Solving Kakuros

Kakuro is a kind of logic puzzle in which that is often referred to as a mathematical transliteration of the crossword. A sample kakuro is shown below. The numbers in the lower half stand for the squares below it and those in the upper half stand for the squares to its right.

The object of the puzzle is to insert a digit from 1 to 9 inclusive into each white cell such that the sum of the numbers in each entry matches the clue associated with it and that no digit is duplicated in any entry. It is that lack of duplication that makes creating Kakuro puzzles with unique solutions possible. The solution to the above kakuro will be as follows.

I had included such puzzles in each of the 4 sets we had prepared for the Vasco-de-Gamea event in Kritansh 2010-medium level. However, it was quite disheartening to see about only 10 teams being able to solve kakuros correctly. While invigilating and paper correction, i saw 2 common misunderstandings-

1. Each clue must not have numbers repeated in it. e.g. In the above kakuro, 16 over 2 squares(1st clue) can only be 9+7 (or 7+9) and not 8+8.
2. The numbers can be repeated in a row or column if and only if they are parts of different clues. e.g. In the first row 9 is repeated for the clues 16 and 24.

Now to most of u this new type of puzzle may seem difficult but trust me-it's not! Even the hard ones r not very tough if u get the hang of it.

Attacking Kakuros

The first objective is to find out the combinations of the clues given. In many cases u will get unique combinations. Here is a push 4 u...

3 over 2 squares->1+2
6 over 3 squares->1+2+3
10 over 4 squares->1+2+3+4
15 over 5 squares->1+2+3+4+5
21 over 6 squares->1+2+3+4+5+6
.
.
.
and so on.

Now we will also have unique combinations if we increase the above clues by 1 in each case... Take a look....

4 over 2 squares->1+3
7 over 3 squares->1+2+4
11 over 4 squares->1+2+3+5
16 over 5 squares->1+2+3+4+6
22 over 6 squares->1+2+3+4+5+7
.
.
.

OK? Now Let us calculate backwards...

17 over 2 squares->9+8
24 over 3 squares->9+8+7
30 over 4 squares->9+8+7+6
etc etc etc....

And similarly as before, if we reduce the above clues by 1 in each case we have..

16 over 2 squares->9+7
23 over 3 squares->9+8+6
29 over 4 squares->9+8+7+5
etc...

This will greatly reduce the possibilities and also the solving time reqd to solve the kakuro.

Now the question is what to do if we do not get a unique combination...

Dont worry guys, that was just a head start. Several other clues will be there which wont have a huge many number of combinations to it and many a times if 1 particular no. gets known, it eliminates the possibilities of other combinations as well leaving u with just the permutation part. This varies with the difficulty of the puzzle.

Now take a shot at kakuros. The puzzles were generated using THIS software. Generate the puzzles and try solving them on pen and paper after a while. Enjoy! :)