Latin Puzzles

According to the 2016 namesake article by Miguel G. Palomo, <nowiki/>Latin Puzzles are a generalization of Latin square puzzles and Sudoku regarding board shape, regions, symbols and inscriptions inside the board. This results in new categories of puzzles in addition to the existing ones to which Sudoku belongs.
In what follows we adopt the puzzle-Puzzle naming convention proposed in the mentioned article: puzzle refers to a partially filled board, whereas Puzzle is a set of similar puzzles, as in "a Sudoku puzzle" and "the Sudoku Puzzle" respectively.<nowiki/><nowiki/><nowiki/><nowiki/><nowiki/><nowiki/><nowiki/>
The Latin Square Puzzle
A Latin square of order n is a square arrangement of n x n cells in which every row and every column holds symbols 1 to n. Latin squares are well known objects, so named because 18th century mathematician Leonhard Euler used Latin letters as symbols in his paper De Quadratis Magicis.
We can remove symbols from Latin squares and challenge players to complete the result to the initial Latin square: this is the Latin Square Puzzle.
In 1956, W. U. Behrens introduced what he called Gerechte squares: regular Latin squares with the extra condition that all symbols be also present in each of the n regions with n cells each in which the board was partitioned.
The Sudoku Puzzle
Sudoku is a Puzzle with a square board holding 81 cells and 27 regions (9 rows, 9 columns and 9 3x3 subsquares) of 9 cells each. A set of 9 different symbols (usually numbers 1 to 9) must be placed on every region. A completed Sudoku is both a Latin square and a Gerechte square with each 3x3 subsquare being an additional region.
Sudoku became popular in Japan after the company Nikoli started publishing it in the eighties. It spread to the rest of the world when The Times of London started featuring 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 not based on Latin Squares
After creating Puzzles Moshaiku (2010) and Konseku (2011), Palomo investigated the possibility of a non-square Sudoku of sorts.
This resulted in Latin Puzzles Canario (2012) (inspired by the Pintaderas found in the Spanish Canary Islands), Monthai (2013) (inspired by the namesake Thai pillow) and Douze France (2013). These Puzzles had split regions, a characteristic shared by Tartan (2013) but on a square board. Helios (2013) on its side, had a sparse, star-shaped board that contrasted with the existing compact ones. All of these Puzzles had solutions that were not Latin squares, a departure from Sudoku and many variants thereof.
Latin Puzzles with repeated symbols
In the article Latin Polytopes(2014) a generalization of Latin squares to boards with different topologies and repeated symbols was proposed. Latin Puzzles with symbols repeated, like Sudoku Ripeto (2014), appeared afterwards. This was a departure from their uniqueness in Sudoku.<ref name=":12" />
Latin Puzzles with inscriptions
Repeated symbols opened the door to puzzles with inscriptions: the possibility of including generic words inside the board in any language and alphabet,<ref name=":12" /> like Custom Sudoku (2014) and Custom Quadoku (2014).

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