Most Perfect Magic Square 64 Math Puzzle

$24.00

Can you arrange the blocks such that every row, column and main diagonals add to the same number?   Many fascinating math qualities can be explored with this puzzle and are illuminated in the instructions below.  The Video will provide this same information.

In recreational mathematics, a magic square is an arrangement of integers in a square grid where each number is used only once. The numbers in each row, each column, and the numbers in the two main diagonals all add up to the same number.   A magic square has the same number of rows as it has columns, and in conventional math notation, "n" stands for the number of rows (and columns) it has.  Thus, a magic square always contains n squared (n x n)  numbers, and its size (the number of rows [and columns] it has) is described as being "of order n".   A magic square that contains the integers from 1 to n squared is called a normal magic square.  Normal magic squares of all sizes can be constructed as long as n>2. 

In this puzzle, n=8 as there are 8 numbers on each row and column.  The digits 1 to 64 are used.

The number constant that is the sum of every row, column and diagonal is called the Magic Sum, M.   Every normal magic square has a constant dependent on n, calculated by the formula M = [n(n x n + 1)] / 2.

Thus, for the case of our n=8 magic square, M= 260.   That is, every row, column and diagonal must sum to 260.

This particular magic square is called a “Most Perfect Magic Square” because it has certain qualities:

-Every 2 x 2 block of cells (including wrap-around) sum to 2T (where T= n x n + 1) or in this case T =65  and 2T = 130

-Any pair of integers distant ½ n along a diagonal sum to T.   That is, if you select a number and mover 4 places along a connected diagonal, the sume of the original number and the number you land on will equal 65

-It is a doubly-even pandiagonal normal magic square using integers from 1 to 64.  A pandiagonal magic square is a magic square with the additional property that the broken diagonals, i.e. the diagonals that wrap round at the edges of the square, also add up to the magic constant. (260 in this case)

There are a number of other variations of magic squares dependent on certain qualities of the square. Examples are Panmagic, Multimagic, Semi-magic, Multiplicative magic and others.  We leave it to the reader to research these things. 

Magic squares have a long history, dating back to 650 BC in China. At various times they have acquired magical or mythical significance, and have appeared as symbols in works of art. We encourage you to do added research on this fascinating topic.

Puzzle comes packed unsolved, but doescome with written solution.  Made USA by CreativeCrafthouse

 


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  • Model: Perfect Square 64
  • Shipping Weight: 0.95lbs
  • Manufactured by: Creative Crafthouse


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