Editing Multimagic cube (section)

{{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 [[exponentiation|powers]] for 1&thinsp;≤ ''k'' ≤ ''P''. {{nowrap|2-multimagic}} cubes are called '''bimagic''', {{nowrap|3-multimagic}} cubes are called '''trimagic''', and {{nowrap|4-multimagic}} cubes '''tetramagic'''.<ref name=Multi>{{MathWorld|id=MultimagicCube}}</ref>  A {{nowrap|''P''-multimagic}} cube is said to be '''semi-perfect''' if the ''k''th power cubes are [[perfect magic cube|perfect]] for 1&thinsp;≤ ''k'' < ''P'', and the ''P''th power cube is [[semiperfect magic cube|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 magic cube|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.<ref name=Bi>{{MathWorld|title=Bimagic Cube|id=BimagicCube}}</ref>  

[[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.<ref name=Tri>{{MathWorld|id=TriMagic|title=Trimagic Cube}}</ref>  It also reports that he discovered the only two known tetramagic cubes, a semiperfect cube of order 1024, and perfect cube of order 8192.<ref name=Tetra>{{MathWorld|title=Tetramagic Cube|id=TetramagicCube}}</ref>