Selecting points intersecting polygon

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In ArcGIS 10.2 ArcMap am attempting to label a grid of varying size polygons overlaid by a grid of evenly spaced (1km) points with an associated value X by the the value of the point. If a polygon is intersected by more than 1 then I want it to be labelled with the maximum X value. If a polygon doesn't intersect with a point I want it to be labelled with the nearest point.

I used spatial join with one to one intersect and maximum value for X to be selected. This allowed me to get the maximum value for multiple points that intersected. However it doesn't allow me to label the polygons where a point does not intersect it. I put a search radius on it and then it can label polygons with points where X is greater but are not contained in the actual polygon.

Any assistance appreciated.



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