Real game engines use this pattern (or its 3D cousin, the Octree) for broad-phase collision detection: the quadtree quickly identifies candidate pairs, and a more expensive narrow-phase check tests the actual geometry.
I wanted to test this claim with SAT problems. Why SAT? Because solving SAT problems require applying very few rules consistently. The principle stays the same even if you have millions of variables or just a couple. So if you know how to reason properly any SAT instances is solvable given enough time. Also, it's easy to generate completely random SAT problems that make it less likely for LLM to solve the problem based on pure pattern recognition. Therefore, I think it is a good problem type to test whether LLMs can generalize basic rules beyond their training data.
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What we know so far about the deadly boat shooting off Cuba’s coast
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