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Kakuro
Kakuro, sometimes called "cross sums," is a numeric crossword puzzle popularized in Japan by the publisher Nikoli in the 1980s. Instead of words, you fill runs of white cells with digits that total the clues given in the black header cells. It marries crossword structure with arithmetic deduction.
Kakuro Rules
The grid mixes black and white cells like a crossword. Black cells carry clue numbers split by a diagonal: the upper-right number is the sum of the white run going across, and the lower-left number is the sum of the run going down.
Fill each horizontal and vertical run of white cells with digits 1 through 9 so the run adds up to its clue. Crucially, a digit cannot repeat within any single run, though the same digit can appear in a crossing run.
Each white cell sits at the intersection of one across run and one down run, so its value must satisfy both sums at once. The puzzle is solved when every run hits its target with no repeats, giving a unique solution.
Kakuro Strategy & Tips
Learn the unique sum combinations
Certain clue-and-length pairs allow only one set of digits. A 3-in-two-cells is always {1,2}; a 24-in-three is {7,8,9}; a 6-in-three is {1,2,3}. These locked sets are your foothold.
Cross-reference intersections
A cell belongs to both an across and a down clue. Find the digits each run allows, then keep only the values common to both — often that narrows the cell to one number.
Exploit short runs first
Two- and three-cell runs have far fewer combinations than long ones. Solve the short, constrained runs early and let their fixed digits ripple into the longer crossings.
Use the 45 ceiling
No run of nine cells can exceed 45 (1+2+...+9), and lengths cap the highest and lowest possible sums. Compare a clue to its run length to rule out impossible digits at a glance.
Frequently Asked Questions
How do you play Kakuro?
Fill the white cells with digits 1 to 9 so each horizontal and vertical run equals its clue number, never repeating a digit within the same run.
Can numbers repeat in Kakuro?
Not within a single run. A digit may appear only once per across run and once per down run, but it can show up again in a different crossing run.
What is the diagonal number in a Kakuro clue cell?
The number above the diagonal is the sum for the run going to the right; the number below the diagonal is the sum for the run going down.
Is Kakuro harder than Sudoku?
Many solvers find it harder because it requires arithmetic as well as logic, and there are no starting digits — every white cell must be deduced from the sums.