# Multimagic Squares

@article{Derksen2007MultimagicS, title={Multimagic Squares}, author={Harm Derksen and Christian Eggermont and Arno van den Essen}, journal={The American Mathematical Monthly}, year={2007}, volume={114}, pages={703 - 713} }

In this paper we give the first method for constructing n-multimagic squares (and hypercubes) for any n. We give an explicit formula in the case of squares and an effective existence proof in the higher dimensional case. Finally we prove that n-multimagic squares do not exist for certain orders.

#### Topics from this paper

#### 22 Citations

A generalization of product construction of multimagic squares

- Mathematics
- 2015

In this paper, constructions of multimagic squares are investigated. Diagonal Latin squares and Kronecker products are used to get some constructions of multimagic squares. Consequently, some new… Expand

A family of multimagic squares based on large sets of orthogonal arrays

- Mathematics
- 2016

Large set of orthogonal arrays (LOA) were introduced by D. R. Stinson, and it is also used to construct multimagic squares recently. In this paper, multimagic squares based on strong double LOA are… Expand

Multimagic rectangles based on large sets of orthogonal arrays

- Computer Science, Mathematics
- Discret. Math.
- 2013

Large sets of orthogonal arrays (LOAs) used to construct resilient functions and zigzag functions by Stinson are applied in constructing multimagic rectangles. Expand

Existence of normal bimagic squares

- Mathematics, Computer Science
- Discret. Math.
- 2012

It is shown that a normal bimagic square of order m n exists for all positive integers m, n such that m , n ∉ { 2, 3, 6 } and m ≡ n ( mod 2 ) , and a normalbimagicsquare of order 4 m exists if and only if m ≥ 2. Expand

Large Sets of Orthogonal Arrays and Multimagic Squares

- Mathematics
- 2013

Large sets of orthogonal arrays (LOA) have been used to construct resilient functions and zigzag functions by D. R. Stinson. In this paper, a special kind of LOA, strong double large sets of… Expand

A construction for doubly pandiagonal magic squares

- Computer Science, Mathematics
- Discret. Math.
- 2012

A doubly magic rectangle is introduced to construct a doubly pandiagonal magic square and an answer to problem 22 of [G. Abe, Unsolved problems on magic squares, Discrete Math 127 (1994) 3] is given. Expand

Gaston Tarry and multimagic squares

- Mathematics
- The Mathematical Gazette
- 2011

It is well known that G. Tarry [1] was the first to publish a proof that the famous thirty-six officers problem posed by L. Euler [2] in 1779 has no solution but it appears to be less well known that… Expand

Powers of doubly-affine integer square matrices with one non-zero eigenvalue

- Mathematics
- 2017

When doubly-affine matrices such as Latin and magic squares with a single non-zero eigenvalue are powered up they become constant matrices after a few steps. The process of compounding squares of… Expand

Commuting Magic Square Matrices

- Mathematics
- 2020

We review a known method of compounding two magic square matrices of order m and n with the all-ones matrix to form two magic square matrices of order mn. We show that these compounded matrices… Expand

Bimagic Squares of Bimagic Squares and an Open Problem

- Mathematics
- 2011

In this paper we have produced different kinds of bimagic squares based on bimagic squares of order 8x8, 16x16, 25x25, 49x49, etc. A different technique is applied to produce bimagic square of order… Expand

#### References

SHOWING 1-10 OF 25 REFERENCES

Unsolved problems on magic squares

- Computer Science, Mathematics
- Discret. Math.
- 1994

This paper collects 23 unsolved problems or conjectures on magic squares, and some updated results related to these problems are mentioned. Expand

Most-perfect Pandiagonal Magic Squares: Their Construction and Enumeration

- Mathematics
- 1998

Their construction and enumeration by Kathleen Ollerenshaw and David Brée. This book gives a method of construction and enumeration of all pandiagonal magic squares of a class known as… Expand

The Lost Squares of Dr. Franklin: Ben Franklin's Missing Squares and the Secret of the Magic Circle

- Mathematics, Computer Science
- Am. Math. Mon.
- 2001

Franklin's squares still appear today in popular mathematics books such as Theoni Pappas's Joy of Mathematics and Jan Gullberg's encyclopedic Mathematics: From the Birth of Numbers. Expand

Mathematical Recreations and Essays

- History
- Nature
- 1905

THIS edition differs from the third by containing chapters on the history of the mathematical tripos at Cambridge, Mersenne's numbers, and cryptography and ciphers, besides descriptions of some… Expand

MASTER’S THESIS

- 2004

Web mediated communications revolutionized traditional social interactions. It is designed to facilitate information exchange between individuals and to enable people to connect with friends, family,… Expand

How Many Squares Are There, Mr. Franklin?: Constructing and Enumerating Franklin Squares

- Mathematics, Computer Science
- Am. Math. Mon.
- 2004

Story of the smallest trimagic square (January 2003), available at http://www.multimagie. com/English/Tri12story.htm

- 2003