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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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.

Since square f3 is the crossing point, it must contain 6 which is the only common number for both blocks. So [Gb] must be either 1 or 2. Tell us more about it? The in-four block in row 4 has two empty squares that sum up to 6. Unique Partitions Partitioning a number is to break it up into smaller xolving.

The linking squares can be identified without looking at the clues. You’ll still have to somehow determine the correct order, but knowing exactly which digits appear in that row is a great start. In this cell we would get one value if we fill according to the row, and another if we fill according to the column. Cookies make wikiHow better. Go for the smaller numbers first, then the big numbers.

For example, if the above 27 in 4 crossed a 7 in 3, we could aolving that the solvjng in the intersection contained a 4. The gain is that the number of unknowns is smaller than the number of white cells. If the linking dolving is part of a column clue Interchange column and row in the procedure given above. Common Numbers If a row tschniques a sum of 16 over 2 squares and a column has a sum of 17 over 2 squares, the only possible values are for the row and for the column.


Click here to download the free Kakuro combination tool k Note: Step 3 We are now left with two empty squares in column c which must sum tchniques to 3. Look for rows or columns that can only be made with one combination of digits. When I have to start trial and error, it feels like a cop out.

KrazyDad » Blog Archive » An advanced Kakuro technique

There are two possible combinations: By using a divide and conquer strategy, this 48 piece puzzle has been converted into 5 puzzles of 4 pieces each and 3 puzzles of 7 pieces each. The dimension of the null space of A is the number of linearly independent non-zero solutions of A.

This strategy is best when starting off a puzzle. This is a seconf example of elimination using circumstantial evidence. Step 7 The in-five block in column f now misses only 2 and 3.

Otherwise, the Kakuro is badly formed, and you are perfectly justified in writing to the puzzle setter telling her so. To each row we also give a name: Puzzle setters should note that the clue value X has to be larger than Some unique partitions are listed earlier in this page.

Tips Be aware that some numbers only have one possible solution – a two-digit 16 can only be made with a 9 kakkuro a 7; so if it crosses a two-digit 17, the intersecting number MUST be a 9, as the 17 can only be made with a 9 and an 8.


No row or column of successive white cells can have a digit repeated. Compare these restrictions with those in the crossing rows. The other three squares are child’s play. Since the number of clues is usually less than the number of variables, the matrix A is a rectangular matrix. Take the squares Bb, Bc, Cb and Cc.

I call it “unique intersection without unique partition”. I leave this in your, by now, capable hands.

Resolver Kakuro Print Edit Send fan mail to authors. Now look at which of these six numbers can go into the square Fj. As a rule of thumb, the more blank squares a puzzle contains, the harder it is, however this isn’t always true, especially if it is a good quality puzzle.


Eliminating duplicates Using this technique you can eliminate any number combinations which would lead oslving certain patterns of numbers as shown in the examples. The sum in the row b has to be 17, because it must match the clue. Instead we could start by putting a variable a in Db.

How to solve Kakuro

That is the number 9. We have called it a phagocyte because it eats up the block. A satisfactory puzzle is one which lies on the borderline of solvability: Here is an example of a puzzle which can be almost entirely separated into small self-contained blocks, and then replaced by phagocytes which bear the numbers shows in red italics.