Play Kakuro Online: Cross Sums Rules, Combinations, and Strategy
Kakuro turns a crossword-shaped grid into a network of small arithmetic puzzles. Instead of
finding words, you place digits so that intersecting groups match their sum clues. Every entry
has to satisfy two directions at once. A number that looks right across the page may be
impossible down the column, and that tension is the heart of the game.
Play Kakuro online here with easy, medium, hard, and very hard difficulties, a daily puzzle, and
sizes from 4x4 to 30x30. You can work through a compact grid during a short break or settle into
a large number crossword with the camera zoomed in. This guide explains how to read clues,
recognize useful combinations, and turn crossing information into reliable deductions.
How to Play Kakuro
Your objective is to fill all playable cells with digits from 1 through 9. A run is an
uninterrupted group of cells across or down. Each run has a clue showing its required total, and
no digit may appear twice in that run. Black cells separate runs, so the same digit can appear
elsewhere in a row when a black cell separates the two groups.
Clue cells are divided diagonally. Read the upper-right number for the horizontal run
immediately to the right. Read the lower-left number for the vertical run immediately below. A
clue belongs only to that adjacent run; do not continue adding beyond the next blocked cell.
These are the core rules described by puzzle publisher Nikoli's Kakuro guide.
Every playable cell starts empty. The white-cell region is connected, every row and column has
playable cells, and each generated board is checked to have exactly one valid solution. Difficulty
sets the longest allowed run: six cells on easy, seven on medium, eight on hard, and nine on very
hard.
Controls and the Number Pad
Click an empty cell to open a nine-button number pad. Click the selected cell again to close it.
Choose a number or type it on your keyboard. WASD and the arrow keys move the selection, skipping
blocked cells; when the pad is open, it follows the selected cell. Delete, Backspace, zero, and
the trash button clear an entry. Press Enter to reopen the pad after moving with the keyboard, or
turn the pad off in Settings to use keyboard entry only.
Click a clue triangle to see its possible digit combinations. You can also open the selected
cell's across or down combination list from its number pad. The list always shows every
combination for the clue; combinations that no longer fit the entered digits appear dimmed. Each
combination is a reference for the set of digits, not a statement that those digits belong in the
displayed order.
Kakuro Combinations Worth Learning
Start with clues that permit very few combinations. A two-cell sum of 3 must contain 1 and 2. A
two-cell sum of 4 must contain 1 and 3: 2 plus 2 reaches the total but violates the no-repeat
rule. At the other end of the range, 17 in two cells must contain 8 and 9. These small facts
often unlock the first useful crossing.
- 3 in two cells: 1 + 2.
- 4 in two cells: 1 + 3.
- 16 in two cells: 7 + 9.
- 17 in two cells: 8 + 9.
- 6 in three cells: 1 + 2 + 3.
- 24 in three cells: 7 + 8 + 9.
- 10 in four cells: 1 + 2 + 3 + 4.
- 30 in four cells: 6 + 7 + 8 + 9.
A unique combination does not fix the order. A two-cell 17 still has two arrangements until its
crossings distinguish them. Suppose one cell also belongs to a two-cell 4. That crossing permits
only 1 or 3, so it cannot intersect a two-cell 17 in a valid puzzle. Spotting incompatible
candidate sets is just as useful as finding a forced digit.
For a positive example, intersect a two-cell 4 with a two-cell 3. Their possible digits are 1
and 3, and 1 and 2. The common cell must be 1. You can then place 3 in the other cell of the
first run and 2 in the other cell of the second run.
Beginner Kakuro Strategy
Use Both Clues Before Entering a Digit
Look at the across and down sums for your selected cell. Compare the digits that could appear in
each, then retain only the overlap. A candidate that belongs to a valid across combination can
still fail its down clue. This simple habit prevents many mistakes and makes your deductions
easier to explain when you return to a board later.
Subtract Known Numbers
When a run is nearly complete, subtract its entered numbers from the clue. In a three-cell run
totaling 15, entries of 4 and 8 leave 3. Before entering it, check that 3 is not already in the
run and that it can fit the crossing clue. For two remaining cells, calculate the remaining sum
and eliminate pairs that reuse an existing digit.
Follow the Consequences
Each confirmed number helps two runs. After entering a digit, inspect its crossing before moving
to a distant part of the board. One completed run may settle another, which then reduces a
third. Following these short chains is usually more productive than scanning every clue after
every move.
On your first game, choose easy difficulty and a compact size. Get comfortable with clue
direction and distinct digits before increasing the dimensions. If you stall, open a combination
list and compare it with a crossing list. Use a hint when you want to continue, then inspect
both runs around the revealed digit to understand what changed.
Advanced Kakuro Tips
Reason About the Whole Set
Sometimes you know that two cells must contain 2 and 7 without knowing their order. If they
share a run, neither digit can appear elsewhere in that run. The information is useful
immediately. You do not need to choose one arrangement prematurely to eliminate candidates from
the other cells.
Check Minimum and Maximum Totals
Three distinct positive digits have a minimum total of 6 and a maximum of 24. For a partly
filled run, adjust those bounds using only unused digits. If a proposed number leaves a
remainder smaller than the least possible sum, reject it. Likewise, a remainder greater than the
greatest available sum cannot work. Bounds can eliminate choices before you list every
combination.
