A sign rules numbers out on both sides of it. The smaller side can’t be the top number, and the larger side can’t be 1. More than that: the smaller side must be less than the biggest number the larger side could be, and the larger side more than the smallest the smaller side could be. Follow a chain of signs, and every square along it narrows.
This is one of the Futoshiki techniques, each shown on the same 7×7 from the game, Hard level 5.
The rule
- For each sign, look at what the larger side could be. The smaller side must be less than the biggest of those.
- Look at what the smaller side could be. The larger side must be more than the smallest of those.
- When either side changes, look at the signs next to it: a change travels along a chain.
- If that leaves a square one number, or a number one place in a line, fill it in.
In a real puzzle
On the 7×7, the very first move comes from the signs. Row 5 needs a 1. But five of its squares are on the larger side of a sign, and the larger side is never 1, and the last square is the 4. That leaves one square that could take the 1: column 3.
How often you’ll need it
On every one of the game’s 150 levels, and always for the first move. It’s 15 of the 57 moves on the 7×7 here, and on average 10.4 per Easy level, 13.5 on Medium and 13.4 on Hard.