The Largest Magic Square

A magic square is a quadratic scheme of numbers which adds up vertically, horizontally and diagonally to the same sum.

Example: (sum is 15 for each row, column and diagonal)

There is no such thing like a record for finding the world's largest magic square. There are well-known algorithms for constructing an arbitrarily large magic square. Therefore, it is easy to compute very large magic squares. However, the records in this list are for printing or writing magic squares.

Interesting records for multi-magic squares (not only the sum of the numbers but also the sum of their squares, cubes, etc. must be the same) can be found at www.multimagie.com.

The Games and Puzzles Journal and the web site magictour.free.fr list interesting Magic Knight Tour records.

The Rules

• The magic square must be written/printed on paper. It is not sufficient just to calculate it by a computer.
• It is allowed to compose the magic square from many sheets of paper, but they MUST lay together to form one scheme of numbers. This scheme must be a square, not just any rectangle.
• To verify the sums in each row/column and diagonal a test run of the used computer program should be made under supervision of a computer/ mathematics specialist who can prove that the program is correct.

The World Recordss

 105 x  105 Richard Suntag (Pomona, USA)                    1975
 501 x  501 Gerolf Lenz (Wuppertal, Germany)                1979
 897 x  897 Frank Tast & Uli Schmidt
            (Pforzheim, Germany)                            1987
1000 x 1000 Christian Schaller (Munich, Germany)            1988
2001 x 2001 Sven Paulus, Ralph Bülling, Jörg Sutter
            (Pforzheim, Germany)                            1989
2121 x 2121 Ralf Laue (Leipzig, Germany)                    1991
3001 x 3001 Louis Caya (Sainte-Foy, Canada)                 1994
3559 x 3559 Peter Weber & Tassilo Herbig (Zittau, Germany)  2012

Largest Magic Square Written by Hand

1111 x 1111 Norbert Behnke (Krefeld, Germany)               1990

Most Magic Squares Written by Hand

Harimohan Singh Aithani (India) has written 25,000 magic squares (size 3x3 to 20x20) by hand from 2009 to 2014. The written paper sheets were bound into a book weighing 13 kilograms.