Transformer-decoder language models are a core innovation in text based generative artificial intelligence. These models are being deployed as general-purpose intelligence systems in many applications. Central to their utility is the capacity to understand natural language commands and exploit the reasoning embedded in human text corpora to apply some form of reasoning process to a wide variety of novel tasks. To understand the limitations of this approach to generating reasoning we argue that we need to consider the architectural constraints of these systems. Consideration of the latent variable structure of transformer-decoder models allows us to design reasoning tasks that should probe the boundary of their capacity to reason. We present enigme, an open-source library for generating text-based puzzles to be used in training and evaluating reasoning skills within transformer-decoder models and future AI architectures.