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 triangular numbers are again critical for this step. A satisfactory puzzle is one which lies on the borderline of solvability: For the yellow cells highlighted above, there’s only one way of writing the sum: Fill each cell in the grid with a single digit such that each row or column has the indicated sum without repeating a digit.

This article has also been techniqkes 52, times. If the number is part of a column then it is the sum of all the row clues in the block minus the sum of all the other column clues inside the block. 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.

Kakuro techniques

This would allow us solivng fill up everything uniquely until we get to the pink coloured cell Bd. Completing the vertical 6-in-two block in column a is now straightforward, since only 1 can be placed in square a2. Next find the sum of all the row clues except the one that involves the linking square this was 17 in the example.

A few remaining ambiguities are solved when glueing everything back together. Did you try these steps?

Kakuro techniques

So [Bb] can be one of 9 and 8, as shown tchniques the figure alongside. But first we will state the rule. 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. Call this number N. Step 1 Kakuro puzzles are all about special number combinations. Kakuro puzzles resemble crosswords which use numbers instead of words.


When a block of squares is connected solvinh the rest of the puzzle through exactly one techniqkes, then call this the linking square. Play Kakuro on mobile. Any such set is part of a self-contained block. The techniquex integer programming problem is known to be NP-hard. Tips Be aware that some numbers only have one possible solution – a two-digit 16 can only be made with a 9 and 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.

These rule out individual values for one variable or lines for multiple variables. We’re presenting below several methods to make progress in solving the actual puzzle. As soon as you find a block, it can be replaced by a number computed just from the clues. The two examples on the right communicate through a single column. One can carefully define subclasses of NP complete problems which could be in P.

If you like Sudokuor are tired of it, Kakuro is for you! But keep in mind, in a Kakuro puzzle there is only one unique solution that will work successfully. An example was given above.

If the description of the method sounds more puzzling than Kakuro, then you might want to first visit one of the earlier tutorials here or here. Resolver Kakuro Print Edit Send fan mail to authors.

The number of variables, Dis the dimension of the null space of the linear algebra problem. Step 10 The in-four block in row 4 has two kakuuro squares that sum up to 6. Oslving complete this block, a 3 is placed in square b3. And that’s the whole big tecchniques completely solved!


Therefore the only common number for square f1 is 4. 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. Now it is time to solve the eight simpler and smaller puzzles to which we have reduced this.

Puzzle setters should note that the clue value X has to be larger than Step 8 We now come across a special situation which occurs in the right hand side of the puzzle. This technique works especially well when intersecting a low-sum with a high-sum definition. Partitioning a number is to techniquess it up into smaller pieces. Thats the techniquez time that has happened, and I can figure out how I got it. A spreadsheet contains cells: Help answer questions Learn more.

We give every column a name: 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. With this the state of the puzzle is as shown solvkng. Having an unique way of writing the sum helps, but keep in mind that all permutations are valid and you still need techniqyes figure out which actual permutation to use on the board.

We have converted partial knowledge about four squares into full knowledge of one square.