Easy number cross
Short runs with forced combinations throughout. Solvable by sum-singles alone — no candidate notation needed. Best starting point for new number cross solvers.
Play Easy →Number Cross · Cross Sums · Kakuro
Number Cross Puzzles
A number cross puzzle is a logic crossword where digits 1–9 fill white cells so that every row and column run sums to its clue — without repeating a digit in the same run. It is also known as Kakuro, cross sums, or number crossword.
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What is a number cross puzzle?
A number cross is played on a grid that looks like a crossword. Dark shaded cells contain clue numbers — one for the horizontal run to the right, one for the vertical run below. White cells are empty and must be filled with a single digit from 1 to 9.
The rules are:
- Fill every white cell with a digit from 1 to 9.
- Each row or column run of white cells must sum to the clue in the adjacent shaded cell.
- No digit may appear more than once within the same run.
- Every well-formed puzzle has exactly one valid solution — no guessing is ever needed.
These constraints work together to make number cross puzzles solvable entirely by logical deduction. Every cell can be determined from the clues.
Number cross, Kakuro, cross sums — the same puzzle by different names
This puzzle has accumulated several names as it spread from Japan to the US, UK, and Europe. They all refer to the identical rules.
Kakuro
Japan / globalFrom Japanese "kasan kurosu" (加算クロス). Most widely used name internationally.
Number Cross
UK / EuropeCommon in British newspapers and European puzzle books. Emphasises the crossword structure with numbers.
Number Crossword
UK / EuropeLonger form of "number cross". Highlights the connection to the traditional crossword format.
Cross Sums
USAUsed historically in American Dell puzzle magazines. Focuses on the summation mechanic.
Kasan Kurosu
JapanThe original Japanese name from which "Kakuro" is abbreviated.
"Kakuro" is now the dominant name globally and the one used by most puzzle sites, apps, and books. "Number cross" and "number crossword" remain the standard terms in British publications. Cross sums is the older American term. All describe the same logic puzzle.
Brief history of the number cross puzzle
The number cross was created by Jacob Kogan and first published in Dell Pencil Puzzles and Word Games (USA) in 1966 under the name "Cross Sums." It remained primarily an American puzzle for several decades.
In 1980, the Japanese puzzle publisher Nikoli introduced the format to Japan as Kasan Kurosu (加算クロス, "addition cross"). It became enormously popular, and the abbreviated name Kakuro took hold. Nikoli's rigorous puzzle standards — unique solutions, human-constructable puzzles — shaped how the format was understood globally.
By the mid-2000s, following the global Sudoku boom, Kakuro spread to UK newspapers and European puzzle books where it was relabelled "number cross" and "number crossword." Today the puzzle is published in dozens of countries under all three main names.
See also the cross sums overview and the Kakuro cross sums guide for more on the naming history.
How to solve a number cross step by step
- Find forced combinations. Short runs with extreme sums have only one valid digit set. A 2-cell run summing to 3 must be {1,2}. A 2-cell run summing to 17 must be {8,9}. Place these first — they are free moves.
- Use intersections. Every white cell sits at the crossing of two runs. A digit must be valid in both its across run and its down run. If candidate digit 5 does not appear in any valid combination for the down run, eliminate it from that cell.
- Track candidates. Write small digits in each empty cell to note which values are still possible. As you place digits and prune combinations, remove eliminated candidates. When one candidate remains in a cell, place it.
- Apply residual sums. After placing some digits in a run, subtract their total from the clue. The remaining cells form a new sub-problem with the residual sum — treat it as a fresh forced-combination check.
- Use locked sets for hard puzzles. If two cells in a run share only the same two candidates, those digits are locked to those two cells and cannot appear elsewhere in that run. Remove them from all other cells.
For a deeper walkthrough, read the full how-to-solve guide or the beginner's guide.
Number cross difficulty levels
Medium number cross
Requires candidate notation and cross-intersection checking. Sum-singles open the puzzle; combination pruning and residual sums close it.
Play Medium →Hard number cross
Locked sets and min/max boundary forcing are essential. Multiple technique passes required before the cascade unlocks new cells.
Play Hard →Ultra Hard number cross
All techniques applied simultaneously, often in combination. Only for solvers with a complete technique arsenal and rigorous candidate tracking.
Play Ultra Hard →Number cross vs word crossword
Word crossword
- Fill squares with letters to form words
- Clues are definitions, wordplay, or trivia
- Requires vocabulary and general knowledge
- One correct word per run; letters must cross correctly
Number cross (Kakuro)
- Fill squares with digits 1–9
- Clues are sum totals for each run
- Requires arithmetic logic and deduction only
- No repeated digits within any single run
Both puzzles use the same grid structure — shaded dividers and white cells — which is why "number cross" was the natural name when Kakuro arrived in English-speaking markets. The solving experience is completely different: number cross is pure logic, while word crossword is knowledge-based.
Play free number cross puzzles now
Free Kakuro generates unlimited number cross puzzles in your browser. No account or download needed. Choose your difficulty and start solving.
Number cross puzzle FAQ
- What is a number cross puzzle?
- A number cross puzzle is a logic puzzle played on a crossword-style grid where each run of white cells must be filled with digits 1–9 that sum to the clue value in the adjacent shaded cell. No digit can repeat within a single run. Number cross is the same puzzle as Kakuro — they are different names for the same game, with "number cross" more common in British and European publications.
- Is number cross the same as Kakuro?
- Yes. Number cross and Kakuro are identical puzzles. The name "Kakuro" came from the Japanese abbreviation of "kasan kurosu" (加算クロス, meaning "addition cross"), while "number cross" and "number crossword" are the English names used in British newspapers and puzzle books. Cross-sum is another common name. All refer to the same arithmetic logic puzzle.
- How do you solve a number cross puzzle?
- To solve a number cross puzzle: (1) Find short runs (2 or 3 cells) with extreme sums — for example, a 2-cell run totalling 3 must be {1,2}, and a 2-cell run totalling 17 must be {8,9}. These forced combinations are free placements. (2) Use intersections — every cell belongs to both an across and a down run, so a digit must be valid in both. Eliminate candidates that break either constraint. (3) Keep subtracting placed digits from run totals to create residual sub-problems. Repeat until the grid is complete.
- Where can I play number cross puzzles online for free?
- Free Kakuro offers unlimited free number cross puzzles across four difficulty levels — Easy, Medium, Hard, and Ultra Hard — with no account, no ads blocking play, and no download required. Puzzles are generated in your browser, so you get a fresh puzzle every time.
- What is the difference between number cross and a word crossword?
- In a word crossword you fill squares with letters to form words. In a number cross puzzle you fill squares with digits 1–9 that sum to arithmetic clue values. Both share the crossword grid structure — shaded divider cells with numbers, and white cells to fill in — but number cross requires arithmetic deduction rather than vocabulary knowledge.
- Are number cross puzzles hard?
- Number cross puzzles range from easy to very hard depending on grid size and clue complexity. Beginner puzzles (Easy level) require only basic sum-combination lookup and short-run analysis — ideal for players new to the format. Medium puzzles introduce candidate notation. Hard and Ultra Hard puzzles require advanced techniques like locked sets, residual sums, and combination pruning. Every well-formed number cross has a single unique solution reachable through pure logic, never guessing.