Cross sums (also known as Kakuro) are number-logic puzzles that work like a crossword but with digits instead of letters. Each clue cell shows a target sum, and you fill the blank white cells with digits 1–9 so the run adds up to the clue total. No digit may repeat within the same run. The puzzle combines arithmetic with deduction — every correct solution follows purely from logic, no guessing required.

Are cross sums the same as Kakuro?

Yes. Cross sums and Kakuro are identical puzzles under different names. "Cross sums" is the older American name, popularised by Dell Magazines from the 1980s onwards. "Kakuro" is the Japanese abbreviation of "Kasan Kurosu" (Addition Crossword), which became the internationally recognised name after the Nikoli-driven puzzle boom of the 2000s. If you grew up solving Dell cross sums, you already know how to play Kakuro.

Where can I play cross sums online for free?

Free Kakuro (freekakuro.com) lets you play unlimited cross sums puzzles directly in your browser at no cost. Four difficulty levels are available: Easy, Medium, Hard, and Ultra Hard. No download, no account, and no paywall. The game includes candidate notation, a hint system, and automatic error detection — all the tools that make online solving faster than pencil-and-paper.

How do you solve a cross sum puzzle?

Start with the runs that have only one valid digit combination — for example, a 2-cell run summing to 3 can only be {1,2}. Use candidate notation to track possible digits in each cell, then eliminate candidates when a digit is confirmed in a crossing run. Cross-check intersections: if two runs share a cell, only the digit valid for both can go there. Forced combinations at extreme sums (like 16 in 2 cells = {7,9}) are reliable starting points. See the techniques page for locked-set and residual-sum methods for harder puzzles.

What is the difference between easy and hard cross sums?

Easy cross sums have short runs with mostly forced single-combination clues — every move is straightforward, so no candidate tracking is needed. Hard cross sums have longer, denser runs where multiple combinations are possible; you need to cross-check intersections, track candidates, and use logical elimination techniques to resolve cells. Ultra Hard puzzles add deeply chained intersections where standard deduction must be applied across several runs simultaneously.

Can I print cross sums puzzles?

Yes. Open any puzzle in the browser and use your browser print function (Ctrl+P on Windows/Linux, Cmd+P on Mac). The grid renders cleanly for paper. For a fresh puzzle each time, click New Game before printing — the generator creates a unique puzzle on demand at your chosen difficulty.

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.

Play cross sums now Start with easy

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

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

Play Easy Easy guide →

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

Play Medium Medium guide →

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

Play Hard Hard guide →

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

Play Ultra Hard Ultra Hard guide →

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

What are cross sums?: Cross sums (also known as Kakuro) are number-logic puzzles that work like a crossword but with digits instead of letters. Each clue cell shows a target sum, and you fill the blank white cells with digits 1–9 so the run adds up to the clue total. No digit may repeat within the same run. The puzzle combines arithmetic with deduction — every correct solution follows purely from logic, no guessing required.
Are cross sums the same as Kakuro?: Yes. Cross sums and Kakuro are identical puzzles under different names. "Cross sums" is the older American name, popularised by Dell Magazines from the 1980s onwards. "Kakuro" is the Japanese abbreviation of "Kasan Kurosu" (Addition Crossword), which became the internationally recognised name after the Nikoli-driven puzzle boom of the 2000s. If you grew up solving Dell cross sums, you already know how to play Kakuro.
Where can I play cross sums online for free?: Free Kakuro (freekakuro.com) lets you play unlimited cross sums puzzles directly in your browser at no cost. Four difficulty levels are available: Easy, Medium, Hard, and Ultra Hard. No download, no account, and no paywall. The game includes candidate notation, a hint system, and automatic error detection — all the tools that make online solving faster than pencil-and-paper.
How do you solve a cross sum puzzle?: Start with the runs that have only one valid digit combination — for example, a 2-cell run summing to 3 can only be {1,2}. Use candidate notation to track possible digits in each cell, then eliminate candidates when a digit is confirmed in a crossing run. Cross-check intersections: if two runs share a cell, only the digit valid for both can go there. Forced combinations at extreme sums (like 16 in 2 cells = {7,9}) are reliable starting points. See the techniques page for locked-set and residual-sum methods for harder puzzles.
What is the difference between easy and hard cross sums?: Easy cross sums have short runs with mostly forced single-combination clues — every move is straightforward, so no candidate tracking is needed. Hard cross sums have longer, denser runs where multiple combinations are possible; you need to cross-check intersections, track candidates, and use logical elimination techniques to resolve cells. Ultra Hard puzzles add deeply chained intersections where standard deduction must be applied across several runs simultaneously.
Can I print cross sums puzzles?: Yes. Open any puzzle in the browser and use your browser print function (Ctrl+P on Windows/Linux, Cmd+P on Mac). The grid renders cleanly for paper. For a fresh puzzle each time, click New Game before printing — the generator creates a unique puzzle on demand at your chosen difficulty.