How rare are magic squares? So far, the exact number of magic squares of order n is only known for n ≤ 5. For larger squares, we need statistical approaches for estimating the number. For this purpose, we formulated the problem as a combinatorial optimization problem and applied the Multicanonical Monte Carlo method (MMC), which has been developed in the field of computational statistical physi...

Introduction There is no known general formula to calculate the total number of magic squares of a given order. However, using various methods, the number of magic squares has been calculated for orders smaller than 6. In this work we describe an approach to bounding the computational complexity of enumerating order-6 squares and provide a related method to approximate the number of such square...