Latin square

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Related to Latin squares: Orthogonal latin squares

La·tin square

(la'tin sqwār),
A statistical design for experiments that removes from experimental error the variation from two sources that may be identified with the rows and columns of a square. The allocation of experimental treatments is such that each treatment occurs exactly once in each row and column. For example, a design for a 5 × 5 square is as follows:
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References in periodicals archive ?
1 2 3 2 1 3 3 2 1 2 3 1 3 2 1 1 2 3 3 1 2 1 3 2 3 1 2 Latin Squares of Order (n) constructed by creating a row of n distinct symbols.
Let [N.sub.1] and [N.sub.2] be 2 Latin Squares with Order (n).
Mullen, Discrete Mathematics Using Latin Squares, John Wiley Ans Sons, Inc., 1998, 305.
A Latin Square of order n is an n by n array containing symbols from some alphabet of size n, arrenged so that each symbol appears exactly once in each row and exactly once in each column.
For a fixed n, all n x n Latin squares have the same mean squared errors (MSE) and are, therefore, equally efficient.
It is known that for a given n, all n x n Latin squares have the same [R.sub.2] value.
Discuss this Latin square with your students, noting that other arrangements are possible.
Back to Sudoku, which has an extra constraint compared with a regular 9x9 Latin square. Each of the nine non-overlapping 3x3 sub-grids along the edges and in the centre of the larger grid must also contain the digits 1 to 9 without repetition.
The number of treatments determines the size of the Latin square. The data are represented by [X.sub.ij(k)] and are [r.sup.2] in number for a Latin square of r rows and r columns.
Smarandache Mukti-squares Two Smarandache Mukti-Squares are said to be orthogonal if the Latin squares contained in them are orthogonal.
Write or email me with your solution to the Latin Square puzzle.
The Latin square problem can be extended by making each set of 1 to N counters a different colour.