The what-if technique says: suppose a square is one of its numbers, and follow what that forces. If a rule breaks, cross that number out. It’s the technique for when nothing simpler works anywhere.
This is the last of the Futoshiki techniques, each shown on the same 7×7 from the game, Hard level 5.
The rule
- Check that no simpler technique finds anything: no single, no sign with something to say, no pair.
- Pick a square with two numbers left, and suppose it’s one of them.
- Follow what that forces: singles, places, and every sign it touches.
- If a square runs out of numbers, a number runs out of places in a line, or a sign can’t hold, the supposition was wrong. Cross that number out, and if one number is left, that’s the square’s.
In a real puzzle
On the 7×7, it’s first needed at step 7. The square in row 4, column 1 can be 2 or 3. Suppose it’s 3. That forces 16 other squares, one after another, through the lines and the signs, until column 7 has nowhere left for its 2. So row 4, column 1 can’t be 3. It’s 2.
The chain here is long; on paper you’d rarely follow one that far. In practice, try what-if on squares with two numbers left, next to signs, where a choice runs into trouble quickly.
How often you’ll need it
Never on Easy or Medium, and on every Hard level, about 11 times per puzzle on average. On the 7×7 here it’s 3 of the 57 moves.