Multimagic squares records

(*) In his book published in 1976, William Benson points out that he built this 32nd-order trimagic square as far back as 1949.
(**) Another tetramagic square of order 256 was constructed nearly simulteanously by two Chinese, Wu Shuoxin et Gao Zhiyuan. Information announced February 24th 2003 by Gao Zhiyuan. See his site.

    Magic square is a typical difficult NPC problem, its calculation complexity increases sharply when order n increasing, there are some questions that can not be solved completely even the order smaller than 10.

    The table above only lists the same order multimagic square which is first discovered.

To construct a multimagic square, we can use the methods as follows:

1. Arranging the multimagic squares ingeniously by the methods of combinatorics.

  2. Using the searching algorithm to find the multimagic squares by computer.

   The order of the multimagic squares produced by the former method is big, like trimagic squares or above, their orders are all above 32. The latter is affected by the speed of the computer greatly：The order increases 1 every time, then the difficulty would increase thousand times. It is extremely difficult to find a 13^th or higher multimagic square at present.

   Therefore, all the 12^th to 31^st multimagic squares are difficult problems. In this region, there are only the 12^th trimagic square discovered by Walter Trump (German), and the 16^th and the 24^th discovered by Chen Qinwu, Chen Mutian (Shantou University, China).

If you have the following inventive multimagic square which hasn’t been published, welcome to mail this Magic square website for publication:

1) 13^th to 31^st trimagic squares

2) 13^th to 31^st bimagic squares, but the same order trimagic squares of which doesn’t exist or hasn’t been published.

3) Magic squares with 4 or higher power, but smaller order than the “Multimagic square records” above.