Easy
Easy Cross Sums
Short runs with forced single-combination clues. Every cell placement follows immediately from the sum — no candidate tracking needed.
Best for: Newcomers to cross sums
Also known as Kakuro
Cross Sums Puzzles — Free Online
Cross sums are number-logic puzzles that work like a crossword grid with digits instead of letters. Each clue shows a target sum; you fill the blank cells with digits 1–9 so each row and column run adds up correctly — no digit repeating within a run. The puzzle is also called Kakuro, its Japanese name, which became standard in the 2000s.
Free Kakuro generates unlimited cross sums puzzles in your browser at four difficulty levels. No download, no account, no cost — just open a puzzle and start solving.
What are cross sums?
A cross sums grid looks like a crossword: a black-and-white grid where the black cells contain clue numbers and the white cells are filled with your answers. In a crossword you write letters; in cross sums you write digits 1–9.
Each clue cell carries a number in its top-right corner (for a horizontal run reading right) or bottom-left corner (for a vertical run reading down). That number is the sum the run must reach. You fill the white cells so the digits in each run add up to the clue, with no digit appearing twice in the same run.
The rules are simple but the logic is deep. Short runs are often forced to a single combination — a 2-cell run summing to 3 can only use the digits 1 and 2. Longer runs allow many combinations, and the key is eliminating options through intersection logic: a cell belongs to both a horizontal and a vertical run, so only digits valid for both can go there.
Fully correct cross sums puzzles have exactly one solution reachable by pure deduction — no guessing, no trial-and-error.
How to solve cross sums
- 1
Start with forced combinations
Find runs where only one set of digits is possible. A 2-cell sum of 3 must use 1 and 2; a 2-cell sum of 16 must use 7 and 9. These give you certain digits before you touch the rest of the grid.
- 2
Use candidate notation
In each unsettled cell, write down every digit the run allows. In the online game, toggle candidate mode to track these notes automatically. This makes intersection logic much easier to apply.
- 3
Cross-check intersecting runs
A cell at the intersection of a horizontal and vertical run must satisfy both clues simultaneously. Eliminate any candidate that does not appear in the allowed set for the crossing run. Often a single intersection resolves the cell completely.
- 4
Apply residual sums
Once you confirm a digit in one cell of a run, subtract it from the run total. The remaining cells must sum to the residual. This narrows combinations for the rest of the run and often forces the next cell.
For more advanced methods — locked sets, naked pairs, pigeonhole — see the full technique library.
Why play cross sums online at Free Kakuro
∞
Unlimited puzzles
New cross sums generated on demand at any difficulty — you never play the same puzzle twice.
✎
Candidate notation
Toggle pencil mode to track possible digits in each cell, just like paper notes but without the erasing.
💡
Hint system
Stuck on a run? Request a hint and the solver highlights the most productive next cell to work on.
✓
Error detection
Conflicting digits are flagged in real time so mistakes surface before they cascade through the grid.
Choose your cross sums difficulty
Medium
Medium Cross Sums
Longer runs where candidate notation speeds things up. Cross-checking intersections is required to resolve most cells.
Best for: Casual solvers
Hard
Hard Cross Sums
Dense grids with overlapping runs. Locked-set elimination and residual-sum logic are regularly needed to break deadlocks.
Best for: Experienced solvers
Ultra Hard
Ultra Hard Cross Sums
Maximum-density grids with long intersecting run chains. Expert-level logic throughout — every cell is a deduction exercise.
Best for: Cross sums enthusiasts
Cross sums vs Kakuro — the history of the name
The same puzzle carries two names because it was invented in Japan and popularised in America under different labels. Here is the timeline that explains both names:
- 1946 The puzzle first appeared in a Japanese puzzle magazine under the name "Kasan Kurosu" (Addition Crossword).
- 1966 Dell Magazines introduced the puzzle to American audiences as "Cross Sums" in its puzzle publications.
- 1980s Cross Sums became a regular feature in Dell puzzle books; the name stuck in the US market.
- 1987 Nikoli, the Japanese puzzle publisher, popularised the shorter name "Kakuro" and standardised modern grid conventions.
- 2000s The Sudoku boom carried Kakuro to a global audience; "Kakuro" displaced "Cross Sums" as the universal term.
- Today The two names remain interchangeable. Solvers who grew up with Dell cross sums are playing the same puzzle as Kakuro fans.
Whether you call it cross sums or Kakuro, the rules are identical. The combination reference, solving techniques, and online game on this site work for both names. See the Kakuro cross sums page for more on the puzzle's history.
Cross sums FAQ
- Are cross sums and Kakuro the same puzzle?
- Yes. Cross Sums is the older American name and Kakuro is the Japanese name that became the modern standard. The grid, clue sums, no-repeat rule, and solving logic are identical.
- How do you solve a cross sums puzzle?
- Start with short runs that have only one possible digit set, then use each confirmed digit to eliminate candidates from the intersecting across and down runs.
- Can I play cross sums online for free?
- Yes. Free Kakuro generates unlimited cross sums puzzles in the browser with no account, download, or payment.