Futoshiki guide: turn inequalities into bounds
Use chains, extreme values and row-column checks to narrow the grid.
The rules
Fill each row and column with 1 through the grid size, once each, while respecting the inequality signs. Easy, normal and hard use 4×4 / 5×5 / 6×6. There are no Sudoku-style box constraints. Digits may repeat nearby if they occupy different rows and columns.
The pointed end of a sign faces the smaller value. A horizontal < means the left cell is smaller; a vertical ∧ means the upper cell is smaller. Givens are fixed, and generation checks that the solution is unique.
Getting started
Find the longest inequality chain first. It needs distinct values along its increasing path, so you can bound cells before solving them. Then inspect nearly full rows and columns, subtracting their used digits from those ranges.
Write the whole possible range rather than assuming the smaller side is 1. In A<B<C, B needs both a smaller and a larger value. The diagrams isolate one row of a 4×4 grid and show every candidate allowed by that row’s givens, no-repeat rule and signs. A full puzzle adds the column constraints.
A full-length chain
Fill a chain that spans the whole row in order. A<B<C<D in a 4×4 row must be 1,2,3,4: four distinct increasing values use the entire range. If a sign reverses partway through, stop treating the path as one increasing chain and read the next relationship separately.
One row in isolation
Bounds from a shorter chain
Record bounds when a chain is shorter than the row. A<B<C allows {1,2}, {2,3}, {3,4}. A needs two larger values after it, so it cannot exceed 2; C needs two smaller values before it, so it is at least 3. The fourth cell has no sign and still permits every digit from 1 to 4.
One row in isolation
Place the extremes
Eliminate impossible extreme values first. If A>B, A cannot be 1 and B cannot be the maximum. With 4 given on the left, all three remaining cells allow {1,2,3}. Even the signed neighbor remains unresolved: both 4>1 and 4>3 are valid. The sign does not require consecutive values.
One row in isolation
Intersect row and column information
Check a row with only one missing digit. With 1,3,4 present here, the final cell needs 2. On a full board, verify its column and attached inequalities too. Also count locations for a digit: a cell with several candidates can still be its row’s only place for one of them.
One row in isolation
Common mistakes
Do not add constraints that are not drawn. There is no Sudoku box rule, and unsigned neighbors have no separate ordering requirement. Read a vertical sign by naming its smaller side before entering a value.
Do not add the lengths of branching chains as if they formed one path. Cells on different branches may reuse a value when they share neither row nor column. Bound an actual increasing path, propagate tighter bounds to its neighbors, then return to row and column checks after a placement.
Records and challenges on this site
Each puzzle allows 3 hints. A hint fills the selected cell and adds 60 seconds to the ranked time. Undo does not restore the allowance.
The server regenerates the puzzle and replays your entries to verify completion. Rankings are by difficulty, with shorter penalized times first. Submission rounds remain valid for 120 minutes; refreshing or leaving the tab does not stop elapsed time. When daily challenges are enabled and Futoshiki is selected, players share that day’s puzzle. The daily boundary is UTC midnight.
Frequently asked questions
Are there box constraints?
No. Use rows, columns and the inequalities that are actually shown.
Do signs mean consecutive digits?
No. They compare size only, so the difference can exceed one.
Can I resume later?
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