Euler is frequently cited as the source of the puzzle, but examples of Latin Squares were engraved in ancient architecture as numerological talismans. Euler made no changes to their rules. Arabic numerologists had already compiled an exhaustive list of order 3 through order 9 Greco-Latin Squares in the Jabirean Corpus by 990 AD.
The modern puzzle Sudoku was invented in Indianapolis in 1979 by Howard Garns. Garns contributed his puzzles to Dell Magazines, which published them under the moniker "Number Place". Interest in Sudoku surged from a revival in Japan in 1986, when puzzle publisher Nikoli discovered the game in older Dell publications, and republished the format leading to widespread international popularity in 2005.
The numerals in Sudoku puzzles are used for convenience; arithmetic relationships between numerals are irrelevant. Any set of distinct symbols will do; letters, shapes, or colours may be used without altering the rules. In fact, ESPN published Sudoku puzzles substituting the positions on a baseball field for the numbers 1-9. Dell Magazines, the puzzle's originator, has been using numerals for Number Place in its magazines since they first published it in 1979.
The attraction of the puzzle is that the rules are simple, yet the line of reasoning required to solve the puzzle may be complex. The level of difficulty can be selected to suit the audience. The puzzles are often available free from published sources and may be custom-made using software.