Futoshiki Tips: How to Solve Inequality Puzzles Fast
Futoshiki ("not equal" in Japanese, also published as More or Less) is Sudoku's sharp-tongued cousin: fill the grid so every row and column holds 1–N exactly once, while every ‹ and › sign between cells tells the truth. Good boards give you almost no starting numbers — the signs carry the logic. Here's the technique ladder, from first move to the tricks that crack a bare 7×7. Every board on our free Futoshiki is solvable with these steps alone.
0. Read the signs right
The point of the sign always aims at the smaller number — including vertical signs, where the point aims up or down. Misreading one sign poisons everything downstream, so make this automatic before anything else.
1. Chase the chains
Signs chain into ladders, and ladders are the strongest clue on the board. In a ‹ b ‹ c ‹ d, the cell a is at most N−3 and d is at least 4; on a 5×5, a four-cell ladder pins its ends to 1-ish and 5-ish immediately. Trace every chain when you first look at the board — the longest one is usually the intended way in.
2. Place the extremes first
The 1 can never sit on the open (larger) side of any sign; the N can never sit on the point side. Scan each row and column asking just two questions: where can its 1 go? where can its N? Very often only one cell qualifies — that's a placement, no other technique needed. This single habit solves most 5×5 boards nearly alone.
3. Think in ranges
Treat every empty cell as a range of possible values. Each sign trims a range: "less than a neighbor whose maximum is 4" cuts you to 1–3. Each placed number trims every range in its row and column. When a range collapses to one value, write it in and propagate. This is exactly how our teaching hints reason when you ask for help — they'll show which neighbors and signs did the squeezing.
4. Hidden singles finish the middle game
Straight from Sudoku: if a value fits in only one cell of a row or column — even though that cell has other candidates — it must go there. In Futoshiki the "fits" check includes signs, which eliminate more cells than beginners expect. When ranges stall, sweep each row/column value by value; a hidden single is almost always hiding (the Sudoku version of this technique transfers directly).
5. The two-candidate test
Endgame cells often come down to two candidates. Test one mentally: follow the signs and the uniqueness rule a step or two; if some cell runs out of options, the tested value was wrong and the other is forced. This isn't guessing — it's a bounded proof by contradiction, and boards never require more than one step of it on our generator.
Common mistakes
- Sign blindness mid-solve. A number placed next to a sign constrains the neighbor immediately — re-check all four signs around every entry.
- Treating it as Sudoku with decoration. The signs aren't hints, they're the spine. A row with three signs is usually easier than a row with a given number.
- Forgetting uniqueness away from signs. Rows and columns need 1–N once each everywhere, signed or not.
- Random-filling small boards. 4×4 tolerates it; 6×6 will punish you. The extremes-first habit is faster anyway.
Play free unlimited Futoshiki — 5×5 to 7×7, near-zero givens, a shared daily with streaks, and hints that explain the deduction instead of just filling the cell. If you like latin-square logic, our Sudoku and the binary-balance SunMoon are natural next steps.