Sudoku Origins

Here's some background to the long and interesting history of the Sudoku puzzle.

The name Sudoku or more correctly comes from Japan and consists of the Japanese characters Su (meaning 'number') and Doku (meaning 'single') but the puzzle itself originates from Switzerland and then travels to Japan by way of America.

Sudoku has its deep roots in ancient number puzzles. For many centuries people have been interested in working out solutions to puzzles. This has been the basis of much of modern mathematics and science.

Magic Squares

A magic square is a puzzle involving the ordering of consecutive numbers into a square (of size at least 3x3) comes to us from the mists of history.

The first known form is the Magic square that is first documented in China two thousand years ago. In this puzzle it is both a numerical and positional problem, as all the rows, columns and diagonal lines through the grid must add up to the same number. Just like in Sudoku a number can only be used once. in the grid. The aim of the puzzle was to try to devise a new ordering of the numbers to complete the puzzle starting from scratch. Solutions were considered to have mystical properties and became entangled in the I Ching (Book of Changes) method of divination.

The 3x3 solution shown is called the Lo Shu diagram. It was considered the gift of the turtle from the River Lo (the turtle had the Chinese pattern enscribed on its back). It was first recorded in print in the first or second century AD. The magic square probably reached Europe from China by way of the arabs who brought news of many of the Chinese inventions with them along the Silk Road. Thabit ibn Qurrah (from the ninth century AD) is credited with introducing the magic square to the Western World.

In Europe the most famous first appearance of the square is in Albrecht Dürer's engraving called 'Melancholia' in 1514 where a 4x4 magic square is clearly shown with an arrangement of the first sixteen numbers gives a sum of 34 in each row, column and diagonal. Any philosopher of the renaissance age would have known and understood the properties of magic squares.

Chinese Puzzle

It is worth mentioning in passing the Chinese Puzzle that may well be familiar to many, it consists of a 9x9 grid of squares with one square missing.

The squares are scrambled and have to be shifted one at a time to form an ascending numerical sequence 1 to 8. The early versions used the digits 1 to 8 with the 9 missing but modern ones use pictures (which comes to the same thing). Like Sudoku it is a matter of finding a strategy of ordering squares in a grid in a particular way.

Swiss Genius

The great mathematician Leonhard Euler is the man chiefly credited with the creation of the puzzle that we now know as Sudoku. Born in Basle,Switzerland in 1707 just after the giant leap forward in mathematics pioneered by Isaac Newton and Gottfried Leibniz, he both consolidated and pioneered mathematical knowledge in many fruitful areas. When he moved from Basle to St Petersburg, Russia, it was to study medicine but by the chance happenings of fate he ended up as the chief mathematician at the St Petersburg Academy, Russia. In 1741 he moved to Germany for 25 years but eventually returned to the Academy in Russia where he died at the grand age of 76. He was totally blind for the last seventeen years of his life.

Euler turned his mind to all sorts of mathematical problems. Amongst other things he is responsible for the symbol pi being denoted by the familiar greek letter π and also i to denote the square root of -1. His pioneering work on imaginary numbersusing his new notation transformed key fields of mathematics.

May be only as a hobby, Euler developed the basics of 'Sudoku' which he termed 'Graeco-Roman Squares' or Latin Squares - he used letters as the grid square symbols rather than numbers. He mused on what would happen if you removed the rule for magic squares that the sum of the diagonals must add up to the same number as the rows and columns and turn it into a puzzle of permutations. His thoughts on the subject were first published in 1782 in Verhandelingen uitgegeven door het zeeuwsch Genootschap der Wetenschappen te Vlissingen 9, Middelburg pp. 85-239. This dissertation was probably first given as a lecture to the Academy on October 17th 1776.

Journey to America

Euler's immense legacy of pioneering research has been much used by mathematicians and scientists ever since but the rather obscure puzzle he created was not taken up by others, not even as a pastime.

It took two centuries before the puzzle was used by Howard Garnesin an American magazine. As in every good story the puzzle took on an extra twist. Instead of requiring just rows and columns to be permutations a new rule was added so that the grid was split into 3x3 regions of 9 squares and these regions must also have only one occurrence of each symbol. This makes it a more challenging problem for people to solve. Howard Garnes called the puzzle 'Number Place' when it was first published by Dell Puzzle Magazines, New York in 1979.

Over the Pacific to Japan

It didn't take that long for the puzzle to move to Japan. Although the Japanese like brain teasers as much as anybody else, it is believed that it is the property of the Japanese language itself that caused Sudoku to undergo its final transformation into a worldwide phenomenon.

The Japanese language is a little tricky for crosswords as it is symbolic rather than phonetic. It is not so easy to devise a grid of crossword letters in the same way as you can in English. So the 'Number Place' puzzle that the Japanese saw in Dell Puzzle Magazine had great potential as a replacement for the familiar crossword puzzle in newspapers and magazines.

The American name 'Number Place' was translated as Suji Wa Dokushin Ni Kagi meaning 'the numbers must occur once only', but was quickly abbreviated to or in Western script Su Doku 'number only' or 'number single'

First introduced in Monthly Nikolist magazine in April 1984 it rapidly became a very popular pastime for the first time.

The Japanese added yet another twist to the Sudoku puzzle too. They imposed the rule that the pattern of revealed squares had to be symmetric and not just random. Although the first computer programme to generate and solve it was developed to in 1989, the best puzzles are still reckoned to be devised by human skill and judgement.

A worldwide phenonemon

The original idea of the puzzle can then be traced from China, through Persia to Europe and then across the Atlantic to New York. It then jumped over to Japan and it is now a great craze in the U.S. and Europe, published in most newspapers and magazines with championships and conventions all over. It's one of the few puzzles that can claim to be truly international by nature. It has no cultural baggage and just needs a logical mind to solve it.

'Sudoku' Characters

If you know the Japanese language you may know that the Su Doku characters are actually ones that originally came from the Chinese language. These two characters have the same meaning in China (number single) but in Mandarin Chinese (pinyin) would be pronounced 'Shu du'. The written version of the characters tells a tale that goes back into the mists of history. The first character Shu is in two parts. The phonetic radical is lou consists of the two characters 'middle' above 'woman' and denotes 'leisure' (meant to represent woman in the middle of nothing). The second part of Shu has 'strike' represented by a hand with a stick. These two parts together represent 'number' perhaps symbolising counting by scratching marks on the ground. The second character is the one for du or 'only'. It again has two parts the first symbol is for a dog and then a phonetic part (shu) which has no especial meaning. These two parts together represent 'only'.

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External References

China and the Magic square

The Arabian connection

Alchemy and Durer

Euler Biography

Original Euler papers on Latin Squares derived from Magic Squares

Dell Magazine pioneer in America

Nikoli magazine

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