  Donald A. Preece gave two talks in 2013, in which he introduced the notion of
tredoku patterns. These are certain configurations of diamond-shaped tiles,
inspired by the sukodu-like puzzle that appears in newspapers. Very sadly,
Prof. Preece died in January 2014, before he was able to complete his work on
this problem. This paper reconstructs his work, and settles (in the
affirmative) the conjectures he proposed.
