Latin Squares: For Dummies Lauren Marsh Chaquana Dunton SEARCH

The Beginnings A Latin square is an nxn array, when each member of the array is one of the numbers from 1 to n. Each number being between 1 to n is written once in each row and column. An Orthogonal pair are two Latin squares combined to create one array on the other, each of those pairs (n 2 ) are written once in each row and column. Latin Squares are more than 200 years old It is possible to find a pair of nxn orthogonal Latin squares for every n except 2 and 6. Leonhard Euler introduced Latin squares in 1783 as, a new kind of magic squares. Leonhard Euler believed that there are no orthogonal latin squares for orders 2, 6, 10, 14, and indeed for all orders of the form 4n+2. This Conjecture was later proven false in 1960 by Bose, Shrikhande.

Latin Square Usage  Latin Squares are important in all types of mathematic forms: Experimental Designs Geometry Graph Theory Grouped Multiplication Tables Prime (easy) – Magic Squares 2,3,5,7 In Between – Magic Squares 4=2 2,8=2 3,9=3 2 Impossible or hard - Magic Squares 6,10,12,14

The Impossible 4x *This Latin Square doesn’t have An Orthogonal pair Because The inverse Would Create All Rows Of 2,3,4,and 1’s no matter what order they’re in.*

Latin Squares 4 x 4 Latin Squares Box..1..BottomsBox..2..Tops..Legend.. (4)Navy Blue - Capri’s (4)Hot pink - Black Tee (3)Gray - Skirts (3)Green - No Sleeves (2)Black - Shorts (2)Pink - Short Sleeves (1)Red – Pants (1)Baby Blue - Long Sleeves

Graeco Squares Box..1..Bottoms Box..2..Tops..Legend.. Navy Blue - Capri’s Hot pink - Black Tee Gray - Skirts Green - No Sleeves Black - Shorts Pink - Short Sleeves Red – Pants Baby Blue - Long Sleeves

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