9855

9855 (nine thousand eight hundred fifty-five) is an odd, composite, four-digit number. The number 9855 is the magic constant of an n × n normal magic square as well as n-Queens Problem for n = 27.[1] It can be expressed as the product of its prime factors:

${\displaystyle 9855=3^{3}\times 5\times 73}$[2]

9855 is also the Magic constant of a Magic square of order 27.[3] In a magic square, the magic constant is the sum of numbers in each row, column, and diagonal, which is the same. For magic squares of order n, the magic constant is given by the formula ${\displaystyle {\frac {n(n^{2}+1)}{2}}}$.[4]

The magic constant 9855[5] for the magic square of order 27 can be calculated[2] as follows:

${\displaystyle 9855={\frac {1}{27}}\sum _{k=1}^{27^{2}}k={\frac {27\times (27^{2}+1)}{2}}}$

This square contains the numbers 1 to 729, with 365 in the center. The square consists of 9 nine power magic squares. It has been noted that the number of days in 27 years (365 days per year) is 9855, the constant of the larger square.[6][2] This was first discovered and solved by ancient Greeks: Aristotle understood this magic square, but it is noted from numeris Platonics nihil obscuris that Cicero was unable to solve it.[2] The 27 years as alluded to by the square was mentioned in reference to Greek generation time.[2]