Hello everyone, I wanted to share an observation that might bridge the gap between classical mathematics and AI reasoning. During my experiments with models like GPT-4 and Claude 3.5, I stumbled upon something intriguing: combinatorics—the branch of mathematics dealing with combinations, permutations, and state spaces—can significantly enhance a language model’s ability to solve logic problems. Let me explain how I arrived at this. The Problem I’ve been testing large language models with classic puzzles, such as the Wolf, Goat, and Cabbage problem: A farmer must transport a wolf, goat, and cabbage across a river using a small boat. The boat can carry only one item at a time. If left alone, the wolf eats the goat, or the goat eats the cabbage. How does the farmer transport all items safel...
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