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This paper considers the generation of a strong stray magnetic field using rare-earth permanent magnets. Generating a strong field in a region displaced from a magnet is considered here in the context of magnetic resonance hardware design; however, optimizing magnetic field strength is of broad utility in many areas. The local magnetization direction in a permanent magnet is related to the field strength at a position outside of the magnet. This local direction can be optimized to obtain the strongest field. The paper derives, for a magnet of fixed volume, expressions for the dimensions yielding the strongest field. It discusses practical magnet arrangements that approximate the ideal magnetization pattern and demonstrates that a field greater that 80% of the optimal value can be obtained from a relatively simple arrangement of magnetized blocks.