# Fermat's Magic Cube

Fermat's Magic Cube

In 1640, Pierre de Fermat sent a letter to Marin Mersenne about an order-4 magic cube with 64 magic sums out of 76 possible. In a perfect magic cube the rows, columns, pillars, space diagonals, and the diagonals of each n×n orthogonal slice sum to the same number. For the order-4 case, numbers 1 to 64 are required. In 1972, Richard Schroeppel proved that a perfect order-4 magic cube was impossible (see Details).

In 2004, Walter Trump found an order-4 cube with eight more lines that summed to 130.