Professor Preece's tredoku tilings

Abstract

Shortly before he died in 2014, Donald Preece gave two talks about what he called tredoku tilings, inspired by the puzzle of the same name. In these talks he presented a conjecture about the existence of these tilings that has been proved recently by Simon Blackburn. This paper provides an overview of Donald's work in this area, including his work on a natural generalisation of a tredoku tiling that he called a quadridoku tiling. Additionally, the paper gives alternative proofs of some parts of the existence theorem for tredoku tilings, presents a computer enumeration of the isomorphism classes of tredoku tilings with up to 16 tiles and provides a brief introduction to tilings with holes.