1.
Which of the following is denoted as the magic constant in magic hypercubes?
Correct Answer
C. Mk(n)
Explanation
In magic hypercubes, the magic constant is denoted as Mk(n). The magic constant represents the sum of each row, column, and diagonal in the hypercube, which remains constant regardless of the size of the hypercube. Therefore, the correct answer is Mk(n).
2.
Out of all the theorems used in hypercube, who proved the one below?
'A p-dimensional magic hypercube of order n exists if and only if p > 1 and n is different from 2 or p = 1.'
Correct Answer
A. Marian Trenkler
3.
What is the directions within the hypercube called?
Correct Answer
A. Pathfinders
Explanation
In a hypercube, the directions are referred to as "pathfinders" because they represent the different paths or routes that can be taken within the hypercube. Each direction in a hypercube corresponds to a different path or route, and these paths are often used in various mathematical and computational applications.
4.
What is the formula of Aspectical variants?
Correct Answer
D. NH~R perm(0..n-2); R = ∑n-1 ((reflect(k)) ? 2k : 0) ; perm(0..n-1) a permutation of 0..n-1
Explanation
The formula for Aspectical variants is nH~R perm(0..n-2); R = ∑n-1 ((reflect(k)) ? 2k : 0) ; perm(0..n-1) a permutation of 0..n-1. This means that the formula calculates the number of aspectical variants, which are permutations of 0 to n-1 with a certain reflection property. The value of R is determined by summing up the expression ((reflect(k)) ? 2k : 0) for each value of k from 0 to n-1. The correct answer is nH~R perm(0..n-2) because it correctly represents the formula for aspectical variants.
5.
What is described as the change of [i] into [perm(i)] alongside the given "axial"-direction?
Correct Answer
A. Monogonal permutation
Explanation
Monogonal permutation is described as the change of [i] into [perm(i)] alongside the given "axial"-direction. This suggests that there is a transformation happening where each value [i] is being replaced by its permutation [perm(i)] in a specific direction. The term "monogonal" implies that this transformation is happening in a specific geometric direction, possibly orthogonal or perpendicular to the axial direction. Therefore, the correct answer is monogonal permutation.
6.
Which formula denotes the Latin prescription construction—modular equations?
Correct Answer
D. LP = ( ∑n-1 LP x + LP ) % m
7.
Which procedure makes use of the isomorphism of every hypercube that changes the hypercube?
Correct Answer
A. Dynamic numbering
Explanation
Dynamic numbering is a procedure that makes use of the isomorphism of every hypercube to change the hypercube. Isomorphism refers to the property of two objects being structurally identical despite their different appearances. In the case of hypercubes, dynamic numbering uses this property to transform one hypercube into another by assigning new numbers to its vertices while preserving the relationships between them. This procedure allows for efficient manipulation and transformation of hypercubes in various applications.
8.
Who proved the theorem that 'a p-dimensional magic hypercube of order n exists if and only if p > 1 and n is different from 2 or p = 1'?
Correct Answer
B. Marian Trenkler
Explanation
Marian Trenkler proved the theorem that a p-dimensional magic hypercube of order n exists if and only if p > 1 and n is different from 2 or p = 1.
9.
Which procedure is used when calculating the sum for p-multimagic hypercubes?
Correct Answer
A. Faulhaber's formula and divide it by mn-1
Explanation
When calculating the sum for p-multimagic hypercubes, Faulhaber's formula is used. The sum is then divided by mn-1.
10.
Which of the following is a variation of magic hypercubes?
Correct Answer
B. Nasik magic hypercubes
Explanation
Nasik magic hypercubes are a variation of magic hypercubes. While Faulhaber, Marian, and Planck magic hypercubes are not mentioned or known variations of magic hypercubes, Nasik magic hypercubes are a well-known variation.