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Point buffer overlap

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I have a map with about 300 data points, and I want to find out how many 'neighbouring' points each point has (within 300 meters). I thought it might be possible to achieve this by creating a buffer around each data point and than counting the number of overlapping buffers. I have made these buffers and used intersect between them, but I have no idea how to find out how many points each buffer overlaps. Maybe it is an easy problem but does anyone have an idea?

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