What Do You Know About Magic Hypercubes?

1. Which of the following is a variation of magic hypercubes?

Faulhaber magic hypercubes

Nasik magic hypercubes

Marian magic hypercubes

Planck magic hypercubes

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.

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.

2. Which of the following is denoted as the magic constant in magic hypercubes?

Mk(n)+2

Mk(n)+1

Mk(n)

Mk(n)-1

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).

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).

3. 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.'

Marian Trenkler

John Hendricks

James Stoner

Kathleen Ollerenshaw

not-available-via-ai

Explanation

not-available-via-ai

4. What is the directions within the hypercube called?

Pathfinders

Digit changing

Reflection

Aspect

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.

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.

5. 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'?

C. Planck

Marian Trenkler

Samuel Walker

J. R. Hendricks

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.

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.

6. Which procedure is used when calculating the sum for p-multimagic hypercubes?

Faulhaber's formula and divide it by mn-1

Faulhaber's formula and divide it by mn-2

Faulhaber's formula and divide it by mn+1

Faulhaber's formula and divide it by mn+2

When calculating the sum for p-multimagic hypercubes, Faulhaber's formula is used. The sum is then divided 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.

7. Which formula denotes the Latin prescription construction—modular equations?

LP = ( ∑n-2 LP x + LP ) % m

LP = ( ∑n+2 LP x + LP ) % m

LP = ( ∑n+1 LP x + LP ) % m

LP = ( ∑n-1 LP x + LP ) % m

not-available-via-ai

Explanation

not-available-via-ai

8. What is the formula of Aspectical variants?

NH~R perm(0..n+2); R = ∑n-1 ((reflect(k)) ? 2k : 0) ; perm(0..n-1) a permutation of 0..n-1

NH~R perm(0..n+1); R = ∑n-1 ((reflect(k)) ? 2k : 0) ; perm(0..n-1) a permutation of 0..n-1

NH~R perm(0..n-1); R = ∑n-1 ((reflect(k)) ? 2k : 0) ; perm(0..n-1) a permutation of 0..n-1

NH~R perm(0..n-2); R = ∑n-1 ((reflect(k)) ? 2k : 0) ; perm(0..n-1) a permutation of 0..n-1

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.

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.

9. What is described as the change of [i] into [perm(i)] alongside the given "axial"-direction?

Monogonal permutation

Digitchanging

Component permutation

KnightJump construction

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.

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.

10. Which procedure makes use of the isomorphism of every hypercube that changes the hypercube?

Dynamic numbering

Monogonal permutation

Digitchanging

Pathfinders

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.

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.