Futoshiki looks decorative—little comparison signs floating between cells—but the rules are crisp. This guide states them without fluff, ties them to how ProPuz presents puzzles, and shows where beginners usually misread the board. If you want habits more than definitions, pair this page with our beginner tips.
The grid and the digit set
A Futoshiki puzzle is an n×n square. You place integers from 1 through n so that each number appears exactly once in every row and exactly once in every column. There are no 3×3 boxes like classic Sudoku. The uniqueness rule is the Latin-square requirement: same alphabet of symbols, row and column constraints only.
On ProPuz, n tracks difficulty: Easy uses 4, Medium 5, Hard 6, Expert 7. Larger n means more digits to track and more possible inequality edges between neighbors—bookkeeping grows even when the sentence of rules stays the same.
Inequalities between neighbors
Between some horizontally or vertically adjacent cells you will see a comparison: typically > or < (vertical glyphs may look like chevrons pointing up or down). The two cells sharing that edge must satisfy the comparison with their final digits. Equal values are never allowed across an inequality edge because the relation is strict.
Not every edge carries a sign. Empty channels are free of inequality constraints—though the Latin-square rules still apply. Never invent a comparison where none is printed. Conversely, never ignore a printed sign because the digits “almost” work.
How to read a sign consistently
Horizontal > between left cell L and right cell R means L is greater than R. Horizontal < means L is less than R. Vertical signs follow the same idea along the column: the relationship is between the upper and lower cells according to the glyph orientation used on the board. If a site’s art style confuses you, translate each glyph into a plain sentence before placing digits.
A useful mnemonic: the open side of a chevron faces the smaller number. Practice it on a tiny example until your eyes stop flipping the meaning under stress.
Givens
Some cells start filled. Those givens are part of the puzzle statement. You may not change them. They interact with inequalities the same way your own fills do: a given 4 next to a less-than edge toward a blank cell immediately forbids 4 in that blank, and often forbids other highs depending on n.
Givens also reserve digits in their row and column. Treat each given as both a Latin-square claim and an inequality participant. Skipping either view is how “almost finished” boards fail validation.
What counts as solved
A grid is solved when every cell holds a digit from 1 to n, every row and column contains each digit once, and every printed inequality is true. Partial grids can look promising and still be illegal. On ProPuz, Check grid compares your entry against the stored solution for that puzzle ID—so play aims at the unique intended completion, not an alternate Latin square that happens to satisfy the visible signs if one existed.
Well-designed Futoshiki puzzles are generated to be uniquely solvable from the given clues. If you feel two fills both “work,” one of them usually violates a sign you have not re-checked or a uniqueness constraint you have not scanned.
What Futoshiki is not
It is not Sudoku: no boxes, and clue density often sits in inequalities rather than dozens of given digits. It is not a magic square: line sums do not need to match. It is not KenKen: there are no cage operations beyond the pairwise comparisons shown. Keeping those boundaries clear stops you from importing the wrong checklist mid-solve.
It is also not a race by definition. Timed play is optional. Accuracy with inequalities is the core skill; speed is a side effect of cleaner scanning.
Worked micro-example (4×4 thinking)
Suppose a row shows blank, blank, blank, blank with a > between the first and second cells and a given 1 in the fourth cell. The first cell cannot be 1 (already used in the row via the given) and must exceed the second cell. The digit 4 is a strong candidate for early placement somewhere that can sit on the large side of comparisons. You would next scan the column of each blank for conflicts. This is the whole game in miniature: combine local comparisons with global uniqueness.
If an inequality chain A > B > C appears, then A > C automatically even if A and C do not share an edge. That transitive idea is still “basic rules” plus elementary logic—you are not inventing new laws, only applying the printed ones carefully.
Interface rules on ProPuz
Select a cell, type a digit 1–n for that puzzle size, erase when needed, and move with clicks or arrows. Generate a new puzzle from the sidebar when you want a fresh layout. Daily challenges freeze a shared puzzle per date and tier so friends can compare notes on the same board. Printable views help offline practice; the rules on paper are identical to the rules on screen.
If Check reports an error, believe the checker and hunt the broken contract. Debating the interface rarely fixes a duplicated 2 or a reversed inequality.
Glossary-style recap
Order / size — side length n. Latin square — rows and columns each contain 1..n once. Inequality / clue — strict comparison on an adjacent edge. Given — pre-filled cell. Solution — complete legal grid matching the puzzle’s intended answer on ProPuz.
Memorize those five terms and you can read almost any Futoshiki help page without getting lost in branding differences between sites.
Keep going
Rules are short; skill is scanning. Practice them on an Easy ProPuz grid, review how to play, study common mistakes, or follow a structured walkthrough in solve a 4×4 step-by-step. Return to the articles hub whenever you want the next guide in the series.