Try this: Solve a Kakuro

You will need

  • A copy of some Kakuro puzzles
  • Pencil and eraser

What to do

A Kakuro consists of a grid of boxes, some empty and some filled. Lines of empty boxes run across and down. These lines each have a clue – to the left of horizontal lines and above vertical ones. The aim is to write a digit from 1 to 9 in each empty box following two rules:

  • No two boxes in a line contain the same digit
  • Adding up all the digits in the line will equal the clue

There are a lot of tricks to this puzzle, so we’ll explain how to solve Puzzle A step by step:

  1. The top line, going left, has two boxes and adds up to 3. That means one of those boxes must be a 1 and the other must be a two. We don’t know which is which though.
  2. The first line going down has two boxes adding up to 4. 2 + 2 = 4, but that has a repeated digit, so we can’t use that sum. That means one of those boxes must be a 1 and the other must be a 3.
  3. Using these two clues, we find the top left box must be a 1, and we can fill in the other two as well.
  4. Now we look at the second line going across. Three boxes add up to a total of 6, and the only sum that works is 1 + 2 + 3 = 6, so the empty boxes are 2 and 1. If we look at the second row going down, there’s already a 2, so the 1 has to go in the middle box.
  5. From here, it shouldn’t be too hard to fill in the remaining boxes.

Once you’ve finished the example, have a go with puzzle B.

What’s happening?

Kakuro is a very mathematical game, but it’s not just because there is a lot of addition. Trying to fit the numbers in the grid requires a lot of logical thinking.

When you’re starting a new puzzle, it can be very difficult to work out where to look first. Some of the best clues are small totals with lots of boxes and large totals with very few boxes. For example, three boxes adding up to 7 must be 1, 2, 4 in some arrangement, and 17 in two boxes must be 8, 9 or 9, 8.

Often it can help if you write down all the possible equations that add up to the total for a line. Sometimes, you can use that information to prove certain digits can’t be in a line, or use a few numbers in the line to work out what all the others in that line must be.

You might want to write notes in the boxes to remind you what numbers might be in a box. Instead of writing little numbers, you could imagine the box as the numbers on a phone. Then, put a dot where the key would be. So a dot in the top left would be a 1 and one in the centre would be a 5.

experiment photo 1

An example puzzle.

experiment photo 2

The first line must be 1 and 2.

experiment photo 3

Remember that there can't be two of the same number in a sum.

experiment photo 4

Remember that there can't be two of the same number in a sum.

experiment photo 5

The completed puzzle.