Related papers: Inglenook Shunting Puzzles
A puzzle about prisoners trying to identify the color of a hat on their head leads to a version where there are k more hats than prisoners. This generalized puzzle is related to the independence number of the arrangement graph A(m, n) and…
We study the following combinatorial problem. Given a set of $n$ y-monotone wires, a tangle determines the order of the wires on a number of horizontal layers such that the orders of the wires on any two consecutive layers differ only in…
Given a string of parentheses, the task is to find the longest consecutive segment that is balanced, in linear time. We find this problem interesting because it involves a combination of techniques: the usual approach for solving segment…
The problem of maximizing the probability of two trucks being coordinated to merge into a platoon on a highway is considered. Truck platooning is a promising technology that allows heavy vehicles to save fuel by driving with small…
We consider a set of challenging sequential manipulation puzzles, where an agent has to interact with multiple movable objects and navigate narrow passages. Such settings are notoriously difficult for Task-and-Motion Planners, as they…
The reader is reminded of several puzzles involving randomness. These may be ill-posed, and if well-posed there is sometimes a solution that uses probabilistic intuition in a special way. Various examples are presented including the well…
Railway scheduling consists in ensuring that a set of trains evolve in a shared rail network without collisions, while meeting schedule constraints. This problem is notoriously difficult, even more in the case of uncertain or even unknown…
A tromino tiling problem is a packing puzzle where we are given a region of connected lattice squares and we want to decide whether there exists a tiling of the region using trominoes with the shape of an L. In this work we study a slight…
In many tasks, in particular in natural science, the goal is to determine hidden system parameters from a set of measurements. Often, the forward process from parameter- to measurement-space is a well-defined function, whereas the inverse…
The Shortest Path Reconfiguration problem has as input a graph G (with unit edge lengths) with vertices s and t, and two shortest st-paths P and Q. The question is whether there exists a sequence of shortest st-paths that starts with P and…
A shuffle of two strings is formed by interleaving the characters into a new string, keeping the characters of each string in order. A string is a square if it is a shuffle of two identical strings. There is a known polynomial time dynamic…
Pancake Flipping is the problem of sorting a stack of pancakes of different sizes (that is, a permutation), when the only allowed operation is to insert a spatula anywhere in the stack and to flip the pancakes above it (that is, to perform…
We study algorithmic aspects of bending wires and sheet metal into a specified structure. Problems of this type are closely related to the question of deciding whether a simple non-self-intersecting wire structure (a carpenter's ruler) can…
We present an algorithm determining where to relocate objects inside a cluttered and confined space while rearranging objects to retrieve a target object. Although methods that decide what to remove have been proposed, planning for the…
The knapsack problem is a classic optimisation problem that has been recently extended in the setting of groups. Its study reveals to be interesting since it provides many different behaviours, depending on the considered class of groups.…
This paper presents a systematic method to solve difficult 9 x 9 Sudoku puzzles by hand. While computer algorithms exist to solve these puzzles, these algorithms are not good for human's to use because they involve too many steps and…
Triangular peg solitaire is a well-known one-person game or puzzle. When one peg captures many pegs consecutively, this is called a sweep. We investigate whether the game can end in a dramatic fashion, with one peg sweeping all remaining…
Warnsdorffs rule for a knights tour is a heuristic, i.e., it is a rule that does not produce the desired result all the time. It is a classic example of a greedy method in that it is based on a series of locally optimal choices. This note…
The oval track group, $OT_{n,k}$, is the subgroup of the symmetric group, $S_n$, generated by the basic moves available in a generalized oval track puzzle with $n$ tiles and a turntable of size $k$. In this paper we completely describe the…
This paper presents a review of instantaneously trained neural networks (ITNNs). These networks trade learning time for size and, in the basic model, a new hidden node is created for each training sample. Various versions of the…