Kakuro, Logic and Computer Science – problem-solving brain teasers

by Paul Curzon, Queen Mary University of London

To be a good computer scientist you have to enjoy problem solving. That is what it’s all about: working out the best way to do things. You also have to be able to think in a logical way: be a bit of a Vulcan. But what does that mean? It just means being able to think precisely, extracting all the knowledge possible from a situation just by pure reasoning. It’s about being able to say what is definitely the case given what is already known…and it’s fun to do. That’s why there is a Suduko craze going on as I write. Suduko are just pure logical thinking puzzles. Personally I like Kakuro better. They are similar to Soduko, but with a crossword format.

What is a Kakuro?

Kakuro Fragment
Part of a Kakuro puzzle

A Kakuro is a crossword-like grid, but where each square has to be filled in with a digit from 1-9 not a letter. Each horizontal or vertical block of digits must add up to the number given to the left or above, respectively. All the digits in each such block must be different. That part is similar to Soduko, though unlike Soduko, numbers can be repeated on a line as long as they are in different blocks. Also, unlike Soduko, you aren’t given any starting numbers, just a blank grid.

Where does logic come into it? Take the following fragment:

Kakuro Start - part of a Kakuro puzzle
Part of a Kakuro Puzzle

There is a horizontal block of two cells that must add up to 16. Ways that could be done using digits 1-9 are 9+7, 8+8 or 7+9. But it can’t be 8+8 as that needs two 8s in a block which is not allowed so we are left with just two possibilities: 9+7 or 7+9. Now look at the vertical blocks. One of them consists of two cells that add up to 17. That can only be 9+8 or 8+9. That doesn’t seem to have got us very far as we still don’t know any numbers for sure. But now think about the top corner. We know from across that it is definiteley 9 or 7 and from down that it is definitely 9 or 8. That means it must be 9 as that is the only way to satisfy both restrictions.

A Kakuro for you to try

A Kakuro puzzle for you to try

Here is a full Kakuro to try. There is also a printer friendly pdf version. Check your answer at the very end of this post when you are done.

Being able to think logically is important because computer programming is about coming up with precise solutions that even a dumb computer can follow. To do that you have to make sure all the possibilities have been covered. Reasoning very much like in a Kakuro is needed to convince yourself and others that a program does do what it is supposed to.


This article was included on Day 11 (The proof of the pudding… mathematical proof) of the CS4FN Advent Calendar in December 2021. Before that it was originally published on CS4FN and can also be found on page 16 of CS4FN Issue 3, which you can download as a PDF below. All of our free material can be downloaded here: https://cs4fndownloads.wordpress.com/


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This blog is funded through EPSRC grant EP/W033615/1.

The answer to the kakuro above

Answer for the kakuro
A correctly filled in answer for the kakuro puzzle