Kasan Kurosu Play now

How to play Kakuro

Kakuro is a crossword where the clues are totals and the answers are digits. Four rules, a handful of patterns, and you can solve your first grid today.

The rules

  1. Fill every white cell with a digit from 1 to 9.
  2. A run is a line of white cells, across or down. The clue at its start gives the run's total.
  3. A digit can't appear twice in the same run.
  4. There is exactly one solution, and you can reach it by logic. No guessing.

Reading a clue cell

Above the slash
The across clue: the total of the run to its right. Here, 16.
Below the slash
The down clue: the total of the run beneath it. Here, 7.
A solved 4×4 grid. Every across and down run adds up to its clue, with no digit repeated.

The sum rule

Because digits in a run must be different, most totals can be made only a few ways. Knowing them is most of the game. Take a run of two cells:

  • 4 in 21 + 3 only. 2 + 2 repeats a digit.
  • 10 in 24 + 6, 3 + 7, 2 + 8, 1 + 9. Never 5 + 5.
  • 17 in 28 + 9 only.

Longer runs work the same way. The combinations chart lists every total for runs of two to nine cells, 502 sets in all.

Magic blocks

A magic block is a clue that can be made only one way. There are 34 of them, and they are where most solves begin. The short ones are worth learning by heart:

  • 3 in 2 1 + 2
  • 4 in 2 1 + 3
  • 16 in 2 7 + 9
  • 17 in 2 8 + 9
  • 6 in 3 1 + 2 + 3
  • 7 in 3 1 + 2 + 4
  • 23 in 3 6 + 8 + 9
  • 24 in 3 7 + 8 + 9

The pattern: the smallest and largest totals for each length, and the ones just inside them. A nine-cell run is always 1 to 9, and an eight-cell run is 1 to 9 minus one digit, so every eight-cell total is a magic block too.

A worked example

This is the grid from the app's tutorial. Six clues, seven cells, and three ideas: magic blocks, crossings and totals.

The empty grid. Across clues: 3, 6 and 10. Down clues: 4, 7 and 8.

  1. 1. Start with a magic block

    The across 3 has two cells. Two different digits that make 3 can only be 1 and 2. The down 4 is the same kind of clue: only 1 + 3 works, because 2 + 2 repeats a digit. Clues with a single recipe like these are magic blocks, and they are the usual way in.

  2. 2. Look where runs cross

    The top-left cell sits in both runs. The across 3 allows 1 or 2; the down 4 allows 1 or 3. Only 1 fits both, so it goes there.

  3. 3. Use the totals

    The across 3 now has a 1, so its other cell needs 3 − 1 = 2. The down 4 has a 1 as well, so the cell below needs 4 − 1 = 3.

  4. 4. Cross again

    The across 6 in three cells can only be 1 + 2 + 3, and the down 7 can only be 1 + 2 + 4. The middle cell is in both. Its across run already has the 3 and its down run already has the 2, so the only digit left for both is 1.

  5. 5. Finish each run

    The across 6 has 3 and 1, so its last cell takes 2. The down 7 has 2 and 1, so its last cell takes 4. The final cell ends both the across 10 and the down 8: 10 − 4 and 8 − 2 both give 6.

From Gentle to Expert

Every puzzle is graded by the hardest technique it needs, so a tier name tells you what to expect. After each solve the app shows the key step, and a hint always names the technique it uses.

Gentle
Magic blocks, run candidates, intersections, naked singles and sum remainders, with plenty of ways in.
Easy
Everything in Gentle, plus hidden singles and min/max bounds.
Medium
Everything in Easy, plus must-contain digits, cannot-contain digits and combination elimination.
Hard
Everything in Medium, plus subsets in a run and run shaving, needed more than once.
Expert
Everything in Hard, plus area sums and parity, or short chains. Never a guess.

Play a Gentle puzzle Open the combinations chart