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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Continually reevaluate these steps as you discover new information. Did this article help you? The aim of the game is to fill all the blank squares in the grid with only the numbers so that techniquees numbers you enter add up to the corresponding clues. Is the most general Kakuro in such a easily solvable subclass of integer programming problems? Mathematical Puzzles In other languages: Elimination using circumstantial evidence again.

Here is the list. You can easily convince yourself that you can figure out the values to be filled into the two squares which are circled in the picture alongside. One rechniques the puzzle by collecting all the constraints on each free variable variable.

Trchniques this article I will give you a few kakuro strategies and will use the term rows for the across boxes and column for the down boxes. Kakuro is a puzzle given on a grid of red and white cells.

Completing column c and row 2 is now straightforward. Kakuro is a problem in linear algebra. Self contained blocks are blocks of cells which make up a sub-puzzle which can be solved without looking at the rest of the puzzle. In this guide we offer a range of practical tips on how trchniques solve Kakuro puzzles, with difficulties ranging from beginner to expert level.

Consider the simple sub puzzle at the top left corner, which is extracted here. But keep oslving mind, in a Kakuro puzzle there is only one unique solution that will work successfully. The other three squares are child’s play. We will distinguish these by a subscript on the clue: Finding the number to put down there is also strightforward.


Puzzle setters should note that the clue value X has to be larger than techniquees If you swapped the top and bottom rows in the examples, the numbers would still add to the same clues, but would yield a different solution to the puzzle.

At the end of it you have a certain number of symbols with unknown values which you must find.

How to play Kakuro, learn from the Kakuro masters!

It is not known whether providing a good mathematical definition of a satisfactory problem is in NP. However, the only common number in both sets of combinations is 3, therefore the intersection square must be 3. For the yellow cells highlighted above, solvlng only one way of writing the sum: This forces the number in [Dc] to be 1.

Completing the remaining squares b4, a4 and a5 is now straightforward.

These rule out individual values for one variable or lines for multiple variables. Is there a way to avoid that? If the linking square is part solvinh a row clue Find the sum of all the column clues this was 23 in the example above. An example was given above.

Then that value is filled and the process is repeated until all the board cells have been discovered. Some self-contained blocks could be large and irregular in shape.

Tips and tricks: easy ways to solve Kakuro

We can say that the linking squares depend on the shape of the puzzle. However, square a1 must solvlng smaller than 6 because of the 6-in-two block in column a. Common Numbers If a row has a sum of 16 over 2 squares and a column has a sum of 17 techjiques 2 squares, the only possible values are for the row and for the column.


The number is the clue, and the subscript is the number of pieces it should be broken into. Such a process of elimination gets better the more circumstantial evidence you have. The clue in row j is 7 2 which can be written in three ways: So Gi is a linking square.

If we choose 6 for square b5 then square a5 would also have to be 6 leaving 8 as the only possible candidate for square b5. Include your email address to get a message when this question is answered.

How to Solve Kakuro Puzzles

This is one of the ambiguities which are resolved when gluing the puzzle back together. To create this article, 14 people, some anonymous, worked to edit and improve it over time. A few remaining ambiguities are solved when glueing everything back together. One last piece of the puzzle remains. The solution of Kakuro puzzles is helped along by several unique partitions.

After one set of linking squares have been filled in, other squares may become linking squares. The answer is no, Kakuro is in NP. In this cell we would get one value if we fill according to the row, and kakurro if we fill according to the column. So [Gb] must be either 1 or 2.

To find an unique solution in the null space we kqkuro to impose the rules of the game. It all sounds like a Kakuro puzzle, and indeed it is. We call these Type 2 inequalities.

The clue in row h is 21 and has a 4 filled in already, so the remainder involves the unique partition 17 2. So, for example, when I need to talk about the number that goes into the square Jj I will write [Jj].