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We consider a class of generalized planning problems based on the idea of quantifying over sets of similar objects. We show how we can adapt fully observable nondeterministic planning techniques to produce generalized solutions that are easy to instantiate over particular problem instances. We also describe how we can reformulate a classical planning problem into a quantified one. The reformulation allows us to solve the original planning task without grounding every action with respect to all objects in the problem, and a single solution can be applied to a possibly infinite set of related classical planning tasks. We report experimental results that show our approach is a practical and promising technique for solving an interesting class of problems.