Also called Cross Sums · Free · No download
Kakuro Cross Sums
Kakuro cross sums — also known simply as Cross Sums — is the original Western name for Kakuro puzzles. The rules are the same: fill each run of white cells so the digits sum to the clue, using each digit 1–9 at most once per run.
Free Kakuro lets you play cross sums online for free, with unlimited puzzles at four difficulty levels, candidate tracking, hints, and a full combination reference. No download, no account — open the page and start solving.
Cross Sums and Kakuro — the same puzzle, two names
The puzzle now known worldwide as Kakuro first appeared in American print under the name Cross Sums, popularised by Dell Magazines through the 1980s. The grid, rules, and solving logic were identical to what Japan would later call Kakuro.
Kakuro is short for Kasan Kurosu — "Addition Crossword" in Japanese. Nikoli, the Japanese puzzle publisher, adopted and named it in 1980, and the name became the global standard after the Sudoku boom of the mid-2000s brought Japanese logic puzzles to mass international audiences.
Today "Cross Sums" is mostly used by solvers who grew up with Dell publications or who learned the puzzle before the Kakuro name arrived. If you search for cross sums puzzles online, you will find the same puzzle under the Kakuro name on most modern sites. Free Kakuro uses both names interchangeably.
Cross sums rules
A cross sums grid looks like a crossword with numbers instead of letters. Black cells with triangular dividers are clue cells. The number in the upper-right triangle is the across clue — the sum that the white cells to the right must reach. The number in the lower-left triangle is the down clue — the sum for the white cells below.
Two rules govern every cross sums puzzle:
- Sum rule: The digits in each run of white cells must add up to the clue exactly.
- Uniqueness rule: No digit may repeat within a single run. Digits 1–9 only.
Every well-formed cross sums puzzle has exactly one solution reachable by logic — no guessing required. See the full rules page for an annotated grid walkthrough.
How to solve cross sums puzzles
Step 1 — Find forced combinations. Some sum–length pairs have only one valid digit set. A 2-cell run summing to 3 can only be 2. A 2-cell run summing to 17 can only be 9. Start by marking these forced cells — they constrain everything that intersects them. The combination reference lists every valid set for every sum and run length.
Step 2 — Intersect across and down candidates. Each white cell belongs to one across run and one down run. The valid digits for that cell are those that appear in both candidate sets. Cross-referencing two short, constrained runs often pins a cell to a single digit with no arithmetic at all.
Step 3 — Use residual sums. If you know several digits in a run but not all of them, subtract the known digits from the clue to get the residual sum. The remaining unknown cells must account for that residual using the allowed digits. This step becomes essential on longer runs in harder cross sums puzzles.
For a deeper walkthrough of these techniques, see the technique library — it covers sum-singles, cross-run intersection, residual sums, naked pairs, and combination pruning with worked examples.
What Free Kakuro includes
Identical to Kakuro
Cross Sums and Kakuro are the same puzzle. Same grid, same rules, same deduction logic — just a different name from a different era.
Pure number logic
No words, no trivia, no vocabulary. Cross sums are solved by arithmetic and deduction alone, making them language-independent.
Candidate overlay
Toggle a 3×3 mini-grid in each empty cell to track which digits are still valid without relying on memory or a pencil.
Combination reference
Every valid digit set for every sum–length pair is one click away. No mental enumeration needed mid-solve.
Four difficulties
Easy cross sums for beginners through Ultra Hard for experienced solvers. The generator produces a new verified puzzle every time.
Hints on demand
Tap Hint to highlight the next forced cell and see why that digit is locked in — useful when a deduction chain is hard to spot.
Cross sums difficulty levels
Easy cross sums
Short runs with many forced combinations. Most cells can be solved by listing the valid digit set for the clue. Ideal for beginners learning the puzzle for the first time. Easy Kakuro guide →
Medium cross sums
Longer runs and more intersection constraints. Candidate tracking and cross-run logic become necessary. Good for solvers who find easy too quick. Medium Kakuro guide →
Hard cross sums
Dense grids where forced moves are rare and intersection logic is required throughout. Residual-sum chains and naked-pair detection start to matter here. Hard Kakuro guide →
Ultra Hard cross sums
Maximum density. Every constraint is relevant and small errors compound. For experienced cross sums solvers who want a serious test. Ultra Hard Kakuro guide →
Cross sums solving tools
Combination reference: A complete table of every valid digit set for every sum and run length. When you are stuck on a run, look up the clue and length — the table tells you exactly which combinations are possible. Open combination reference →
Kakuro helper calculator: Enter a target sum and run length to instantly see all valid digit combinations and filter out digits already placed in the run. Open helper calculator →
Technique library: Covers the strategies that go beyond basic forced moves — cross-run intersection, residual sums, combination pruning, and naked pairs. Opens in a new tab so your puzzle state is preserved. Open technique library →
Kakuro solver: Analyse a specific puzzle configuration or see how an automated solver approaches a position. Open solver →
Kakuro cross sums FAQ
- What are Kakuro cross sums?
- Kakuro cross sums (or just Cross Sums) is the original Western name for Kakuro puzzles. The puzzle appeared in American puzzle books under this name before the Japanese name Kakuro became standard worldwide. The rules are identical.
- Are cross sums the same as Kakuro?
- Yes — exactly the same puzzle under two different names. Cross Sums was popularised by Dell Magazines in the US during the 1980s. Kakuro (short for Kasan Kurosu) is the Japanese name that became the global standard after the Sudoku boom.
- How do you solve cross sums puzzles?
- Start by finding runs with only one valid combination (e.g. a 2-cell run summing to 3 can only be 2). Then cross-reference intersecting across and down candidates to eliminate digits. Use residual sums to constrain longer runs once some cells are solved. The combination reference at freekakuro.com/combinations/ lists every valid set.
- Where can I play cross sums puzzles online for free?
- Right here at freekakuro.com. No download, no account, no cost. Generate unlimited puzzles at Easy, Medium, Hard, or Ultra Hard difficulty.
- How is Cross Sums different from a regular crossword?
- A crossword uses letters and word knowledge. Cross sums uses digits 1–9 and arithmetic. Each run must sum to its clue with no repeated digit. No vocabulary or language skills are needed — only addition and logical deduction.
- What is the hardest type of cross sums puzzle?
- Ultra Hard cross sums feature maximum grid density, where every constraint is relevant and even small oversights cascade into dead ends. See the Ultra Hard Kakuro guide for what makes these puzzles difficult and how to approach them.