Futoshiki

The board, and how you win

The grid is a square in one of four sizes — 4×4, 5×5, 6×6 or 7×7 — and every row and every column holds every digit from 1 to N exactly once, the same rule Sudoku uses without needing 3×3 boxes to enforce it. A cell holds a given digit that cannot be changed, a digit you entered, or nothing, and any cell can also carry pencil notes.

A sign sits between some pairs of squares that touch each other edge to edge — never diagonally — and always points at the smaller of the two. Not every neighboring pair carries one, and how many do depends on the level.

• You win when every square is filled, every row and column is some order of 1 through N, and every sign is satisfied. That is checked against the rules themselves, not against a stored answer — and because a legal solution is always the only one, checking the rules and checking the answer could never disagree anyway.
• There is no mistake limit, no lives and no game over. Getting something wrong costs you nothing but the time it takes to fix it.

Sudoku packs its digits into a snug 9×9 because a box shares its edges with its neighbors. Futoshiki needs a visible gap between every pair of neighboring squares for a sign to live in, so the same phone screen holds less — which is why this grid tops out at 7×7 instead of climbing as high.

Controls

• Select any square, including a given one — that highlights every other square holding the same digit and softly marks that square’s own row and column.
• Tap a digit on the pad to place it, or tap it again to erase it. The pad only shows the digits that exist on this board: four keys on a 4×4, seven keys on a 7×7.
• Switch to notes mode and the same pad adds and removes pencil marks instead of digits. A square that already holds a digit cannot take notes.
• Placing a digit clears that square’s own notes and also removes the same digit from the notes of its row and its column — two lines, not three, because there is no box here to make it three.
• Erasing a digit empties the square and its notes, but does not restore whatever that auto-clearing removed elsewhere — bringing that back is Undo’s job. The pad also shows how many of each digit remain, counting givens, and disables a digit once every one of them is on the board.

The pad never clears notes across a sign the way it does across a row or column. Reading that a filled square rules out a value on the other side of a sign is the puzzle’s own reasoning, not bookkeeping, so it stays yours to do — Hint is there for when you want a nudge.

Mistakes, Undo and Hint

There is no mistake limit and no game over here either. Getting something wrong never ends anything.

• Rule violations are shown at all times: two of the same digit sharing a row or column, or a sign whose two squares are both filled but point the wrong way. A sign with only one side filled says nothing yet — it only breaks once both squares are.
• Show mistakes marks a digit that differs from the puzzle’s one solution — separately from rule violations, and only about matching the answer. It is on by default and can be turned off in Settings; rule violations stay visible either way.
• Undo is unlimited and free. It steps back placing a digit, erasing one, or changing a note, though it never rewinds the mistake count or the Hint count — those already happened.
• Hint is unlimited and free too. It settles exactly one new square using the same logic every puzzle promises never needs guessing, and highlights the row, column or chain of signs that proves it — it places nothing for you.

Undo exists here because placing a digit is not trivially reversible: it also erases matching notes from that square’s row and column, and there is no way to tap those back by hand. Takuzu never needed Undo for the opposite reason — tapping its one kind of square just cycles a single state, so every move there already undoes itself.

The no-guess promise

Every puzzle here can be finished using four techniques, repeated until nothing more gives: reading what a sign rules out at both its ends, and further down a chain of signs; filling a square whose candidates are down to one; filling a digit into the one square of a row or column where it still fits; and spotting a pair of squares or digits that lock each other in. No trial and error is ever required.

Because none of those four ever writes a digit that is not true in every legal completion, a board that yields to them completely has exactly one legal completion of its own — uniqueness follows from that, so it never needs a separate check.

• There are no difficulty tiers. Difficulty comes from two numbers only — how many signs a board carries and how many digits it gives you — because measuring what the 160 shipped boards actually needed found that only two of the four techniques were doing real work on most of them (see the table).
• A tier is not named after a technique that is not doing the work — the same reasoning behind Sudoku’s own Hard tier, which is defined by what it can guarantee rather than by the hardest technique you might be forced to use.

A tier named for the pair techniques would be named for something only one board out of 160 actually required. We measured before naming anything.

Levels and the Daily

• Levels run 1–100 and unlock in order. Any level you have already unlocked can be replayed, and it is always the same board — generated on your device from a seed, never downloaded.
• Inside a band, the number of signs and the number of givens both step down in a straight line, so neighboring levels never jump. The step back up at each new size is deliberate: the same density is harder on a bigger board, because a chain of signs reaches further and a hidden single takes longer to spot — so a fresh band opens a little gentler instead of starting at a wall.
• The Daily puzzle is one per day and always 6×6 with 23 signs and 9 givens — no difficulty name, and nothing that shifts with the day of the week. The past 30 days are always open, with no requirement to clear yesterday before playing today, and a finished day is recorded with no streak counted or shown anywhere.
• Levels and the Daily each keep their own paused game, so starting one never costs you your place in the other.

Tips

• Work a chain of signs from both ends at once. On a 4×4, four squares linked so that every sign points back at the square before it can only be filled 1 2 3 4 in that reading direction — the chain is exactly as long as the board, so there is no room to be anything else.
• Treat the pad’s remaining count as a fact about the solution, not just a display: every digit appears exactly N times in the finished board, once per row, so “how many of this digit are still missing” is never just decoration.
• A filled square next to a sign narrows its neighbor right away. If the sign points at the neighbor, the neighbor must be smaller — next to a filled 2, only a 1 fits. If it points at the filled square, the neighbor must be larger than it — without needing anything else on the board.
• Write notes early on the larger boards. Most of what signs and lines rule out shows up as a pattern across several squares’ notes rather than as one single deduction.
• When you are stuck, take a Hint. It costs nothing, it is not limited, and it shows the reasoning rather than just filling the square for you.

Questions people ask