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The Appeal of Sudoku

Why is Sudoku an obsession?

In the winter of 2005, I was in my office early in the morning preparing my classes ahead of me when I got an unexpected call from a reporter at the Associated Press who, having read my book The Puzzle Instinct, wanted to gauge my opinion on a new puzzle craze that was spreading throughout the world-Sudoku. I had to humbly admit that I had never heard of Sudoku. When the reporter explained the puzzle however, it immediately became obvious to me why it would appeal so broadly. Like the crossword puzzle before it, Sudoku has a simple structure, a simple set of rules for solving it, but it still presents a challenge. Unlike the crossword, however, it requires no "external knowledge" (names of people, events, linguistic knowledge, etc.). It just requires us to place symbols (usually the first nine digits) in cells in a logical way.

Why do puzzle crazes like Sudoku occur? Let me suggest something that might, at first thought, seem preposterous. As we all know, life's real puzzles do not have clear-cut solutions (or often any solutions at all). Crosswords and Sudoku puzzles do. The satisfaction that comes from solving a puzzle seems to provide "relief" from the large-scale puzzles inherent in everyday life. This may be a bit of a stretch on my part, but it would seem to explain puzzle crazes. Crosswords, Sudoku, Rubik's Cubes, and Jigsaw puzzles seem to restore within us a sense of order, don't they? They are a powerful form of escapism from the ups and downs of everyday life. To paraphrase a well-known (and very sage) saying-an hour of crosswords or Sudoku a day, keeps the doctor (and everyone else for that matter) away.

Despite its Japanese name, the concept behind Sudoku crystallized in the United States in the form of "Numbers in Place," which appeared for the first time in the May 1979 issue of Dell Pencil Puzzles and Crossword Games magazine. It went virtually unnoticed, except by readers of the magazine. By the way, the late architect Howard Garns is pegged as being its inventor. In 1984, an editor for Nikoli magazines in Japan came across one of the puzzles, changed its name to Sudoku (meaning "only single numbers allowed") and included it in his magazines. Within a year, major Japanese dailies were carrying the increasingly popular puzzle. In 1997, a retired judge from New Zealand, named Wayne Gould, saw a Sudoku puzzle and started making his own. These appeared in 2004 in the Conway Daily Sun of New Hampshire. A few months later Sudoku puzzles started appearing in The Times of London. By early 2005, Sudoku became a craze in Britain, quickly spreading throughout the globe from there, joining crosswords as a permanent feature of puzzle pages in newspapers.

For the sake of historical accuracy, it should be mentioned that number placement puzzles started appearing in newspapers in the latter part of the nineteenth century in Europe, and especially in France. These were not really Sudoku yet, since they could be solved in more than one way. But they had a similar layout. And, of course, there are magic squares, which go back to ancient times in China. Magic squares are number placement puzzles, but are solved by considering the actual value of a number since, in a magic square, the rows, columns, and diagonals must all add up to the same total (known as the magic constant). After being told by the AP reporter what Sudoku was all about, I pointed out to her that the idea can probably be traced back to magic squares or to "Latin Squares," invented by Swiss mathematician Leonhard Euler (1707-1783). A Latin square is a square arrangement of digits placed in such a way that no digit appears twice in the same row or column. Sudoku, I mentioned to the reporter, seems to simply expand upon Euler's invention. It is unclear whether Garns was familiar with either Euler's puzzle or the prototype puzzles carried by the French newspapers in the late nineteenth century. Whatever the case, Garns' number placement puzzle is now considered to be the blueprint for modern-day Sudoku.

There are now websites which contain new puzzles daily, information on how to solve them, general information on sudoku groups and competitions, descriptions of different kinds and styles of sudoku puzzles, downloadable software, and so on and so forth. Sudoku has been featured on American television, in shows such as Numbers and House, among others. There have even been television quiz shows dedicated to Sudoku in Britain and other countries. It is, by any definition of the word, a craze! And like crosswords, it is a beneficial craze, unlike other kinds of fads such as pet rocks. As a matter of fact, the Alzheimer's Association in the United States has endorsed Sudoku as a preventive strategy against the dreaded disease. Their recommendation is based on published studies, which suggest that Sudoku may prevent dementia (at least in part).

Sudoku is a simple puzzle with no tricks or twists built into it. In its usual form, it is made up of a nine-by-nine grid, with heavy lines dividing it into nine three-by-three boxes. The challenge is to fill the layout with the digits from 1 through 9, so that every row, every column, and every three-by-three box contains these digits, without repeating-that is, once and only once. The puzzle-maker provides some of the numbers in the layout, and these are the initial clues to be used in solving the puzzle. How is the level of difficulty determined? I am not sure, really, although the implicit principle seems to be that that the fewer the initial clues given, the harder it is to solve the puzzle. However, in having constructed many of these myself, there seems to be much more to it than that. But I can't quite get a firm grasp on the criteria that mark difficulty levels. Maybe readers of this blog can write to me about it, if they know something concrete. The one below is moderate in difficulty, in my estimation, although determining difficulty level might be more a matter of familiarity with the puzzle than anything else. If someone has never done a Sudoku puzzle, then he or she might find it hard; on the other hand, someone familiar with the puzzle genre might find it too easy.

(Scroll down for answer.) The solution involves logical thinking-deducing where numbers can or cannot be placed. There seem to be two basic logical processes involved, as far as I can see: (1) exclusion ("This number cannot go here because..."), (2) inclusion ("This is the only number that can go here because..."). Sometimes, both are involved in tandem ("When considered together with another number, this number can only occur here..."). Of course, trial-and-error, hypothesis-testing, and the process of elimination all come up in the process of deducing number placement through exclusion and inclusion. And, perhaps, it is the use of such logical strategies that gives Sudoku its appeal. We seem to like this kind of practical logic when it is applied to the solving of mysteries of all kinds, from detective stories to Sudoku. By the way, you can get a very detailed analysis of the logic behind Sudoku in Denis Berthier's The Hidden Logic of Sudoku (published by in 2007). And I should mention that the most comprehensive book on the history and psychology of the puzzle is Fiorella Grossi's The Addict's Guide to Everything Sudoku (Fair Winds, 2007).
Crossword aficionados defend their puzzles as being more interesting, noting that they offer more variety and entail knowledge of the world, as well as knowledge of grammatical and word structure. Defenders of Sudoku respond by saying that their puzzle is an exercise in pure intelligence, independent of external knowledge sources. I straddle the fence on this debate. I like them both for exactly the fact that they are different. But there is something that unites the two genres of puzzle. Both present us with empty cells, which must be filled with letters, numbers, or symbols in a specific way. It seems that we cannot leave the cells empty, once we start solving the puzzles.

So, why do puzzle crazes occur from time to time? I am really not sure why, nor do I think anyone else really is. I have put forward a specific hypothesis here and I would lie to ascertain your response to it. To reiterate, I believe that we need to escape from the realm of daily life, where solutions rarely seem to exist, into an imaginary realm that has definite solutions, where mysteries are deciphered, and where order is restored. Puzzles are, in a word, a form of escapism. Maybe that's why I always used to do puzzles as a teenager when exams were around the corner or today when a deadline is imminent.


The solution to the sudoku puzzle is as follows:

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