Magic squares and cubes
โ Scribed by Schrutka
- Publisher
- Springer Vienna
- Year
- 1909
- Tongue
- English
- Weight
- 68 KB
- Volume
- 20
- Category
- Article
- ISSN
- 0026-9255
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
A general method to construct third-order magic cubes and hypercubes is described. It is shown that magic hypercubes of order 3 must be symmetrical and there are exactly 58 such hypercubes in 4-dimensional space, not counting rotations and reflections.
A multiplicative magic square is a square array of numbers such that the product of the numbers in each row, column or main diagonal is equal to a constant. We give various methods for the construction of multiplicative magic squares with a special interest in those with small product constants.
results for natural fifth order magic squares from exact backtracking calculations we find 652 with m = 2, and four with m = 4. There are also 20,604 singular seventh order natural ultramagic (simultaneously regular and pandiagonal) squares with m = 2, demonstrating that the co-existence of regulari