Multimagic cube

{{One source|date=October 2011}}

In mathematics, a P-multimagic cube is a magic cube that remains magic even if all its numbers are replaced by their k th powers for 1 ≤ k ≤ P. {{nowrap|2-multimagic}} cubes are called bimagic, {{nowrap|3-multimagic}} cubes are called trimagic, and {{nowrap|4-multimagic}} cubes tetramagic.{{MathWorld|id=MultimagicCube}} A {{nowrap|P-multimagic}} cube is said to be semi-perfect if the k th power cubes are perfect for 1 ≤ k < P, and the P th power cube is semiperfect. If all P of the power cubes are perfect, the {{nowrap|P-multimagic}} cube is said to be perfect.

The first known example of a bimagic cube was given by John Hendricks in 2000; it is a semiperfect cube of order 25 and magic constant 195325. In 2003, C. Bower discovered two semi-perfect bimagic cubes of order 16, and a perfect bimagic cube of order 32.{{MathWorld|title=Bimagic Cube|id=BimagicCube}}

MathWorld reports that only two trimagic cubes are known, discovered by C. Bower in 2003; a semiperfect cube of order 64 and a perfect cube of order 256.{{MathWorld|id=TriMagic|title=Trimagic Cube}} It also reports that he discovered the only two known tetramagic cubes, a semiperfect cube of order 1024, and perfect cube of order 8192.{{MathWorld|title=Tetramagic Cube|id=TetramagicCube}}