Estimates of the number of magic squares, cubes, ... (hypercubes) |
E-Number of a magic hypercube |
Dimension: n Order: m |
W = m^{n}! | normal number hypercubes |
A = n! · 2^{n} | aspects of hypercubes |
p = N_{n}(m) / c(m, m^{n}) | probability of the first magic line |
u_{sm} = m^{n} - (m - 1)^{n} - 1 | unforced magic lines in a semi-magic hypercube. |
u_{m} = m^{n} - (m - 1)^{n} - 1 + 2^{n-1} | unforced magic lines in a regular magic hypercube. |
E = m^{n}! · p^{u} / A | with | p = N_{n}(m) / c(m, m^{n}) | and | A = n! · 2^{n} |
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