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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Kakuro techniques

Kakuro live to play unique Kakuro puzzles online. But usually this does not happen.

If the description of the method sounds more solvijg than Kakuro, then you might want to first visit one of the earlier tutorials here or here. The number is the clue, and the subscript is the number of pieces it should be broken into. Resolver Kakuro Print Edit Send fan mail to authors.

Step 3 We are now left with two empty squares in column c which must sum up to 3. Kakuro puzzles are all about special number combinations.

The clue in row j is 7 2 which can be written in three ways: The pattern shown the examples, with the numbers on the top row being the same as the bottom row albeit in a different ordercan never occur anywhere on a valid Kakuro board as it would lead to more than 1 solution. Here is the list.

Since the number of clues is usually less than the number of variables, the matrix A is a rectangular matrix.

Solve Kakuro puzzles

Simplify using unique partitions Some clues have an unique partition. One solves the puzzle by collecting all the constraints on each free variable variable.


The phagocyte marked 15 also needs this twist in the count. Therefore the intersection of low and high digits is likely to contain only one candidate for the actual cell value. Because 6 is relatively low it will force low digits in the sum representation, and 29 will force high digits in order to attain these sums using the given number of cells.

It is not known whether providing a good mathematical definition of a satisfactory problem is in NP. Play mahjong against the world.

It might seem that finding [Eh] is more complicated, but actually it is not. There are two possible combinations: In those cases each of the possibilities needs to be explored on its own and eliminated through contradictions until only one course of action remains. It has a kernel, ie, A. We have now solved a large part of the puzzle.

Divide and conquer Divide the puzzle into smaller pieces, if possible, by finding linking squares. At this stage, the clues have yielded up all their information and are no longer of use. Turns out that the 26 vertical definition helps us: The full list of unique partitions upto length five are so important to Kakuro that a case may be made to hold them in one’s mind always. A final convention before we move on to solving the puzzle above.

And that’s the whole big puzzle completely solved! Look at the square Gi. The traditional way to solve a Kakuro puzzle is incremental: The two clues intersect at the square Hh, so [Hh] must have a value which is common to these two unique partitions.


Kakuro techniques

To summarize the rules: The sum in the row b has to be 17, dolving it must match the clue. Compare these restrictions with those in the crossing rows. The values in the linking squares can be easily filled in by the rule of divide and conquer. Since the value in the cell must be unique, we must equate the two. Start with the piece containing the squares Ei, Ej, Fi kwkuro Fj.

KrazyDad » Blog Archive » An advanced Kakuro technique

Since D is not exponentially smaller than Man exponential in D cannot be polynomial in M. Completing the vertical 6-in-two block in column a is now straightforward, since only 1 techhiques be placed in square a2. To complete this block, a 3 is placed in square b3.

Like sudoku, there are many techniques in solving a kakuro puzzle. Step 6 The 8-in-three block in technjques 2 still has two empty squares which sum up to 5. We can now complete the in-two block with 9 in square e1, and the in-two block with 3 in square e2.

Cookies make wikiHow better. An “across” clue, 13 over 4 squares.

If the linking square is part of a column clue Interchange teechniques and row in the procedure given above. In the example here, that row or column is indicated by the red lines inside the ellipses. For example, suppose a 23 in 3 intersects a 28 in 7. This article has also been viewed 52, times.