How to take the process of buffer and do it backwards?

[ConnorRapley]

Hi! I'm trying to do something that is reverse-buffer esque. What I mean simply is buffer does "How many of thing X are within Y distance?" I.E. With a 1km buffer you have 3 schools. What I want is "How much distance X do you need to cover Y amount of things?" I.E. Somehow finding out the distance from a dairy to the closest 200 people is 127 metres. I've been stuck for hours. Any suggestions?

[DanPatterson_Retired]

If you have the appropriate license level, explore

Near—Help | ArcGIS for Desktop 

Generate Near Table—Help | ArcGIS for Desktop 

When you get your inner feature distance, you can decide how you want to delineate the space.  There are other tools that you can use once you have made that decision