Abstract
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 wagons into a desired order (often a randomly chosen order). This article answers the question: When can you be sure this can always be done? The problem of finding a solution in a minimum number of moves is also addressed.
Highlights
This paper provides an analysis of when an inglenook puzzle can be solved, and how many moves are needed in the worst case
Most of the paper assumes that the reader has a background in discrete mathematics or computer science, but the first part of this introduction provides a summary of the results of the paper for readers who do not necessarily have this background
Puzzles involving the movement of locomotives, wagons and carriages have a long history, with well-known examples such as Sam Loyd’s Primitive Railroading puzzle and The Switch Problem [17] and Dudeney’s The Mudville Railway Muddle [10] dating back well over 100 years
Summary
This paper provides an analysis of when an inglenook puzzle can be solved, and how many moves are needed in the worst case. Most of the paper assumes that the reader has a background in discrete mathematics or computer science, but the first part of this introduction provides a summary of the results of the paper for readers who do not necessarily have this background. The remaining parts of this introduction describes some of the previous academic work on related problems, and describes the structure of the rest of the paper
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