Related papers: Cookie Monster Devours Naccis
The Fibonacci numbers are familiar to all of us. They appear unexpectedly often in mathematics, so much there is an entire journal and a sequence of conferences dedicated to their study. However, there is also another sequence of numbers…
We generalize the well-known Coupon Collector Problem (CCP) in combinatorics. Our problem is to find the minimum and expected number of draws, with replacement, required to recover $n$ distinctly labeled coupons, with each draw consisting…
The Rubik's Cube is the most popular puzzle in the world. Two of its studied aspects are God's Number, the minimum number of turns necessary to solve any state, and the first law of cubology, a solvability criterion. We modify previous…
We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…
The move-minimizing puzzles presented here are certain types of one-player combinatorial games that are shown to have explicit solutions whenever they can be encoded in a certain way as diamond-colored modular or distributive lattices. Our…
In this note, we establish $\Gamma_{1}(N)$-analogues for the monster denominator formula.
Puzzles based on coloured cubes and other coloured geometrical figures have a long history in the recreational mathematical literature. One of the most commercially famous of these puzzles is the Instant Insanity that consists of four…
We discuss some categorical aspects of the objects that appear in the construction of the Monster and other sporadic simple groups. We define the basic representation of the categorical torus $\mathcal T$ classified by an even symmetric…
We play a variation of Nim on stacks of tokens. Take your favorite increasing sequence of positive integers and color the tokens according to the following rule. Each token on a level that corresponds to a number in the sequence is colored…
We investigate the state complexity of the star of symmetrical differences using modifiers and monsters. A monster is an automaton in which every function from states to states is represented by at least one letter. A modifier is a set of…
We consider a class of self-interacting random walks in deterministic or random environments, known as excited random walks or cookie walks, on the d-dimensional integer lattice. The main purpose of this paper is two-fold: to give a survey…
In this paper we give a mathematical model for a game that we call picture cube puzzle and investigate its properties. The central question is the number of moves required to solve the puzzle. A mathematical discussion is followed by the…
The sudoku puzzles have a long history, with variations going back more than a hundred years, but its current and perhaps surprising world-wide prominence goes back to certain initiatives and then puzzle-generating computer programmes from…
In this paper we study the problem of the Malicious Maitre d', as described in Peter Winkler's book Mathematical Puzzles: A Connoisseur's Collection. This problem, attributed to computer scientist Rob Pike, involves seating diners around a…
In a previous paper we have presented a partition formula for the even-index Fibonacci numbers using the preprojective representations of the 3-Kronecker quiver and its universal cover, the 3-regular star. Now we deal in a similar way with…
In this article we study domino snake problems on finitely generated groups. We provide general properties of these problems and introduce new tools for their study. The first is the use of symbolic dynamics to understand the set of all…
Many practical search problems concern the search for multiple hidden objects or agents, such as earthquake survivors. In such problems, knowing only the list of possible locations, the Searcher needs to find all the hidden objects by…
We study the quantum walk in momentum space using a coin arranged in quasi-periodic sequences following a Fibonacci prescription. We build for this system a classical map based on the trace of the evolution operator. The sub-ballistic…
We study a popular puzzle game known variously as Clickomania and Same Game. Basically, a rectangular grid of blocks is initially colored with some number of colors, and the player repeatedly removes a chosen connected monochromatic group…
We study the Hausdorff and box-counting dimensions of cookie-cutter-like sets formed by sequential dynamics of a finite number of expanding maps. Under some natural conditions, these dimensions turn out to be the minimum and maximum of the…