Definitions

from The American Heritage® Dictionary of the English Language, 4th Edition

  • n. A square that contains numbers arranged in equal rows and columns such that the sum of each row, column, and sometimes diagonal is the same.
  • n. A similar square containing letters in particular arrangements that spell out the same word or words.

from Wiktionary, Creative Commons Attribution/Share-Alike License

  • n. A palindromic square word arrangement, usually in the form of a magic amulet.
  • n. An n-by-n arrangement of n2 numbers such that the numbers in each row, in each column and along both diagonals all have the same sum.

from the GNU version of the Collaborative International Dictionary of English

  • adj. numbers so disposed in parallel and equal rows in the form of a square, that each row, taken vertically, horizontally, or diagonally, shall give the same sum, the same product, or an harmonical series, according as the numbers taken are in arithmetical, geometrical, or harmonical progression.
  • n.

from WordNet 3.0 Copyright 2006 by Princeton University. All rights reserved.

  • n. a square matrix of n rows and columns; the first n^2 integers are arranged in the cells of the matrix in such a way that the sum of any row or column or diagonal is the same

Etymologies

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  • I had to grab my combinatorics text off my bookshelf to refresh my memory. Euler proved that an order 6 Latin square does not exist, and conjectured that it was also true for all odd multiples of 2. It turned out he was wrong about everything except 6.

    January 23, 2008

  • Yes, yes seanahan. That's all well and good. But can you find me a hyper-Graeco-Latin square of order 6?

    I think not.

    Why, I'll bet you can't even make me a Graeco-Latin square of order 6.

    January 22, 2008

  • There's actually some cool combinatorics one can do with these magic squares.

    January 22, 2008

  • A grid where all columns or rows (filled with numbers) add up to the same sum. To construct: draw a 4 X 4 grid and around 2 adjacent sides (i.e., one for rows and one for columns)--but outside the grid--put any numbers you like that add to the sum you wish the magic square to reflect (for instance, numbers 1, 6, 0, 2--for rows-- and 11, 7, 4, and 8--for columns--could be used for a "39" magic square), then put these outside number's row/column sum inside the grid at the appropriate intersection. Once you erase the numbers outside the grid, the magic square is complete!

    Here's more

    January 22, 2008