Kakuro – Play Online for Free

At first sight a Kakuro looks like a crossword, except that the white squares take digits instead of letters. The clues are sums in the black squares, and the digits that follow must add up to exactly that sum, with no digit repeated. The Japanese name hides where the puzzle comes from: around 1950 it appeared as "Cross Sums" in the American puzzle magazines of Dell, which still prints it under that name. About thirty years later Maki Kaji, the founder of the puzzle magazine Nikoli who later gave Sudoku its name too, brought the idea to Japan. He called the number crosses "kasan kurosu," from the Japanese word for addition and the English "cross," and the name was shortened to Kakuro.

In the Japanese press Kakuro was the most popular logic puzzle until Sudoku overtook it in 1992. In Britain the Guardian was the first paper to print Kakuro, in the fall of 2005, at the launch of its new format and at the height of the Sudoku craze. It is not to be underestimated: in the early 2000s Japanese computer scientists proved that solving grids of any size is NP-complete, which puts it among the problems for which no fast general method is known. Here you can solve Kakuro online for free on three levels, no account needed.

Sums Instead of Words: Rules, Combinations and Tricks for Kakuro

The grid is made of black and white squares. An unbroken line of white squares forms a run, and every run has its sum in the black square in front of it:

• Reading the sums: a black square is split diagonally. The number at the top right belongs to the run across to its right, the number at the bottom left to the run going down below it.
• The rule: every white square takes a digit from 1 to 9. Together the digits of a run add up to its sum, and no digit may appear twice within a run. A black square in between starts a new run, where the same digit is allowed again.
• Entering digits: click a square and type the digit or pick it from the bar below the grid. Backspace, Delete, the 0 or the delete button next to the 9 clears a square again, and the arrow keys skip black squares to reach the next white one.
• Notes: with the "Notes" button, the N key or Shift plus a digit you jot small candidates into a square. When you later set a digit, it disappears from the notes of both runs the square belongs to.
• Combinations: below the grid you see both runs of the selected square, such as "→ 16 in 2: 79," meaning 16 in two squares, which only works with 7 and 9. Up to three combinations are spelled out there; with more, only their number is shown.
• Help along the way: a repeated digit in a run turns red. When a run is full, the number in its black square fades as soon as everything fits, and otherwise it turns red.
• Check and Hint: "Check" marks wrong digits without giving away the right ones. "Hint" reveals one digit, in the selected square or else somewhere in one of its runs. Revealed digits turn blue and stay fixed, and the final message counts them.
• Levels: Easy plays on 6 × 6 squares, Normal on 8 × 8 and Hard on 10 × 10, plus a border of sum squares along the top and left. Every puzzle has exactly one solution and can be cracked without guessing, though Hard calls for longer chains of reasoning across several runs.
• Progress: every level keeps its own puzzle, and your browser remembers everything until your next visit. If you have already entered digits or notes, "New Puzzle" asks once more to be safe.

You never need to guess, but a few arithmetic tricks save you a lot of time:

• Learn the unique sums: some sums split only one way. In two squares that is 3 (1 and 2), 4 (1 and 3), 16 (7 and 9) and 17 (8 and 9), in three squares 6, 7, 23 and 24, in four squares 10, 11, 29 and 30. A 7 in three squares, for example, can only be 1, 2 and 4.
• Even sums in two squares: since two equal digits are forbidden, half of the sum is out. A 10 in two squares never contains a 5, and a 12 never contains a 6.
• Work long runs backward: nine squares hold every digit exactly once and always add up to 45. In eight squares exactly one digit is missing, namely 45 minus the sum: with 36 it is the 9, with 44 the 1.
• Use the crossings: every white square belongs to a run across and a run down, so its digit has to fit both. If a 4 in two squares (1 or 3) crosses a 7 in three squares (1, 2 or 4), only the 1 is left for the shared square.
• Work out the last square: when only one digit is missing in a run, there is nothing left to wonder about; it is the sum minus the digits already entered.
• Work with candidates: in tricky corners, note every digit both runs allow and cross out what other squares rule out. Usually one square ends up with a single option, and from there its neighbors fall like dominoes.

More Digits, More Grids: Five Puzzles for Your Next Brain Break

If you enjoy puzzling with numbers and boxes, these games are for you too:

• Sudoku: its famous relative also first appeared in a Dell magazine and got its name at Nikoli. No adding here; all that matters is that no digit appears twice in a row, column or box.
• Crossword: the model for the shape of a Kakuro, with letters instead of digits. Words across and down cross each other, and "Check" and "Hint" help there too when a clue is stubborn.
• Arrowword: here the questions are printed in the grid itself, just like the sums in the black squares, and arrows show the direction of each answer.
• Minesweeper: numbers tell you something about their neighbors here as well, namely how many mines hide there. With clean deduction you open every safe square and leave the mines alone.
• 2048: numbers in a whole new role. You slide tiles across sixteen squares, and two equal values always join into one twice as big.