Best Kakuro - Solving Techniques

To solve a Kakuro puzzle, you must reduce the possible values in each of the white squares to determine the actual digit in that square.

A properly constructed Kakuro puzzle will have a unique solution and be solvable purely by logical means, without having to resort to guessing any values.

In the examples below, the initial diagram shows the current state of the partial puzzle, assuming that values have been filled from other parts of the puzzle.  Any possible values are highlighted in yellow.

The examples below are all regular Kakuro puzzles, using the digits 1 to 9.  In addition, BestKakuro also produces puzzles where zeros are allowed in the solution.  These 'zero allowed' puzzles are more challenging, but the solving techniques are the same as described below.

Compare across and down values

Kakuro - Compare example - 1

Current state of Kakuro puzzle

Yellow shows possible values

Possible values for 13 are 4+9, 5+8, 6+7.

 

The first digit of the 13 total is 1,2 or 4.

 

The values 1 and 2 are not possible for a total of 13 in 2 squares, so the value for the first digit must be a 4.

Kakuro - Compare example - 2

 

Remove impossible values in a sequence

Kakuro - Remove values example - 1

Current state of Kakuro puzzle

Possible values for 8 are 1+2+5 or 1+3+4

Digit A can only be 4 or 5

Therefore digit B cannot be either 4 or 5 as the total would then be greater than 8.  Digit B must therefore be a 3

The combination 1+2+5 does not contain a 3.  Therefore the combination 1+3+4 must be the correct one.

Kakuro - Remove values example - 2

 

High/Low values

Kakuro - High/Low values example - 1

Current state of Kakuro puzzle

The highest possible values are A=4, B=3, C=2, D=8.

These add to the total of 17, so these must be the values.

Kakuro - High/Low values example - 2

 

Note : This technique can also be applied when the lowest possible values add to the required total. 

Remove pairs

Kakuro - Pairs example - 1

Current state of Kakuro puzzle

Digits A and C are 1 and 2.

Digits B and D cannot also be 1 or 2.

D must therefore be 3 and B must therefore be 4.

Kakuro - Pairs example - 2

 

This technique can also be applied to triples, quadruples, or higher values

Kakuro - Quadruples example

Current state of Kakuro puzzle

A,B,C,D all allow some of the values 6,7,8,9 and no other values.  E and F cannot also be 6,7,8,9 which fixes E as 5 and F as 3.

Value must exist

Kakuro - Value must exist example - 1

Current state of Kakuro puzzle

The possible combinations for 27 in 4 squares are 3+7+8+9, 4+6+8+9, 5+6+7+9.

 

All must have a 9, but only the digit A has a 9 as a possible value.

Kakuro - Value must example - 2