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Latin Squares: For Dummies

Latin Squares: For Dummies. Lauren Marsh Chaquana Dunton 7.22.05 SEARCH. 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.

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Latin Squares: For Dummies

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  1. Latin Squares:For Dummies Lauren Marsh Chaquana Dunton 7.22.05 SEARCH

  2. 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 (n2) 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. The Beginnings

  3. 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 2,3,5,7In Between – Magic Squares 4=22,8=23,9=32 Impossible or hard - Magic Squares 6,10,12,14

  4. 3 4 1 3 4 2 1 1 3 4 2 The Impossible 4x4 *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.* 1 2 3 4 2

  5. Latin Squares 4x4 Latin Squares Box..1..Bottoms Box..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

  6. Graeco Squares • ..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 Box..2..Tops Box..1..Bottoms

  7. !!Fun Websites!! • http://www.grogono.com/magic/makeyourown4.php • www.Sudoku.com

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