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Kakuro solving techniques
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Lone square
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
values and then subtract the total from the clue. The remaining value is the
answer for that square.
The lone square in the example therefore has to be 2 as 9-(4+3)=2.
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Cross reference
Find 2 intersecting runs and compare the clue number combinations for each. Any
values which appear in the combinations for both runs are candidates for the square
on which the runs intersect.
In this example, the "down" clue is 6, which has only 1 combination (1+2+3), whereas
the "across" clue 20, has 4 combinations (3+8+9, 4+7+9, 5+6+9 and 5+7+8). However, the
only common number in both sets of combinations is 3, therefore the intersection square
must be 3.
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example 1
example 1, with answer
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Combo reference
This technique works by picking a run and performing a cross reference on every
square along it, weening out combinations until you have only 1 left.
In this example we take the "across" run 12, which has the combinations (3+9, 4+8 and 5+7).
The first square (A) intersects a run with the combinations (1+4 and 2+3). Since neither
5 or 7 appear in these, we can discount the 5+7 combination from the first run. However, this
still leaves us with the combinations (3+9 and 4+8).
The second square (B) intersects with a run which has only 1 combination (7+9), and since the
(4+8) combination shares no common numbers we can remove it, leaving only 1 combination for
our original run (3+9).
Knowing that this run has only 1 combination, we can now fill in this section of the puzzle.
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Filled areas
In this example, we can deduce that the square outside of the blank 2x2 area shown must be a 3, we can do this
using the filled area technique.
Firstly, add together all the "across" clues (4+3=7). Then add together all the "down" clues (4+6=10).
Now work out the difference between those totals (10-7=3) and that will be the value of the square which
is not in the 2x2 area.
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example 1
example 2
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Eliminating duplicates
Using this technique you can eliminate any number combinations which would lead to certain
patterns of numbers (as shown in the examples).
The pattern shown the examples, with the numbers on the top row being the same as the bottom
row (albeit in a different order), can never occur anywhere on a valid Kakuro board as it would
lead to more than 1 solution.
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.
Bearing in mind that a Kakuro puzzle has only 1 solution, you should avoid any numbers which would
create the patterns seen here.
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