If you are a Kakuro player, then you know that it can be quite a challenging type of puzzle if not harder than Sudoku. The object of the puzzle is to fill the white boxes with the correct digits that add up to the sum listed in the triangular box. For example, a row of three blocks with a sum of 10 on the end could be 1-2-7, 1-4-5, or several patterns of numbers.
There are a few key rules in playing:
– There are no zeroes in the puzzle only 1 through 9.
– No digit is repeated within any sum group.
– The order for a string of numbers may vary.
(ex. For a sum of 6, you may use 1-2-3, 1-3-2, 2-3-1, 2-1-3, 3-1-2, or 3-2-1).
– There is only one unique and correct solution to a given puzzle.
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 technique. This can get to a point where it almost looks impossible to solve and may take a long time using a variety of strategies. But keep in mind, in a Kakuro puzzle there is only one unique solution that will work successfully. In this article I will give you a few kakuro strategies and will use the term rows for the across boxes and column for the down boxes.
Strategy #1: Common Numbers
If a row has a sum of 7 over 3 squares and a column has a sum of 4 over 2 squares, the only possible values are 1-2-4 for the row and 1-3 for the column. Therefore, the only common value for the cross box Is a 1. This strategy is best when starting off a puzzle.
Strategy #2: Use Pencil marks
Although it may take extra work, using pencil marks not only greatly reduce the chance for error, it helps to point out obvious hints in solving puzzles. Using pencil marks, it is best to fill in possible values that you know are going to exist in a particular box. Then, as more clues are revealed, you can reduce the pencil marks until only one digit remain and that will be the digit used for that box.
Strategy #3: Pairs, Triples, Quadruples
This is a very good strategy assuming you are using strategy #2. If a box of a given row only has a pencil mark of 1-5 and the box next to it only has a pencil mark of 1-5 then you can remove 1 and 5 from all other boxes in that row. The reason behind this is that the first box must be a 1 or a 5 and the second box must be a 1 or a 5. If the 3rd box was set as a 5 for example, it would cause an obvious error in the row since you are not allowed to have the same digit in a row or column.
Strategy #4: Combo Elimination
This strategy used is how you can further eliminate pencil marks. First, you make a list of all the combos that would add up to a given sum. Then you can eliminate combos based on the digits you already have filled in. For example, a 5 digit sum of 33 is either a 3-6-7-8-9 or 4-5-7-8-9. Now if you already know that one of the boxes is a 4 then you know the other 4 boxes will contain a 5-7-8-9 not a 6-7-8-9, thus permanently eliminating 6 from any box in the row. This strategy can also be used on conjunction with pairs, triples when eliminating combos.
Strategy #5: Only Digits One through Nine
When deciding which digit will fit in a box, you have to take into account which digits already have been used in the row and which digits have already been used in the column. Those you can exclude. On top of that both the row and column combos available will only have several digits in which you can use. Those you can include. From there, you can build a list of potential candidates for that square box. These along with many other techniques can help you get through the logic puzzle Kakuro. Good luck and Happy Kakuro!