## PUZZLE |

**Kakuro Puzzle Rules**

The rules of Kakuro Puzzles are as follows:

- Place numbers in the white squares of the grid
- You must place the numbers 1-9 only and numbers cannot repeat in any across or down run of squares
- The numbers in each run of squares must sum to the number given at the start of that run

Here is an image of the start position of a kakuro puzzle:

So, what do the rules mean? Well, take a look at the example kakuro above. All the sum totals are given in green squares, and they point in either an across or down direction. The first square in row two contains the number 8. This tells you that the three white squares next to it (an across run of three squares) sum to 8. We know we can use numbers 1-9 only and we cannot repeat a number, so that rules out 2,4,2 for instance as an option, as whilst that sums to eight, it requires us to repeat a 2, which is against the rules. We must use logic and our mathematical knowledge (mental arithmetic) to work out the options for each run of squares, and then cross-reference possible values to gradually make progress and enable us to solve the puzzle.

If you would like a visual explanation of the rules, here is a video outlining the kakuro rules as explained above:

**Play A Sample Kakuro Puzzle**

If you'd like to have a go at solving the example puzzle shown in our sample image above (the video uses a different puzzle), then you can do so for free online with our Online Kakuro Puzzle Player

If you enjoy this puzzle type, you can join our online Puzzle Connoisseur's Club for £12 or $17 a year and play a new Kakuro Puzzle puzzle every day of the year, together with many other fun and interesting logic puzzles.

**Strategy and Solving Tips for Kakuro Puzzles**

You won't ever need to guess to solve one of our kakuro puzzles, and all puzzles have a single unique solution. However, that doesn't mean they are easy to solve, particularly when you are first getting used to solving kakuro. Here are some tips to help you get started solving these number crosswords:

- You will need to use pencilmarks when solving kakuro to keep track of the options for each square. In our online player, this means using the small numbers - with a keyboard you can toggle between big and small numbers with the space bar. How thoroughly you pencilmark will depend on your own puzzle-solving style, and how difficult the puzzle is. As it can be hard to keep track of a large number of pencilmarks in a square, you might like to aim to only pencilmark squares that have, say, four options or less, and leave other squares unmarked until you can whittle down the options to this number.
- You will need to build familiarity with the most restricted combinations. For instance, in the sample grid shown in the image at the top of this page, the total 17 from 2 squares appears three times in the grid. Instantly pencilmark those as 8 and 9 as that is the only way to make 17 from 2 squares. There is also a 3 from two squares: pencilmark that as 1 and 2. Generally looking for low numbers or high numbers can often help as these tend to be the most restricted, particularly for a short or long run as relevant.
- When you reduce the options for a square in one direction, see if that helps you in the other direction. We just placed 1 and 2 as the pencilmarks for the squares in the 3 run made from two squares at the lower middle right section of the grid. The second of these squares is in a run of 5 from two squares. Since the first of these two squares must be 1 or 2, we can pencilmark the second square as 4 or 3.
- Practice makes perfect! The best way to start getting familiar with the numbers that can sum up to a given number in a certain number of squares is to play. So keep on playing kakuro and gradually you will start to know instantly how to make a total of 12, say, from 4 squares, and this makes it much easier. In the meantime, you can use a lookup table that lists all the possible combinations for each sum in kakuro, and these can also help you whilst you are learning.