## Magic Cube

A magic cube is the 3-dimensional equivalent of a magic square. It consists of integers arranged in a

*n*x

*n*x

*n*pattern such that the sum of numbers on each row, column, pillar, in addition to four main space diagonals equal the same number.

This number is referred to as the magic constant of the cube denoted by

*M*(

*n*). It can be shown that if a magic cube consists of the numbers 1, 2, ...,

*n*³, then it has magic constant equal to:

An example of a 3 x 3 x 3 magic square is presented in the table below.

It is important to note the slices do not constitute a magic squares and the magic sum of the above magic cube equals 42.

Top Slice | ||

8 | 24 | 10 |

12 | 7 | 23 |

22 | 11 | 9 |

Middle Slice | ||

15 | 1 | 26 |

25 | 14 | 3 |

2 | 27 | 13 |

Bottom Slice | ||

19 | 17 | 6 |

5 | 21 | 16 |

18 | 4 | 20 |

It is important to note the slices do not constitute a magic squares and the magic sum of the above magic cube equals 42.

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