Solving Fred Horn's 'Gloop' puzzle

摘要

The Gloop tile set represents all unique ways in which non-intersecting paths can be drawn within a square tile with two terminal points per side, and the Gloop puzzle game consists of a number of challenges to be attempted with this tile set. This paper describes the computer-based analysis of the key Gloop challenges, including the computer-assisted solution of the most difficult challenge - whether all tiles can be packed into a rectangle to form a single continuous contour - which had stood for over a decade. The resulting proof allows a simple arithmetic for the analysis of Gloop tiles, on square and other potential geometries, and demonstrates how computer analysis can inspire the solution of problems even if it does not yield those solutions itself.