Both Sudoku Ripeto and Custom Sudoku are examples of
Frequency Puzzles, which generalize classical Sudoku with different board shapes, repeated numbers and repeated letters.
The Latin Square Puzzle
A
Latin square of order n is an arrangement of n x n cells in which every row and every column holds numbers 1 to n –other symbols may be used provided they are all different.
Latin squares are well known objects and the base of Sudoku. They are so named because 18th century Swiss mathematician
Leonhard Euler used Latin letters as symbols in his paper
De Quadratis Magicis. Latin squares have a long and rich history. They are mentioned in relation to magic squares as early as the 17th century, although they seem to have been used much earlier in amulets.
We can remove symbols from a Latin square to obtain a partial square that is completable to just the original one. The challenge to complete this partial square is an instance of the Latin Square Puzzle. There are many other puzzles with additional arithmetic or geometric constraints whose solutions are also Latin squares.
French newspapers featured puzzles very similar to Sudoku in the 19th century.
The Sudoku Puzzle
Sudoku is played on a square board holding 81 cells and 27 regions (9 rows, 9 columns and 9 3x3 subsquares) with 9 cells each. A set of 9 different symbols (usually numbers 1 to 9) must be placed on every region. A completed Sudoku is clearly a Latin square.
Sudoku first became popular in Japan, after the company Nikoli started publishing it in the eighties. It spread later to the rest of the world after The Times of London featured it in 2004. It was later discovered by Will Shortz –the crossword puzzle editor for The New York Times– that the Puzzle's author was actually American architect
Howard Garns, whose puzzles first appeared in the Dell Pencil Puzzles and Word Games magazine in 1979 with the name
Number Place.
Latin Puzzles: puzzles with symbols that do not repeat
After creating puzzles
Moshaiku (2010) and
Konseku (2011) Spanish engineer and songwriter Miguel G. Palomo investigated the possibility of using triangular and hexagonal boards for puzzles similar to Sudoku. This first such puzzles were
Canario (2012) –inspired by the
Pintaderas found in the Spanish
Canary Islands–,
Monthai (2013) –inspired by the namesake Thai pillow– and
Douze France (2013). The puzzles had split regions, a characteristic shared by
Tartan (2013) on a square board.
Helios (2013) on the other hand had a star-shaped board. The main characteristic shared by these puzzles was that their solutions were not
Latin squares.
In his articles
Latin Polytopes (2014) and
Latin Puzzles (2016), Palomo formalized some ideas on board shape, and proposed a generalization for both Latin squares and the Latin square Puzzle. These articles contained new puzzles with tetrahedral, cubic, octahedral, dodecahedral and icosahedral boards among others, that were later presented in lectures about
Latin polytopes and the
evolution of Sudoku.
Frequency Puzzles: puzzles with repeated symbols
Frequency squares generalize Latin squares in the sense that numbers may repeat in each row and column. Inspired by them, later experiments in 2014 produced puzzles with symbols repeated, like
Sudoku Ripeto (played with numbers) and
Custom Sudoku (with letters that may form words in the board). They marked yet another departure from Sudoku.
