Pentamagic square, 729th-order

Li Wen (Meishan, Sichuan, China 1966 - )

The Chinese Li Wen, graduated from the University of Science and Technology of Peking in 1986, has constructed in June 2003 a pentamagic square of order 729 that we have immediately checked. Li Wen has enjoyed constructing magic squares since the age of 7, and multimagic squares (and cubes) since the age of 25.

In order to construct his pentamagic square, he used Microsoft Visual Basic 6, with his own multiprecision routines. The multimagic sums of his square are :

• S1 = 193709880
• S2 = 68630183654760
• S3 = 27354644337408897600
• S4 = 11629892691182076559263288
• S5 = 5150496655615858452428359636800

• Download the pentamagic square 729 (zipped ASCII file of 1,8Mb)

It is interesting to notice that this square is of order 3ⁿ (729 = 3⁶), compared to the other big multimagic squares which are of order 2ⁿ.

It is currently the smallest known normal pentamagic square, normal = using consecutive integers. Later, Li Wen has constructed smaller pentamagic squares, but non-normal = using distinct but non consecutive integers:

• in August 2008, a pentamagic square of order 36, this square being the smallest known non-normal pentamagic square
• in February 2009, a pentamagic square of order 396, this square being also a pandiagonal trimagic square

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