Related papers: On the Construction of Even Order Magic Squares
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 families of compound multimagic squares are…
The problem of the construction of magic squares occupied many mathematicians of the 17th century. The Polish Jesuit and polymath Adam Adamandy Kocha\'nski studied this subject too, and in 1686 he published a paper in Acta Eruditorum titled…
An additive-multiplicative magic square is a square grid of numbers whose rows, columns, and long diagonals all have the same sum (called the magic sum) and the same product (called the magic product). There are numerous open problems about…
We describe a generalization of most-perfect magic squares, called type-p most-perfect squares, and in prime-power orders we give a linear construction of these squares reminiscent of de la Loubere's classical magic square construction…
Several specific Franklin squares and magic squares are decomposed into their quotient and remainder squares. The results support the conjecture that Franklin used the Eulerian composition method to construct many of his squares. This…
We give a short proof -- not relying on ideal classes or the geometry of numbers -- of a known criterion for quadratic orders to possess unique factorization.
A construction of the magic square, and hence of exceptional Lie algebras, is carried out using trialities rather than division algebras. By way of preparation, a comprehensive discussion of trialities is given, incorporating a number of…
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 orders m and n can then be used to generate…
We re-examine previous constructions of infinite binary words containing few distinct squares with the goal of finding the "simplest", in a certain sense. We exhibit several new constructions. Rather than using tedious case-based arguments…
Benjamin Franklin constructed three squares which have amazing properties, and his method of construction has been a mystery to date. In this article, we divulge his secret and show how to construct such squares for any order.
For any odd prime power q we provide a quick construction of a complete family of q(q-1) mutually orthogonal sudoku squares of order q^2.
In this short note we propose a new method for construction new nice arrangement on the sphere $S^d$ using the spaces of spherical harmonic.
We present a simple yet powerful technique for forming iterative methods of various convergence orders. Methods of various convergence orders (four, six, eight and ten) are formed through a modest modification of the classical Newton…
We recall the Alon-Tarsi conjecture on the number of even latin squares. We introduce a map which switches the parity of a latin square under certain requirements. An example is included.
An associative magic square is a magic square such that the sum of any 2 cells at symmetric positions with respect to the center is constant. The total number of associative magic squares of order 7 is enormous, and thus, it is not…
We present systematic methods of constructing pandiagonal sudoku squares of order k*k and Knut Vik sudoku squares of order k*k not divisible by 2 or 3. Pandiagonal magic squares are constructed from these squares. Examples of all these…
A magic series is a set of natural numbers that, by virtue of its size, sum, and maximum value, could fill a row of a normal magic square. In this paper, we derive an exact two-dimensional integral representation for the number of magic…
We demonstrate the existence of $K$-multimagic squares of order $N$ consisting of distinct integers whenever $N>2 K(K+1)$. This improves upon our earlier result in which we only required $N+1$ distinct integers. Additionally, we present a…
In this paper, we study the concept of "binary color-coded magic squares" by assigning two distinct colors to the even and odd numbers within a magic square. We investigate the uniqueness of patterns within these squares using three…
We give a variety of magic hexagons of Orders from 3 to 7, many of which are extensions of known results. We also give a theorem that their are an infinite number of magic hexagons of Order $n$ for any fixed positive integer $n$ for any…