Remember the Total of All Nine Digits
The digits 1 through 9 add up to 45. A nine-cell run therefore contains every digit once. An
eight-cell run totaling 40 excludes 5, because 45 minus 40 is 5. Similar subtraction helps with
seven-cell runs, although the two missing digits may have several possible combinations.
Crossings determine which omission is valid.
Recheck Assumptions at a Contradiction
If every combination is dimmed, the current entries do not fit any distinct-digit set for that
clue. It does not mean the puzzle requires an unusual rule. Look for a duplicate, an incorrect
subtraction, or a number entered from only one direction. Undo lets you back out of a tentative
chain; redo restores it if your original reasoning was sound.
Board Sizes and Difficulty
Kakuro has no single compulsory board dimension. Publishers offer compact grids, squares, and
wide rectangular layouts. This game provides 4x4, 5x5, 7x7, 9x9, 11x11, 13x13, 15x15, 16x16,
20x20, 15x30, 25x25, and 30x30 boards. Dimensions include clue and blocked cells as well as
cells you fill.
Size mainly determines how much there is to solve. Easy puzzles favor smaller digits and fewer
combinations, with an opening number you can find by comparing crossing clues. Every easy puzzle
can be completed by narrowing combinations and placing a number when it is the only candidate for
a cell or has only one possible position in a run. Medium, hard, and very hard allow more ambiguous
clues and more demanding deductions. The maximum run lengths are six cells for easy, seven for
medium, eight for hard, and nine for very hard. These labels describe this game's difficulty scale
rather than a universal Kakuro rating. Every generated puzzle has exactly one solution, connected
fillable cells, and a playable cell in every interior row and column. Clue and number cells
together occupy at least 86% of the board.
For a 25x25 or 30x30 puzzle, use the camera menu to zoom into a comfortable working area. Drag
the background to pan. Center board restores the full-board view when you want to choose another
region. The optional magnifying glass enlarges the area around the pointer, and the save setting
lets you return to an unfinished game with your move history intact.
Daily Kakuro, Hints, and Scores
The daily game supplies a date-based board and difficulty, so players choosing the same date
receive the same challenge. Ordinary new games are fetched as pre-generated puzzles. Leaderboards separate board size
and difficulty, keeping a compact easy puzzle distinct from a giant very hard puzzle.
Your score is elapsed seconds plus 60 points for each hint, with lower scores ranking higher. A
hint fills an empty cell first. When no empty cell remains, it repairs a number marked invalid;
if none is marked invalid, it corrects a wrong number. The selected cell is preferred within
each priority. You can undo a revealed entry, but the hint remains counted. The game records
actions separately, including undo and redo.
Use hints according to your purpose. For practice, a well-timed reveal can help you resume a
chain of deductions. For a leaderboard attempt, inspect sum combinations first and decide
whether the time saved is worth the hint cost. Reading combinations does not add a hint penalty.
Where Kakuro Comes From
Kakuro also goes by the English name Cross Sums. It combines the intersecting layout of a
crossword with arithmetic constraints. Its name abbreviates the Japanese phrase kasan kurosu, meaning addition cross. The puzzle publisher Grandmaster Puzzles describes its history as a mid-twentieth-century puzzle that later became well known through Japanese publishing.
That background helps explain why Kakuro appeals to both crossword and number-puzzle players.
You get the connected structure of intersecting entries without needing vocabulary or trivia.
The arithmetic stays modest; the challenge comes from deciding which combinations can coexist.
Common Mistakes
- Repeating a digit: reaching the correct total is only half the rule. Every digit
in a run must differ.
- Reading the wrong triangle: the upper-right clue goes across, and the lower-left
clue goes down.
- Treating a combination as an order: a list such as 1 + 3 gives the required set,
not the placement.
- Continuing through a block: a new run starts after a blocked cell and has its own
clue.
- Assuming no highlight means correct: immediate error feedback catches run conflicts;
an entry can still conflict with a later deduction.
Kakuro Frequently Asked Questions
Is Kakuro the same as Sudoku?
No. Sudoku uses row, column, and box restrictions. Kakuro uses separate
horizontal and vertical runs with sum clues. Both reward elimination, but only Kakuro asks you to
match those totals.
Can I use zero or a two-digit number?
No. Playable cells accept only the digits 1–9. A clue can be greater than 9 because it describes
a sum. In this game, pressing zero clears the selected editable cell.
Can a number repeat in the same row?
Yes, if the appearances are in different runs separated by blocked cells. It cannot repeat
inside one uninterrupted run. Apply the same distinction vertically.
Are large boards always harder?
They usually take longer, but size and deduction difficulty are separate choices. Try a small
hard board if you want concentrated reasoning, or a large easy board if you prefer many shorter
deductions.
Can I continue later?
Enable “Start game from where you left off” in settings. Progress, elapsed time, and undo
history are saved in this browser. Returning in another browser or after clearing site data will
not restore that local save.
When is the puzzle complete?
You win when every playable cell contains a valid digit and every across and down run matches
its sum without repeated digits. There is no need to submit the board manually.
Start Your Next Cross Sums Puzzle
Choose a comfortable size, look for a short or extreme sum, and compare its crossings. Keep each
deduction tied to both clues. As familiar combinations become easier to recognize, increase the
difficulty or try a larger board. The next useful Kakuro move often begins with one small sum
you can resolve with certainty.
Sound Effects Credits
The sound effects used on the game come from multiple parties. The credits and
respective licenses are listed below:
Disclaimer
This game is a property of Lofi and Games. All code and assets are protected and must
not be redistributed or used without prior permission.