- Check that no sandwich, chain move, pair or cut-off is left anywhere.
- Pick a square, often one next to shaded squares or near an edge, and suppose it stays unshaded.
- Follow the chain: shade its twins, circle around every shade, and keep an eye on the joining-up rule.
- If two shaded squares end up side by side, a number repeats, or something gets walled in, the supposition was wrong: the square is shaded. (And the same the other way round.)
In a real puzzle
On the 9×9 every technique page follows, it’s needed once, at step 31. Suppose the 5 in row 3, column 1 stays unshaded. That starts a long chain across the grid: 24 forced moves, each following from the one before. At the end of it, two squares side by side in row 8, columns 8 and 9, would both have to be shaded. That breaks a rule, so the 5 in row 3, column 1 can’t stay. It’s shaded.
The chain here is long; on paper you’d rarely follow one that far. In practice, try what if on squares where the chain is short: next to shaded squares, near the edges, where a choice runs into trouble quickly.
How often you’ll need it
Never on Easy, on 7 of the 50 Medium levels, and on every Hard level, about twice per puzzle. On the 9×9 here it’s 1 of the 55 moves.