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I have two shapefiles, one (Polygon A) is a fishnet of 1 square kilometer polygons, and the second (polygon B) is a multiple polygon with specific attributes. One of the attribute is the total number of objects.

I came up with a scoring system for the fishnet and only a subset of the fishnet-polygons remains. What I would like to do is to generate X number of random points to the polygon A that fall within a section of polygon B. The # X is the attribute of the section of polygon B. Any suggestions?

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This is a common problem people want to solve and have developed tools in the past. Anything like this your first port of call should be the ArcGIS code sharing (previously ArcScripts). Just search for "random points"...

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"Create Random Points" has a Constrained Feature Class option. However, you want the points constrained to a specific Polygon. I would Union the two layers, and then experiment with Create Random Points.

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