The New York Times Connections game has emerged as a popular and challenging pursuit for word puzzle enthusiasts. We collect 438 Connections games to evaluate the performance of state-of-the-art large language models (LLMs) against expert and novice human players. Our results show that even the best performing LLM, Claude 3.5 Sonnet, which has otherwise shown impressive reasoning abilities on a wide variety of benchmarks, can only fully solve 18% of the games. Novice and expert players perform better than Claude 3.5 Sonnet, with expert human players significantly outperforming it. We create a taxonomy of the knowledge types required to successfully cluster and categorize words in the Connections game. We find that while LLMs perform relatively well on categorizing words based on semantic relations they struggle with other types of knowledge such as Encyclopedic Knowledge, Multiword Expressions or knowledge that combines both Word Form and Meaning. Our results establish the New York Times Connections game as a challenging benchmark for evaluating abstract reasoning capabilities in AI systems.