Related papers: Cookie Monster Devours Naccis
The Cookie Monster Problem supposes that the Cookie Monster wants to empty a set of jars filled with various numbers of cookies. On each of his moves, he may choose any subset of jars and take the same number of cookies from each of those…
Given a set of integers $S = \{k_1,\ k_2,...,\ k_n\}$, the Cookie Monster Problem is the problem of making all elements of the set equal 0 in the minimum number of moves. Consider the analogy of cookie jars with distinct numbers of cookies,…
We research a combinatorial game based on the Cookie Monster problem called the Cookie Monster game that generalizes the games of Nim and Wythoff. We also propose several combinatorial games that are in between the Cookie Monster game and…
In this paper, we consider a game played on a rectangular $m \times n$ gridded chocolate bar. Each move, a player breaks the bar along a grid line. Each move after that consists of taking any piece of chocolate and breaking it again along…
Cookie Clicker is a popular online incremental game where the goal of the game is to generate as many cookies as possible. In the game you start with an initial cookie generation rate, and you can use cookies as currency to purchase various…
Chocolate-bar games are variants of the CHOMP game. A three-dimensional chocolate bar comprises a set of cubic boxes sized 1 X 1 X 1, with a bitter cubic box at the bottom of the column at position (0,0). For non-negative integers u,w such…
In the classical coupon collector's problem, every box of breakfast cereal contains one coupon from a collection of n distinct coupons, each equally likely to appear. The goal is to find the expected number of boxes a player needs to…
We consider the problem of determining the minimum number of moves needed to solve a certain one-dimensional peg puzzle. Let N be a positive integer. The puzzle apparatus consists of a block with a single row of 2N+1 equally spaced holes…
Cookie banners, the pop ups that appear to collect your consent for data collection, are a tempting ground for dark patterns. Dark patterns are design elements that are used to influence the user's choice towards an option that is not in…
In 1975 Ogg offered a bottle of Jack Daniels for an explanation of the fact that the prime divisors of the order of the monster are the primes p for which the characteristic p supersingular j-invariants are all defined over the field with p…
Online websites use cookie notices to elicit consent from the users, as required by recent privacy regulations like the GDPR and the CCPA. Prior work has shown that these notices use dark patterns to manipulate users into making…
As a contribution to an eventual solution of the problem of determination of the maximal subgroups of the Monster we show that there is a unique conjugacy class of subgroups isomorphic to $PSU_3(8)$. The argument depends on some…
What has so far prevented us from decrypting quantum mechanics is the Cookie Cutter Paradigm, according to which the world's synchronic multiplicity derives from surfaces that carve up space in the manner of three-dimensional cookie…
Snackjack is a highly simplified version of blackjack that was proposed by Ethier (2010) and given its name by Epstein (2013). The eight-card deck comprises two aces, two deuces, and four treys, with aces having value either 1 or 4, and…
It is well-known by now that any state of the $3\times 3 \times 3$ Rubik's Cube can be solved in at most 20 moves, a result often referred to as "God's Number". However, this result took Rokicki et al. around 35 CPU years to prove and is…
We consider a puzzle such that a set of colored cubes is given as an instance. Each cube has unit length on each edge and its surface is colored so that what we call the Surface Color Condition is satisfied. Given a palette of six colors,…
We describe and axiomatize finite solitaire puzzles and zero sum sequential games graph theoretically. Zermelo's theorem telling that there is a win for one of the players or a draw follows from the definitions. The god number is a…
We calculate twisted denominator identities of the fake monster superalgebra and use them to construct new examples of supersymmetric generalized Kac-Moody superalgebras. Their denominator identities give new infinite product identities.
We consider the model of the one-dimensional cookie random walk when the initial cookie distribution is spatially uniform and the number of cookies per site is finite. We give a criterion to decide whether the limiting speed of the walk is…
We consider two division problems on narrow strips of square and hexagonal lattices. In both cases we compute the bivariate enumerating sequences and the corresponding generating functions, which allowed us to determine the asymptotic…