Kakuro looks like a crossword, but the answers are numbers and the clues are sums. Each row and column of white squares has a fixed sum; You have to fill the boxes from 1 to 9 in such a way that each row or column sums exactly to the target. An additional rule maintains the fairness of the game: no number can appear twice in the same row or column.
If you like Sudoku, Kakuro will feel familiar yet something new. In that too you have to find the correct number by checking the possibilities, but the mathematical process provides you with additional help in finding the solution. Some sums can only be obtained in one way, and that's where any skilled player starts solving.
What Is Kakuro?
Kakuro is a logic puzzle built on addition. The grid has shaded hint cells and white answer cells. The signal cells are divided by a diagonal line: the number on the upper right is the total for the run going down, and the number on the lower left is the total for the crossing run.
From the 1950s, American puzzle magazines printed it as Cross Sums. The Japanese publisher Nikoli later gave it the name it is best known by today, a shortened form of Kasan Kurosu, meaning sum cross. It became a puzzle-page regular around the world in the mid-2000s, riding the same wave as Sudoku.
How to Play Kakuro
Step 1: Read the clues. Each shaded cell represents the sum of the rows of white cells to its right, below, or both.
Step 2: Fill a cell. Tap or click the white box, then select a number from the number pad or type 1 to 9 on the keyboard. You can move between cells by using the arrow keys.
Step 3: Never repeat a digit in a run. If two cell rows add up to 4, they must contain the digits 1 and 3; It can never be 2 and 2.
Step 4: Pencil in candidates. Turn on 'Notes' (or press N) to enter possible small candidate digits in the box. When you place a digit, that digit is removed from the record of all other cells in the same row.
Step 5: Check the combinations. The combinations panel will display all pairs of digits corresponding to the sum of the horizontal and vertical rows for the selected cell. It will remove pairs that don't match the digits you put in and show which digits still match.
Step 6: Complete the grid. When the digits in each row add up to its clue and no digit is repeated, the puzzle is solved.
Kakuro Rules at a Glance
- Use only the digits 1 to 9.
- The sum of the digits in each row must equal the clue given in the shaded box preceding it.
- No digit should be repeated in the same row.
- Every puzzle has only one solution.
Kakuro Levels
- Easy, 6 by 6: small grids where the opening combinations are easy to spot.
- Medium, 8 by 8: more runs that cross each other, so you start working two directions at once.
- Hard, 10 by 10: longer runs and fewer forced combinations at the start.
- Expert, 12 by 12: large grids that need patient cross-checking from start to finish.
Every puzzle is checked by a solver before it reaches you, so each grid has exactly one answer and can be finished with logic alone. You never have to guess.
Kakuro Strategy: Where to Start
Learn the forced combinations
Some totals can only be made from one set of digits. Experienced players call these magic blocks, and spotting them is the fastest way into any grid.
- Two cells: 3 = 1+2, 4 = 1+3, 16 = 7+9, 17 = 8+9
- Three cells: 6 = 1+2+3, 7 = 1+2+4, 23 = 6+8+9, 24 = 7+8+9
- Four cells: 10 = 1+2+3+4, 11 = 1+2+3+5, 29 = 5+7+8+9, 30 = 6+7+8+9
- Five cells: 15 = 1+2+3+4+5, 16 = 1+2+3+4+6, 34 = 4+6+7+8+9, 35 = 5+6+7+8+9
Cross-check every cell
Each white cell is a cross run and a down run, and its digit works for both. If the cross run can only use 1 or 2 and the down run can only use 2 or 4, then the cell is 2. Much of the solution comes down to finding these overlaps.
Think high and low
A small total in the long run forces small numbers, and a big total in the short run forces big numbers. A three-cell run of 23 cannot contain anything below 6, which immediately removes digits from the crossing run.
Finish runs by subtraction
When there is only one empty cell left in the run, its value is the clue minus the digits already placed. It may seem obvious, but it's easy to overlook on a busy grid.
Use Notes on harder grids
On Hard and Expert, pencil marks save you from rechecking the same cell over and over. Write candidates for the most difficult cells and let the automatic clean-up remove them as the digits are placed.
