Devil's Square
The game commences with the board vacant of counters.
Alternate Names
Teufelsquadrat, Latin Square
No. of Players
One
Equipment
A 5x5 square grid and five each of five different colored counters are required for play.
History
The invention of this game is sometimes credited to the mathematician Leonard Euler, who extensively researched the concept of Latin Squares (discussed below).
Objective
The goal is to place all of the counters in cells on the board so that no counters of the same color are in the same row, column or "diagonal". The completed board is completely filled. The given rules printed for this game are often vague as to what is meant by "diagonal". Presumably, no two counters of the same color are allowed on the two diagonals of five cells that cross the center cell. However, a more strict interpretation of this rule would not allow any two counters of the same color along any diagonal of two or more cells. Following the latter interpretation the puzzle can be very difficult, but not impossible.
Play
Counters are simply placed on the board within the cells.
Strategy
Shown at left is one version of a completed Devil’s Square.
One Way to Complete a Devil's Square
Variations
It is important to note that many games are designed to be played with the counters place. This game truly lies at a symbolic doorway between board games and recreational mathematics. The concept is also used in experimental design and various artwork. Devil’s Square is largely a game adaptation of a mathematical concept known as a Latin Square. A Latin Square is an n x n array filled with n different symbols, with each occurring exactly once in each row and once in each column. Latin Squares were researched extensively by the mathematician Leonhard Euler (1707 – 1783), who first named them such.
Magic Squares are another related concept from recreational mathematics. A magic square is an arrangement of distinct numbers (i.e. each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the forward and backward main diagonals, all add up to the same number. A magic square has the same number of rows as it has columns, and in conventional math notation, "n" stands for the number of rows (and columns) it has. Thus, a magic square always contains n2 numbers, and its size (the number of rows [and columns] it has) is described as being "of order n"
See also Sudoku, Kakuro, Kenken, Eight Queens Puzzle, Kamisado
Sources
A simple 3 x 3 Latin Square using alphabet characters.
A design of a 7 x 7 Latin Square of colored tiles can often be found incorporated into art or architecture of temples and schools.
