Like sudoku, there are many techniques in solving a kakuro puzzle. When the simple techniques don’t work, you will need to use a more complicated solving. Basic and advanced methods for solving Kakuro puzzles. This technique works especially well when intersecting a low-sum with a high-sum definition. An empty square that has all its neighbouring squares (either column or row) filled in can easily be solved. simply add together the corrsponding neighbouring .

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Here is the list. So [Bb] can be one of 9 and 8, as shown in the figure alongside. However, square a2 already contains 1 so the number in square c2 must be 2.

After one set of linking squares have been filled in, other squares may become linking squares. Look for rows or columns that can only be made with one combination of digits. So Gi is a linking square. Therefore square d4 must be 5 and square g4 must be 1. Similarly for any square, when you see square brackets around the name of a square, it means the number that goes into that square. The task in Kakuro puzzles is to fill all empty squares using numbers 1 to 9 so the sum of each horizontal block equals the clue on its left, and the sum of each vertical block equals the clue on its top.

Start with the square Fd. The value in the linking square is found as follows: We wish you good luck and lots of fun! And that’s the whole big puzzle completely solved! Whenever the effort in solving a puzzle grows faster than linearly in the number of pieces, it is faster to create a divide and conquer strategy. From this we subtract the row clues which do not involve the linking square: This means that Square f2 must be 1, and Square g2 must be 4.


Step 10 The in-four block in row 4 has two empty squares that sum up to 6. Fill each cell in the grid with a single digit such that each row or column has the indicated sum without repeating a digit. Play a puzzle for real. Any values which appear in the combinations for both runs are candidates for the square on which the runs intersect. The clue in column C reduces becuase of the value already filled in Ch to 4 2. The phagocyte shows the rest of the puzzle a single number.

In the example here, that row or column is indicated by the red lines inside the ellipses. The gain is that the number of unknowns is smaller than the number of white cells. Kakuro is a problem in linear algebra.

How to Solve Kakuro: 6 Steps (with Pictures) – wikiHow

Since it is part of a row clue, take the sum of the column clues behind it: In a properly formed Kakuro this eliminates all but one value for each free variable. In addition, inside each sum group, each digit can appear once at most.

The clue in row j is 7 2 which can be written in three ways: The only digit in common is a 6, so that jakuro be in the intersection. If a puzzle turns out to be entirely decomposable into small self-contained blocks such as the large example abovethen such a puzzle would clearly be simple— perhaps even too simple to give us much pleasure in solving it. That is the number 9.

In addition, no number may be used in the same block more than once. When the simple techniques don’t work, you will need to use a more complicated solving technique. The spreadsheet stage of the method would give a result as shown.

Solve Kakuro puzzles

tecuniques Conclusion Practicing is the best way to see how this advice can be applied in actual Kakuro games. Once one has solved the clues, examined and isolated all the self-contained blocks, one is still left with the last step of the solution: Triangular numbers plus one: Usually you can hover on a Kakuro grid over the definition number and a tooltip will appear containing all the possibilities of writing that sum with unique digits in the number of available cells.


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Lone square An empty square that has all its neighbouring squares either column or row filled in can easily be solved. When I have to start trial and error, it feels like a cop out.

In some situations, there’s no specific board cell having just one possibility. The column clue 4 2 in column D gives two possibilities in the square Dh.

Since there are M white cells in the problem, then there are M Type 1 constraints. The in-four block in row 4 has two empty squares that sum up to 6. The values in the linking squares can be easily filled in by the rule of divide and conquer. The remaining three squares can now be filled in by a simple process of subtraction.

At the end of it you have a certain number of symbols with unknown values which you must find. Since no techniquez in Kakuro can involve partitions into more than 9 pieces therefore the number of Type 2 constraints must be between M and 4M. Continually reevaluate these steps as you discover new information.

KrazyDad » Blog Archive » An advanced Kakuro technique

Resolver Kakuro Print Edit Send fan mail to authors. A spreadsheet contains cells: Play Kakuro on mobile. Look at the square Gi.