# Category: Latin Squares

December 10 2015

## Introduction to Latin Squares

A Latin Square is an array of symbols, (usually numbers) in a Square grid, where the symbols are arranged in such a way that each symbol occurs exactly once in each row and exactly once in each column. One of[…]

December 11 2015

## Latin Square Orders

Let’s review the different layouts of Latin Squares: 1 x 1    Solitary Square 2 x 2    There are two arrangements in one combination 3 x 3    There are 12 arrangements in three combinations, (middle number changes) 4 x 4   […]

December 12 2015

## Latin Squares and the Elements

Latin Squares of order 4 x 4 can be connected to the elements if we designate each of the four digits in a 4 x 4 Latin Square with an element, using their colour characteristics. If we set each of[…]

December 14 2015

## Latin Squares and the Planets

Each of these combinations will now be identified with a Ruling Planet. Challenge Using all seven Latin Square combinations, determine how many Latin Squares of the Elements there are? Click to reveal the solution.. Solution There are 12 combinations of[…]

December 15 2015

## Latin Squares and Magic Squares

One particular Latin Square can generate a Magic Square. Take a look at the numeric Latin Square of the Moon: Moon   Each primary number in an even-ordered square has a root number. For an order-4 square, the primary numbers[…]

December 16 2015

## Graeco Latin Squares

Graeco Latin Squares are also referred to as Orthogonal Squares, in that each cell is comprised of two sets of symbols, each in a different Latin Square arrangement. Consider the Order 3 Latin Square below: If we then apply a[…]

December 17 2015

## Magic Mappings

A Magic Mapping occurs when we map any Latin Square across any Magic Square. Consider the following Latin Square: And the following Magic Square: This Latin Square can be magically mapped by firstly identifying which Latin value corresponds to which[…]

December 18 2015

## Diabolic Magic Squares

A Diabolic Magic Square has the additional property of the magic sum along each of its broken diagonals. The Chautisa Yantra Magic Square drawn below, introduced during the tenth century, is an example of a Diabolic, (also referred to as[…]

December 19 2015

## Constructing a Diabolic Magic Square

Curiously, we can construct a Diabolic Magic Square from an unusual source, a Graeco Latin Square! Consider a 4 x 4 Square grid containing numbers in consecutive order. If we label the rows as A, B, C & D, and[…]

December 21 2015

## Diabolic Mappings

Sun & Moon Sun & Moon Convert this to a numeric Latin Square: The primary diabolic mapping does not generate a Latin Square, but it does have the values in either a Square arrangement or in across an entire row[…]

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