Guide
How to Play Futoshiki
Futoshiki is a logic puzzle of numbers and inequalities. Fill the grid with 1 to N so no digit repeats in a row or column and every < and > sign is true.
Play FutoshikiThe objective
Fill the grid so every rule holds
Futoshiki is played on a square grid. You place the digits 1 to N — where N is the width of the grid — so that every row and every column contains each digit exactly once, and every inequality sign between two neighbouring cells is true.
Some cells are filled in for you, and the signs supply the rest of the clues. There is no timer forcing your hand and no guessing: every puzzle here has exactly one solution that can be reached by logic alone.
The game is free, runs in the browser, and needs no account. Open the board when you want to play; use this guide for the rules, the controls, the board sizes, and the habits that solve puzzles faster.
The grid
Givens, signs, and empty cells
A 5×5 puzzle has 25 cells. A handful already show a digit — those givens are shaded and cannot be changed. Between neighbouring cells you will see small wedge signs. A < between two side-by-side cells means the left digit is smaller; a > means it is larger. Vertical signs compare a cell with the one below it: ∧ means the top cell is smaller, ∨ means it is larger.
Every puzzle is a fresh random grid, checked by a solver before you see it. Use the size buttons to pick 4×4 to 9×9 and the difficulty buttons to switch between Easy and Hard.
Controls
Tap, type, or use the keyboard
Every method enters the same digits. Pick whichever fits the device in your hand.
Mouse and touch
Tap or click a cell, then a number
Select any empty cell, then press a digit on the number pad under the board. Tapping the same digit again clears the cell. Digits that already appear N times are greyed out on the pad.
Desktop
Keyboard: arrows and 1–9
Arrow keys move the selection around the board and the number keys enter a digit. Backspace, Delete or 0 clears the selected cell.
Everywhere
Pencil notes (P)
Switch on Notes and the number pad toggles small candidate marks in the selected cell instead of placing a digit. When you place a real digit, that digit is removed from the notes of every cell in its row and column.
Everywhere
Undo (U or Ctrl+Z)
Unlimited undo steps back through digits, notes, erases and hints one move at a time.
Everywhere
Hint (H)
Fills in one cell with its correct digit — the selected cell if it is empty or wrong, otherwise a random one. Hints are counted, and a solve that used hints does not set a best time.
Everywhere
New puzzle (N) and Mute (M)
N deals a fresh puzzle at the current size and difficulty without reloading the page. M toggles the synthesized sound effects; your choice is remembered on this device.
The loop
Four steps you repeat all puzzle
Reading the clues, then working through these four steps is the whole game.
- 1
Read the grid
The board is an N×N square — 4×4 up to 9×9 here. Some cells already hold a digit. Small < and > signs sit between neighbouring cells, and each one points at the smaller of the two numbers.
- 2
Fill in 1 to N
Every row and every column must contain each digit from 1 to N exactly once, just like a Latin square or a Sudoku with no boxes. In a 5×5 puzzle that means the digits 1 to 5 appear once in every row and once in every column.
- 3
Obey the signs
If a sign says the left cell is smaller than the right cell, the digit on the left must be lower than the digit on the right. A digit like 1 can never sit on the big side of a sign, and N can never sit on the small side — that is where most deductions begin.
- 4
Solve by logic
Every puzzle here has exactly one solution and can be solved without guessing. Use pencil notes to track what each cell could still be, cross candidates out as signs and digits rule them out, and place a digit when only one is left.
Rules
Every rule that decides a digit
One of each digit per row and column
A digit may not repeat within a row or within a column. There are no boxes or regions — only rows and columns.
Signs always point to the smaller number
A < between two horizontal neighbours means the left one is smaller. A > means the left one is larger. Vertical signs work the same way, with the wedge opening toward the larger number: a ∧ means the upper cell is smaller.
Givens are fixed
Digits printed in the starting grid are part of the puzzle and cannot be changed. They appear in a filled, slightly shaded cell.
Signs only join neighbours
A sign compares the two cells it sits between and nothing else. Cells that are not adjacent are never compared directly, though chains of signs let you reason about them.
One solution, no guessing
Each puzzle is checked by a solver before you see it and is guaranteed to have a single solution. If you are ever forced to guess, a candidate has been missed — recheck your notes.
Live rule checking
Duplicate digits and broken inequality signs are highlighted in red as soon as they appear. The board checks rules, not the answer key, so a digit can look fine and still be wrong — that is what hints are for.
Sizes and difficulty
Pick a board that fits your time
Board size and difficulty are the only settings. Best times and streaks are kept separately for each combination.
- 01 · Quick puzzles
4×4 and 5×5
Digits 1 to 4 or 1 to 5. A 4×4 Easy puzzle takes a minute or two and is the best place to learn the signs. A 5×5 is the classic size for a coffee break.
- 02 · Standard puzzles
6×6 and 7×7
Enough digits that pencil notes start to pay off, and long inequality chains that force whole rows. These are the sizes most regular players settle into.
- 03 · Long puzzles
8×8 and 9×9
Large boards with many candidates per cell. Expect to use notes and pairs-style deductions throughout. On a phone the cells shrink, so notes are small — a tablet or desktop is more comfortable.
- 04 · Clue density
Easy vs Hard
Easy keeps roughly nine clues for every ten cells, so most cells fall to a single sign or given. Hard strips clues until removing any more would leave the puzzle without a provably unique solution, so you need chains, pairs and elimination.
Common mistakes
Why solvable puzzles stall
Comparing non-neighbours
A sign compares only the two cells it touches. Two cells with a third cell between them are not directly compared until you know what the middle cell is.
Reading the wedge backwards
The open end of the sign faces the bigger number and the point faces the smaller. If you keep flipping them, say it aloud: "the point picks the small one".
Forgetting the column
Rows are easy to watch and columns are easy to forget. When a digit is placed, check its column for duplicates too — or let the red highlight catch it.
Guessing
Every puzzle has one solution reachable by logic. A guess that happens to look consistent for several moves usually collapses later and wastes more time than another look at the notes.
- Look at the biggest and smallest digits first: N cannot be on the small side of a sign and 1 cannot be on the big side.
- Follow chains. Three cells joined a < b < c cannot start above N−2 or end below 3.
- Use pencil notes early on anything bigger than 5×5 — they turn deductions into simple crossing-out.
- Scan each row and column for a digit that fits in only one cell.
- When two cells in a line share the same two candidates, no other cell in that line can be either digit.
- Undo is free. Try a placement, see whether it causes a red conflict, and take it back.
Where you can play
Same game on phone and desktop
futoshiki.app runs in any modern browser with no app to install. Progress stays on the device you played on.
Phone and tablet
The board scales to fit the screen and the number pad and tools sit right under it, so you can play with one thumb. The interface is designed to fit on one screen without scrolling.
Desktop keyboard
Arrow keys move, number keys enter digits, and P, H, U, N and M cover notes, hints, undo, new puzzle and mute. You never have to reach for the mouse.
Screen readers and contrast
Every cell announces its row, column, value, and the signs attached to it. The interface uses high-contrast colours in both light and dark themes.
Still stuck on a rule? Read the Futoshiki FAQ or jump in and play.
Play Futoshiki free