How to Solve Sudoku: James Crook, Sudoku Killjoy

Look who’s being called a killjoy because he supposedly has a foolproof formula that will show us how to solve Sudoku? It’s American computer scientist James Crook, that’s who.

From the Daily Mail:

He probably thought he was being clever – but no one likes a smarty pants. So instead of being hailed a hero, the mathematician who reckons he’s come up with a formula to solve sudoku puzzles found himself being labelled a killjoy. Millions of us are teased and frustrated every day by sudoku number puzzles like the ones printed in this newspaper.

But American computer scientist James Crook has published a foolproof system which critics say takes the fun out of it all. In a nine-page theory on the American Mathematical Society’s website, he says the solution can be reached by following five logical steps.

Hmmm. We’re not sure we’d like to know Mr. Crook’s five logical steps. We’d rather solve our sudoku the conventional way. Solving sudoku is how we pass the time during a long bus ride, you know. We won’t be so inclined to bring sudoku along with us if it’s going to be that easy to solve.

Colin Dexter, author of the Inspector Morse crime novels, who’s a puzzle enthusiast obviously agrees with us when he was quoted by the Daily Mail as saying: ‘It’s like using a computer program to work out crossword anagrams – it takes all the fun and struggle out of it.’

More from the Daily Mail:

[T]he Crook algorithm is thought to be the first mathematical proof of how to solve the puzzle. Not even Howard Garns, the U.S. architect who devised sudoku in 1979, could promise that. His system requires players to mark up empty boxes in a sudoku grid with all possible remaining numbers and, by comparing number sets, to labour through a ‘tree’ of options that eventually produces a solution.

To complete a puzzle using his theory takes more than an hour, while most sudoku problems can be solved within 20 minutes using logic and intuition.

His formula was quickly dismissed as ‘guesswork’ by one keen fan. Tom Collyer, of Coventry, said: ‘It describes a few techniques listed in the preface of countless sudoku books – before then describing a guessing process. The conclusion? If you make enough guesses, you’ll get the answer. Amazing!’

Uh. Uh. Now we’re confused. Mr. Crook’s formula will make the Sudoku problem solving from 20 minutes to an hour? Maybe it isn’t that much of a formula after all. Isn’t the point of the formula to make things easier and problem solving faster?

[Note: Thanks to Lars in the comments for pointing out that the one-hour formula is the one devised by Howard Garns and not the one made by Mr. Crook.]


Okay. Here’s the paper written by James Crook on how you can solve Sudoku which we blogged about earlier. We must admit that we haven’t read it yet but those of you interested in reading this paper can click at the images to expand and to download them. [Source: American Mathematics Society/PDF version of Mr. Crook’s paper.]

If you can simplify and synthesize the paper into easy steps that non-mathematicians can understand then please share your synthesis in the comments. Thanks and good luck.


An anonymous commenter rose up to the challenge and simplified Mr. Crook’s sudoku problem solving formula for us. We’re publishing it here on the main section so you won’t miss his/her synthesis. Thanks, Anonymous.

Anonymous on James Crook’s Sudoku Formula:
Actually, I think with a little effort any non-mathematician should be able to understand this paper because his so called ‘new algorithm’ is in fact no more than a summary of the logical and intuitive steps that any sudoku-solver will follow in his mind when solving the puzzle. Just maybe not exactly in that order.

I didn’t find any ‘new’ steps in his algorithm that I personally (or anyone I know, for that matter) haven’t already used to solve a sudoku.

So I’m sorry to tell you: he’s not the boogy man of sudoku’s, he’s not a sudoku genius, and he’s not going to take any fun out of solving them…..He just knows how to describe simple logical brainwork in a complicated way:)

Just to be complete: here’s a ‘summary’ of his ‘five’ steps that are actually three:

– fill in all ‘forced numbers’ = all cells that can logically only contain one number (isn’t this everyone’s first step?)
– search all rows, colums and boxes to eliminate or determine the possible numbers in the free cells (anyone surprised yet?)
– and then in the really hard sudoku’s you might have to make a random choice and see if it fits or not

That’s all he says…brilliant, right?:)