Features of the Kakuro Game on PuzzleVuzzle
Kakuro on paper means a lot of erasing and a lot of adding up in the margins. Our version does the bookkeeping for you, so you can spend your time on the logic. Every puzzle comes with:
- Four levels, from 6 by 6 to 12 by 12
- Every puzzle has a single solution you can reach with logic
- Pencil notes that clean themselves up as you place digits
- A combination helper for the selected cell
- Undo, Erase, Check and three free hints per puzzle
- A timer, your best time and win streak for each level
- Your current puzzle is saved if you leave the page
- Keyboard and touch controls, plus light and dark themes
Benefits of Playing Kakuro
Kakuro combines simple sums and fine-grained reasoning to develop multiple skills simultaneously through a single grid.
Quicker mental math
You continuously divide the total into different digits. After solving a few puzzles, you won't have to stop to count; You will immediately realize that the sum of 17 in two places is 8 and 9, or the sum of 6 in three places is 1, 2 and 3.
Clear, step-by-step thinking
The sum is simple. The real work is deciding which digit to put where. Each box has to meet the conditions of two rows (horizontal and vertical) simultaneously, and reaching a certain number from different options is the best use of logic.
Better working memory
When working on a large grid, you keep in mind several possible combinations of numbers and check them along the horizontal and vertical rows. This is an excellent and regular exercise for short-term memory.
Focus and accuracy
One wrong digit can invalidate two sums. Kakuro promotes the habit of working patiently and checking back, a habit that can be useful in many other areas of life.
A relaxed challenge
The timer only records your time and there is no risk of losing. You can spend ten seconds or ten minutes on a cell; Hence, kakuro is an excellent means of relaxing while keeping the mind active.
Why Players Enjoy Kakuro Puzzles
Kakuro has a very good first move. You scan the grid, see a 3 on two cells, and immediately realize that those cells contain a 1 and a 2. That one sure thing leads to another, and the grid begins to unfold from there.
It seems reasonable too. Each grid has an answer and can be solved without guessing, so when you get stuck, the way forward is always somewhere in the clues. Finding the run that breaks the deadlock is the best part of the solution.
And you can feel yourself getting better. Combination lists that initially look like a wall of numbers soon become second nature, and grids that once took you half an hour at a time start to fall apart pretty quickly.
Who Will Enjoy Kakuro?
Sudoku players
Kakuro uses the same no-repeats rule you already know, with the addition above. If Sudoku is starting to feel predictable, this is a natural next step.
Crossword fans
The grid works like a crossword, with clues up and down the run of cells. The only difference is that the answers are numbers.
Anyone comfortable with simple sums
You never need more than adding the digits from 1 to 9. If you can sum up a shopping list in your head, you have all the math Kakuro wants.
Players who like to learn patterns
Kakuro rewards more feel than most puzzles. The more combinations you remember, the faster you solve, and your best time on each level shows progress.
People who don't like guessing
Each grid is checked for an answer that you can arrive at with logic alone. Expert puzzles are hard, but they never ask you to guess.
Play Kakuro Online Anytime on PuzzleVuzzle
You can play Kakuro online here on phone, tablet or computer, with no download and no account. Choose a level, solve at your own pace and then come back. If you leave the page your current grid will be saved.
A simple 6 by 6 fits into a coffee break, and an expert 12 by 12 can fill an evening. When you want something different, try a Nonogram picture logic, a placement puzzle in Queens, or a lighter round of Number Search.
Kakuro FAQ
- What are the rules of Kakuro?
- Fill each white box with a digit from 1 to 9 in such a way that the sum of the digits in the horizontal and vertical rows is equal to the clue given before it. No digit may be repeated within the same row.
- How do I read a clue cell?
- The number in the upper right represents the sum of the vertical rows. The number at the bottom left represents the sum of the horizontal rows.
- Is Kakuro harder than Sudoku?
- It uses logic similar to Sudoku and uses simple sums. Many players find the 'Easy' Kakuro easier than Sudoku, while the 'Expert' level grids are really challenging.
- Does every puzzle have one solution?
- Yes. Each grid is checked to ensure that it has only one solution, which you can arrive at without making any guesses.
- How do hints work?
- Each puzzle gives three free clues. A hint fills the selected box, or any empty box, with the correct digit. After that, coins have to be spent to get additional hints.
- Can I play Kakuro on my phone?
- Yes. Tap a cell and use the on-screen number pad. Notes work the same way on a phone as on a computer.