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 8-in-three block in row 2 still has two empty squares which sum up to 5. The clues specify the sum of the numbers in the row of successive white cells to the right or the column of successive white cells below.

Duplicate numbers You may not enter any duplicate number in the same run, so the example on the left is incorrect as it has two 1’s. But before we do that, let’s polish off the one square whose value we can write down without tricks. Some unique intersections are listed earlier in this page. How to solve Kakuro This web page contains a general description of an method for solving Kakuro puzzles. Since it is part of a row clue, take the sum of the column clues behind it: Kakuro techniques 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.


When I have to start trial and error, it feels like a cop out.

This shows that if enumeration were the only way of solving Kakuro puzzles, then generating a solution of Kakuro would take non-polynomially large time. Did this article help you? Next find the sum of all the row clues except the one that involves the linking square this was 17 in the example. Call this number N. Step 10 Kqkuro in-four block in row 4 has two empty squares that sum up to 6.

Beginner and Intermediate Kakuro Solving Strategies!

Unique sums for specific definitions There are hechniques definitions that can be solved only in a specific way: Play Kakuro on mobile.

The solution of Kakuro puzzles is helped along by several unique partitions. The column clue 4 2 in column D gives two possibilities in the square Dh.

Your puzzles are my on-line favorites. Things You’ll Need Paper puzzle.

Solve Kakuro puzzles

Conclusion Practicing is the best way to see how this advice can be applied in actual Kakuro games. Cross reference Find 2 intersecting runs and compare the clue number combinations for each.

Now look at which of these six numbers can go into the square Fj. If you are a geek you may want to read this para and the next. We can techniqyes complete the in-two block with 9 in square e1, and the in-two block with 3 in square e2.

Kakuro techniques

The values 1 and 2 are ruled out because that can’t give a single digit solvimg for [Id]. The dimension of the null space of A is the number of linearly independent non-zero solutions of A. This web page contains a general description of an method for solving Kakuro puzzles.


So you must fill in every run, using only the numbers without duplicates, so that they add up to the clue square given. Elimination using circumstantial evidence again. We call these Type 1 inequalities. The spreadsheet part of the algorithm takes time of order M and gives D free variables. We will distinguish these by a subscript on the clue: Try the Kakuro computer game.

If we try to place 1 in square d4 we immediately see square d5 will be larger than 9. The answer is no, Kakuro is in NP. Play a puzzle for real. In this especially simple case, the self-contained block comes with two interlocking clues which can be solved by unique partitions. 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. If the 9 is in square c1 then squares c2 and c3 must both contain 1, which is not allowed.

It is useful to give a name to this kind of logic, because that helps us remember it. Cookies make wikiHow better. To complete this block, a 3 is placed in square b3.