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Re: Point Distances without ArcINFO license
Well, it wouldn't be a pretty solution or the quickest to run by any means, but if you really need this functionality but can't justify an ArcInfo license, I'd say what about using the iterators available in Model Builder or a "For feature in featureClass" in python to go in and set up a scratch/temp shapefile/feature class that copies the point to have distances measured from and then loops through copying in each point to be measured to (based on a buffer and select all within buffer) and then measures these two points distance from each other, write that value to the appropriate point in the original feature class (or a temporary table the values of which can be averaged and written to the original feature class, depending on what specifically you're needing), delete the measure to point, and repeat with the next measure to point.
Like I said, it's not pretty, but it would probably work (though you'd have to have a couple scratch work spaces, and you might be nesting loops in loops depending on what specifically you're trying to accomplish...) just an idea, hope it helps.
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