We introduce "Method Actors" as a mental model for guiding LLM prompt engineering and prompt architecture. Under this mental model, LLMs should be thought of as actors; prompts as scripts and cues; and LLM responses as performances. We apply this mental model to the task of improving LLM performance at playing Connections, a New York Times word puzzle game that prior research identified as a challenging benchmark for evaluating LLM reasoning. Our experiments with GPT-4o show that a "Method Actors" approach can significantly improve LLM performance over both a vanilla and "Chain of Thoughts" approach. A vanilla approach solves 27% of Connections puzzles in our dataset and a "Chain of Thoughts" approach solves 41% of puzzles, whereas our strongest "Method Actor" approach solves 86% of puzzles. We also test OpenAI's newest model designed specifically for complex reasoning tasks, o1-preview. When asked to solve a puzzle all at once, o1-preview solves 79% of Connections puzzles in our dataset, and when allowed to build puzzle solutions one guess at a time over multiple API calls, o1-preview solves 100% of the puzzles. Incorporating a "Method Actor" prompt architecture increases the percentage of puzzles that o1-preview solves perfectly from 76% to 87%.

The Connections puzzle is a word association game published daily by The New York Times (NYT). In this game, players are asked to find groups of four words that are connected by a common theme. While solving a given Connections puzzle requires both semantic knowledge and abstract reasoning, generating novel puzzles additionally requires a form of metacognition: generators must be able to accurately model the downstream reasoning of potential solvers. In this paper, we investigate the ability of the GPT family of Large Language Models (LLMs) to generate challenging and creative word games for human players. We start with an analysis of the word game Connections and the unique challenges it poses as a Procedural Content Generation (PCG) domain. We then propose a method for generating Connections puzzles using LLMs by adapting a Tree of Thoughts (ToT) prompting approach. We evaluate this method by conducting a user study, asking human players to compare AI-generated puzzles against published Connections puzzles. Our findings show that LLMs are capable puzzle creators, and can generate diverse sets of enjoyable, challenging, and creative Connections puzzles as judged by human users.

The Connections puzzle published each day by the New York Times tasks players with dividing a bank of sixteen words into four groups of four words that each relate to a common theme. Solving the puzzle requires both common linguistic knowledge (i.e. definitions and typical usage) as well as, in many cases, lateral or abstract thinking. This is because the four categories ascend in complexity, with the most challenging category often requiring thinking about words in uncommon ways or as parts of larger phrases. We investigate the capacity for automated AI systems to play Connections and explore the game's potential as an automated benchmark for abstract reasoning and a way to measure the semantic information encoded by data-driven linguistic systems. In particular, we study both a sentence-embedding baseline and modern large language models (LLMs). We report their accuracy on the task, measure the impacts of chain-of-thought prompting, and discuss their failure modes. Overall, we find that the Connections task is challenging yet feasible, and a strong test-bed for future work.