Inglenook Shunting Puzzles Simon R. Blackburn Department of Mathematics Royal Holloway University of London Egham, Surrey TW20 0EX, United Kingdom
[email protected]. April 4, 2019 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. 1 Introduction 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 as- sumes that the reader has a background in discrete mathematics or computer science, but the first part of this introduction provides a summary of the re- sults of the paper for readers who do not necessarily have this background. arXiv:1810.07970v2 [math.CO] 3 Apr 2019 The remaining parts of this introduction describes some of the previous aca- demic work on related problems, and describes the structure of the rest of the paper. 1.1 A non-technical summary Puzzles involving the movement of locomotives, wagons and carriages have a long history, with well-known examples such as Sam Loyd's Primitive Rail- 1 roading puzzle and The Switch Problem [17] and Dudeney's The Mudville Railway Muddle [10] dating back well over 100 years.