Related papers: The Mutando of Insanity
In the Colored Bin Packing problem a set of items with varying weights and colors must be packed into bins of uniform weight limit such that no two items of the same color may be packed adjacently within a bin. We solve this problem for the…
We make an attempt at proving the Four Colour Theorem in six pages.
A sliding puzzle is a combination puzzle where a player slide pieces along certain routes on a board to reach a certain end-configuration. In this paper, we propose a novel measurement of complexity of massive sliding puzzles with…
We study the number of factorizations of a positive integer, where the parts of the factorization are of l different colors (or kinds). Recursive or explicit formulas are derived for the case of unordered and ordered, distinct and…
Let $X,Y$ be finite sets, $r,s,h, \lambda \in \mathbb{N}$ with $s\geq r, X\subsetneq Y$. By $\lambda \binom{X}{h}$ we mean the collection of all $h$-subsets of $X$ where each subset occurs $\lambda$ times. A coloring of…
Human beings can imagine the colours of a grayscale image with no particular effort thanks to their ability of semantic feature extraction. Can an autonomous system achieve that? Can it hallucinate plausible and vibrant colours? This is the…
Search algorithms are a foundational topic in artificial intelligence education, yet even simple domains can generate large state spaces that challenge learners' ability to form accurate mental models. This paper presents an interactive…
A total coloring of a graph colors all its elements, vertices and edges, with no adjacency conflicts. The Total Coloring Conjecture (TCC) is a sixty year old challenge, says that every graph admits a total coloring with at most maximum…
An inglenook puzzle is a classic shunting (switching) puzzle often found on model railway layouts. A collection of wagons sits in a fan of sidings with a limited length headshunt (lead track). The aim of the puzzle is to rearrange the…
This paper addresses the combinatorial structure of $m$-colored mutation classes. We provide an explicit and purely combinatorial description of the $m$-colored quivers that arise within the $m$-colored mutation class of a quiver of type…
A Costas array is a permutation array for which the vectors joining pairs of $1$s are all distinct. We propose a new three-dimensional combinatorial object related to Costas arrays: an order $n$ Costas cube is an array $(d_{i,j,k})$ of size…
In this paper we study the randomly edge colored graph that is obtained by adding randomly colored random edges to an arbitrary randomly edge colored dense graph. In particular we ask how many colors and how many random edges are needed so…
We approximate a 2D Ising spin glass by tiling an infinite square lattice with large identical unit cells. The interactions within the unit cell are random. Each such sample shows one or more critical points. We examine the scaling of the…
The aim of this of this paper is to study infinite games and to prove formally some properties in this framework. As a consequence we show that the behavior (the madness) of people which leads to speculative crashes or escalation can be…
A first step in investigating colour symmetries of periodic and nonperiodic patterns is determining the number of colours which allow perfect colourings of the pattern under consideration. A perfect colouring is one where each symmetry of…
A random jigsaw puzzle is constructed by arranging $n^2$ square pieces into an $n \times n$ grid and assigning to each edge of a piece one of $q$ available colours uniformly at random, with the restriction that touching edges receive the…
A formal proof has not been found for the four color theorem since 1852 when Francis Guthrie first conjectured the four color theorem. Why? A bad idea, we think, directed people to a rough road. Using a similar method to that for the formal…
The Rubik's cube is a famous puzzle in which faces can be moved and the corresponding movement operations define a group. We consider here a generalization to any $3$-valent map. We prove an upper bound on the size of the corresponding…
Let $2\le k\in\mathbb{Z}$. A total coloring of a $k$-regular simple graph via $k+1$ colors is an {\it efficient total coloring} if each color yields an efficient dominating set, where the efficient domination condition applies to the…
We introduce and investigate the computational complexity of a novel physical problem known as the Pinball Wizard problem. It involves an idealized pinball moving through a maze composed of one-way gates (outswing doors), plane walls,…