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We present a novel approach, MAGIC (manipulation analogies for generalizable intelligent contacts), for one-shot learning of manipulation strategies with fast and extensive generalization to novel objects. By leveraging a reference action trajectory, MAGIC effectively identifies similar contact points and sequences of actions on novel objects to replicate a demonstrated strategy, such as using different hooks to retrieve distant objects of different shapes and sizes. Our method is based on a twostage contact-point matching process that combines global shape matching using pretrained neural features with local curvature analysis to ensure precise and physically plausible contact points. We experiment with three tasks including scooping, hanging, and hooking objects. MAGIC demonstrates superior performance over existing methods, achieving significant improvements in runtime speed and generalization to different object categories. Website: https://magic-2024.github.io/.