
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
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. 


Remove
impossible values in a sequence
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. 


High/Low values
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. 

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

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


