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For instance, the Lo Shu Square – the unique 3 × 3 magic square – is associative, because each pair of opposite points form a line of the square together with the center point, so the sum of the two opposite points equals the sum of a line minus the value of the center point regardless of which two opposite points are chosen. [4]
The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3. In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.
First multiply the quarters by 47, the result 94 is written into the first workspace. Next, multiply cwt 12*47 = (2 + 10)*47 but don't add up the partial results (94, 470) yet. Likewise multiply 23 by 47 yielding (141, 940). The quarters column is totaled and the result placed in the second workspace (a trivial move in this case).
The magic constant or magic sum of a magic square is the sum of numbers in any row, column, or diagonal of the magic square. For example, the magic square shown below has a magic constant of 15. For a normal magic square of order n – that is, a magic square which contains the numbers 1, 2, ..., n 2 – the magic constant is = +.
A pandiagonal magic square remains pandiagonally magic not only under rotation or reflection, but also if a row or column is moved from one side of the square to the opposite side. As such, an n × n {\displaystyle n\times n} pandiagonal magic square can be regarded as having 8 n 2 {\displaystyle 8n^{2}} orientations.
Latin squares and finite quasigroups are equivalent mathematical objects, although the former has a combinatorial nature while the latter is more algebraic.The listing below will consider the examples of some very small orders, which is the side length of the square, or the number of elements in the equivalent quasigroup.
The numbers are based on a $50 a square game, with a $625 payout for the 1st and 3rd quarters, a $1,250 payout for halftime, and a $2,500 payout for the end of the game.
A magic circle can be derived from one or more magic squares by putting a number at each intersection of a circle and a spoke. Additional spokes can be added by replicating the columns of the magic square. In the example in the figure, the following 4 × 4 most-perfect magic square was copied into the upper part of the magic circle. Each number ...