Kakuro

The grid, the clues, and how you win

Every square is either white, where you place a digit from 1 to 9, or a clue square split by a diagonal line. A clue square can carry a sum to its right — the total of the run of white squares that follows it in that row — and a sum below it, for the run in that column. A square with only one diagonal carries only that one sum; a plain square carries neither and is just a block.

That run of white squares is what the two rules act on: no digit may repeat within a run, and the digits in a run must add up to its clue. There are no row-wide or column-wide rules, and no boxes — only the run.

• You win the moment every white square holds a digit and no run breaks either rule — nothing is compared to a hidden solution.
• There is no losing condition — no mistake limit, no lives, and no game over.

Controls

• Tap a white square to select it. Clue squares cannot be selected — they are not a place to put a digit.
• Use the number pad to enter or erase 1–9. In Notes mode the same pad adds or removes candidate digits instead.
• Selecting a square highlights the two runs it belongs to, and both of their clue squares — one across, one down.
• Entering a digit clears that square’s notes, and also clears the same digit from the notes of the rest of its two runs — not the whole row or column, since a clue square marks where one run ends and the next begins.
• You can enter a digit that turns out to be wrong. This layer never stops you — see Mistakes and violations below.

The pad never shows how many of each digit remain, and never grays out a digit you cannot place. Sudoku and Futoshiki can show a remaining count because their solved grid uses each digit a fixed number of times — a fact about the solution that never changes. Kakuro has no such invariant: how often a digit appears depends on the layout and the solution, and the same digit can sit twice in one row if the two squares belong to different runs. Graying out invalid digits would also do the puzzle’s own reasoning for you — that is what Hint is for.

Mistakes and violations

Violation highlighting is always on, and shows exactly three things: a digit repeated within a run, a run whose digits already add up to more than its clue before every square is filled, and a completed run whose total does not match its clue. Both the offending squares and the run’s clue square change color together — it is the run that is broken, not just a square.

• This is a rule check, not an answer check. A digit that breaks no rule is never flagged, even if it differs from the solution.
• Show mistakes is a separate, optional setting, on by default. When it is on, a digit that does not match the puzzle’s one solution is also marked. Turning it off does not turn off violation highlighting.
• Mistakes are counted and shown on the results screen, but they are not added to your statistics.

The reverse case — a run whose remaining empty squares can no longer possibly reach its clue — is just as dead, and the solver actually uses that reasoning. It is not shown as a violation, because nothing wrong has been written into those squares yet. That reasoning lives in Hint instead.

Sizes, levels and the Daily

• There are three sizes. The white-square share rises as you move through a band — fewer clue squares make runs longer, and longer runs are harder for the two techniques below to pin down, so that is where the difficulty comes from within each band.
• Levels unlock in order and can be replayed at any time; the same level number is always the same puzzle, for everyone.
• The Daily puzzle is one per day, always 8×8 with 27 clue squares — the midpoint of the 21–65 band. Past days stay open for 30 days, and finishing an earlier day is never required to unlock the next one.
• Levels and the Daily each keep their own paused game, independently — starting a different level replaces the level slot, but never touches a paused Daily.

The no-guess promise, and Hint

Every clue is a sum of digits from 1 to 9 with none repeated, so a run’s contents always come from a small, countable set of possibilities. Two squares summing to 4 can only be 1 and 3; two squares summing to 3 can only be 1 and 2. A square that belongs to both of those runs can only be 1 — the one digit the two possibilities share.

Every puzzle here is checked to be solvable by carrying that kind of reasoning all the way through the grid, square by square, with no step that requires a guess. That also makes the solution unique — a puzzle that needed a guess somewhere could not be verified this way, so it is never used.

• Hint is unlimited and free. It shows either a square that this reasoning can now fill, or a run where it only narrows the candidates — both count, because "these two squares can only be 7 and 9" is the reasoning itself, not a lesser version of it.
• It highlights the run or runs that prove the deduction — both runs and both clue squares when the answer comes from where they cross — and adds a short sentence. It never enters a digit for you.
• If the board currently breaks a rule, Hint points at that violation first, since no further reasoning is possible while a run is already broken. If nothing is left to work out, it says so and leaves the board untouched — that never happens on a puzzle you have not touched yet.

Undo

Undo is unlimited, with the same practical cap as the rest of this collection — 2000 moves. It steps back placing a digit, erasing a digit, and changing a note.

• Undo exists because entering a digit is not trivially reversible: it also clears matching notes from the rest of both runs, and there is no way to get those notes back by hand except stepping back.
• Undo does not restore your mistake count or your Hint count — making a mistake, or asking for a Hint, stays true even if you undo the move that followed it. A paused game does not save Undo history.

Tips

• Start from the runs with the most extreme clues. A two-square run can only be a clue of 3, 4, 16 or 17 down to one combination; a nine-square run summing to 45 is forced to hold 1 through 9 in some order.
• Work the crossings before the long runs. A square where a tight two-square run meets a longer one is usually the fastest square on the board.
• Use Notes once a run only allows a handful of digits — writing them down keeps the next crossing from becoming a re-count.
• A repeated digit in the same row is not automatically wrong — check whether the two squares are actually in the same run, since a clue square between them starts a new one.
• When you are stuck, take a Hint. It is free and unlimited, and it shows a run that still has something to give rather than the digit itself.

Questions people ask