How to play kakuro (cross sums)
The rules are simple. The challenge comes from how entries intersect.
What is kakuro?
Kakuro is a number puzzle that looks like a crossword made of digits instead of letters. The grid has two kinds of cells: black cells (which hold clues) and white cells (which you fill in). It goes by several names in English, most commonly "cross sums."
Unlike sudoku, kakuro grids come in different sizes. Easy puzzles might be 6x6, while hard ones can reach 14x14 or larger. The grid shape is irregular too, with blocks of white cells forming entries in horizontal and vertical directions, separated by black cells. No two puzzles look the same.
Rules at a glance
- Fill every white cell with a digit from 1 to 9.
- Each black clue cell has a diagonal line. The number below-left is the across clue (sum of white cells to the right). The number above-right is the down clue (sum of white cells below).
- The digits in each entry (horizontal or vertical run of consecutive white cells) must add up to the corresponding clue.
- No digit may repeat within the same entry.
That is the entire rule set. No row/column uniqueness like sudoku, no box regions. The constraint is per-entry only: correct sum, no repeats.
Reading the clue cells
Clue cells are the dark cells with a diagonal slash. They can hold one or two numbers. The number in the top-right corner (above the diagonal) is the down clue, which applies to the vertical entry below. The number in the bottom-left corner (below the diagonal) is the across clue, for the horizontal entry to the right.
Some clue cells have only one number (either across or down, depending on the grid layout). Others have both. Black cells at grid edges or in the interior may have no numbers at all if they just block off areas.
How it differs from sudoku
In sudoku, you start with some pre-filled digits and apply row, column, and box elimination. There is no arithmetic. In kakuro, you start with a blank grid and work from sum clues. You need both arithmetic (figuring out which digit sets produce a target sum) and logic (using entry intersections to pin down cells).
Kakuro also differs in grid structure. Sudoku grids are always 9x9 with a fixed layout. Kakuro grids vary in size and have an irregular crossword-like shape. Entries can be as short as 2 cells or as long as 9.
If you have done killer sudoku, kakuro will feel familiar. Both use sum-and-no-repeat constraints. The main difference is that killer sudoku inherits the full sudoku rule set (row/column/box uniqueness), while kakuro drops those and relies purely on entry constraints.
Solving step by step
Step 1: Scan for forced combinations. Look for short entries with extreme sums. A 2-cell entry with sum 3 can only hold 1 and 2. Sum 4 can only be 1 and 3. Sum 16 is 7 and 9. Sum 17 is 8 and 9. You do not know which cell gets which digit yet, but knowing the combination narrows things fast.
Step 2: Use cross-entry logic. Each white cell sits at the intersection of a horizontal entry and a vertical entry. If the across entry restricts the cell to {1, 2} and the down entry restricts it to {2, 5, 7}, the answer is 2. This is the core technique in kakuro, and it works at every difficulty level.
Step 3: List combinations. For entries with several cells, write out all digit sets that sum correctly without repeats. A 3-cell entry with sum 10 could be 1+2+7, 1+3+6, 1+4+5, or 2+3+5. Check each combination against digits already placed in crossing entries and eliminate the impossible ones.
Step 4: Fill singles. After elimination, check whether any cell has exactly one remaining candidate. Fill it. Each new digit gives you more information for adjacent entries.
Step 5: Repeat. Kakuro solving is iterative. Place a digit, re-check combinations and candidates, place another. The grid unravels once you build enough momentum from initial placements.
Common mistakes
Repeating a digit in an entry. This is the number one beginner error. If your 3-cell entry needs digits summing to 7, you cannot use 1+3+3 even though 1+3+3=7. Each digit appears at most once per entry.
Ignoring the crossing entry. It is tempting to solve each entry in isolation. But the cell you are filling belongs to two entries, and valid digits must satisfy both. Always check the crossing constraint before placing.
Trying to guess. Kakuro does not require guessing. Every puzzle here has a unique solution reachable through logic alone. If you feel stuck, there is a deduction available somewhere that you have not yet spotted. Step back and re-examine entries near your problem area.
Useful references
Our combinations chart lists every valid digit set for each entry length and target sum. Useful to have open while solving, especially for 4-cell and 5-cell entries where memorizing all combinations is impractical.
For solving techniques beyond the basics, the strategy guide covers combination filtering, naked singles, and advanced elimination techniques used in expert and einstein puzzles.
Frequently asked questions
Is Kakuro harder than Sudoku?
Depends on the size. Easy kakuro on a 6x6 grid is more approachable than medium sudoku. Large kakuro grids (12x14) tend to be harder than expert sudoku because you need both arithmetic and multi-entry tracking. The puzzles exercise different skills: sudoku is pure elimination, kakuro adds combination counting.
Is there only one solution?
Yes. Every puzzle on this site has been verified by a constraint solver to have exactly one valid solution. If you find two different fillings that both work, one of them has an error.
Is Kakuro good for the brain?
It exercises working memory, arithmetic, and logical reasoning. Research on number puzzles generally supports cognitive benefits, though there is no specific study comparing kakuro to other puzzle types. The blend of logic and math gives a broader workout than pure logic puzzles.
What is the difference between Kakuro and Killer Sudoku?
Both require digits to sum to a target without repeating. Killer sudoku uses a fixed 9x9 grid and inherits standard sudoku rules (row, column, and box uniqueness). Kakuro drops the box regions and row/column constraints, uses variable grid sizes, and has a crossword-like structure. Kakuro has no equivalent of the "45 rule" because entries do not fill complete rows or boxes.
Do I need to guess?
No. Every puzzle is solvable through logic. If you are stuck, re-examine cross-entry constraints and combination filtering. The strategy guide covers the techniques for each difficulty level.