Kakuro カックロ

Kakuro (カックロ) is a number crossword. Instead of letters you write the digits 1 to 9 into the white cells, and instead of word clues the black cells carry sums. A clue in the top-right corner of a black cell is the total of the run of white cells to its right; a clue in the bottom-left corner is the total of the run below it. No digit may be used twice within a run, so every clue is a small question about which set of different digits can make that sum.

The puzzle began in American puzzle magazines published by Dell, where it was called Cross Sums. It found its biggest audience in Japan through Nikoli, the publisher behind Sudoku, which describes Kakuro as the king of pencil puzzles. British newspapers took it up in the mid 2000s, printing it beside Sudoku.

On LogicPuzzles.io you get a new 8×8 Kakuro every day, the same for every player, plus unlimited puzzles in 6×6, 8×8 and 10×10 grids. Every puzzle is checked by two independent solvers to have exactly one solution, and by a deduction grader to be solvable without guessing. Pencil marks, undo, a timer and a Check button are built in. It is free, there is no account, and your progress, streak and best times stay in this browser.

Start with the clues that can only be made one way. In two cells, 3 is 1+2, 4 is 1+3, 16 is 7+9 and 17 is 8+9. In three cells, 6 is 1+2+3, 7 is 1+2+4, 23 is 6+8+9 and 24 is 7+8+9. In four cells, 10 is 1+2+3+4, 11 is 1+2+3+5, 29 is 5+7+8+9 and 30 is 6+7+8+9. The order is still open, but the set of digits is fixed and every other digit is ruled out of that run.

Then work the crossings. Every white cell sits in one across run and one down run, so it can only hold a digit both runs allow. Where a 3 (1+2) crosses a 4 (1+3), the shared cell is 1; where a 17 (8+9) crosses a run that cannot hold a 9, it is 8. Press P or tap Pencil to note candidates in tight cells.

When a clue has several combinations, use its limits. In a two-cell run each digit is at least the clue minus 9, and an even clue never splits into two equal halves, so a 10 in two cells never holds a 5. A run of 9 cells holds 1 to 9, and a run of 8 misses one digit: 45 minus the clue. On larger grids, if some complete down runs cover the same cells as some complete across runs plus one extra cell, the difference between their clue totals gives the value of that cell.

Common mistakes are reading a clue in the wrong direction, repeating a digit inside a run, and forgetting that a digit may appear again in a different run of the same row. The Check button highlights any run that repeats a digit or overshoots its clue, and tells you whether the digits entered so far match the solution.

Kakuro began in the United States as Cross Sums, a number crossword printed in Dell puzzle magazines. In Japan it became known as kasan kurosu, meaning addition cross, a name shortened to Kakkuro (カックロ). Nikoli, the publisher that also popularized Sudoku, first printed it in the eleventh issue of its puzzle magazine, and it grew into one of the most widely played pencil puzzles in Japan; Nikoli itself calls it the king of pencil puzzles. English publishers adopted the spelling Kakuro, and British newspapers began printing it in the mid 2000s in the wake of the Sudoku boom.