Search results
Results from the WOW.Com Content Network
The sum of any two magic squares of the same order by matrix addition is a magic square. A magic square remains magic when all of its numbers undergo the same linear transformation (i.e., a function of the form f(x) = m x + b). For example, a magic square remains magic when its numbers are multiplied by any constant. [69]
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 = +.
An associative magic square is a magic square for which each pair of numbers symmetrically opposite to the center sum up to the same value. For an n × n square, filled with the numbers from 1 to n 2 , this common sum must equal n 2 + 1.
For example the following sequence can be used to form an order 3 magic square according to the Siamese method (9 boxes): 5, 10, 15, 20, 25, 30, 35, 40, 45 (the magic sum gives 75, for all rows, columns and diagonals). The magic sum in these cases will be the sum of the arithmetic progression used divided by the order of the magic square.
Consequently, all 4 × 4 pandiagonal magic squares that are associative must have duplicate cells. All 4 × 4 pandiagonal magic squares using numbers 1-16 without duplicates are obtained by letting a equal 1; letting b, c, d, and e equal 1, 2, 4, and 8 in some order; and applying some translation.
The game is won by the player who has said three numbers whose sum is 15. [ 26 ] [ 28 ] If all the numbers are used and no one gets three numbers that add up to 15 then the game is a draw. [ 26 ] Plotting these numbers on a 3×3 magic square shows that the game exactly corresponds with tic-tac-toe, since three numbers will be arranged in a ...
A most-perfect magic square of order n is a magic square containing the numbers 1 to n 2 with two additional properties: Each 2 × 2 subsquare sums to 2s, where s = n 2 + 1. All pairs of integers distant n/2 along a (major) diagonal sum to s.
An example of a 3 × 3 × 3 magic cube. In this example, no slice is a magic square. In this case, the cube is classed as a simple magic cube.. In mathematics, a magic cube is the 3-dimensional equivalent of a magic square, that is, a collection of integers arranged in an n × n × n pattern such that the sums of the numbers on each row, on each column, on each pillar and on each of the four ...