Futoshiki
How to solve Futoshiki: reading the signs and following chains
Updated Tuesday, October 27
To solve a Futoshiki, start with what the signs forbid: a square smaller than a neighbour can never hold the largest number, a larger one never holds 1. Follow chains of signs to narrow the squares further, then find the numbers with only one place left. Every Gridarium futoshiki can be finished this way, without guessing.
The rules
Every row and every column holds each number from 1 to the size of the grid exactly once. A sign between two squares says which is larger: the point of the chevron faces the smaller number.
Step 1: what a sign rules out
On a 5 by 5 grid, a square that is smaller than a neighbour can only be 1 to 4, and a square larger than a neighbour can only be 2 to 5. Pencil these limits in as notes.
Step 2: follow the chains
When signs line up, the limits add up. Three squares rising one after another on a 5 by 5 grid: the first is at most 3, the last is at least 3. A written number pushes its whole chain: a square smaller than a 2 must be a 1.
Step 3: the only number, the only place
As in a sudoku, a square left with a single possible number takes it, and a number with a single possible square in its row or column goes there.
Step 4: pairs
Two squares of a row or column that can only hold the same two numbers use them up: no other square of that line can take them. Hard puzzles need this.
The three levels
- Easy: 5 by 5.
- Medium: 6 by 6.
- Hard: 7 by 7.