Can You Assign Different Colors to Areas NOT based on their Attributes?

[RenoGregory]

I have a shape file with a bunch of polygons bordering each other (think like a bunch of counties in a state). I would like to shade them in different colors so you can differentiate them easy. However, these different colors do not need to be based on any attribute whatsoever. How can I do this in ArcMap?

If you're confused what I mean, think like the typical state map like this. The states are all different colors so you can differentiate them, but the colors have no inherent meaning. They only use 4 to 5 colors, so you don't get a rainbow map. Is there a name for this type of color scheme?

[JasonHine]

I'm not aware of a term for the cartographic coloring scheme to which you're referring, but in mathematics it's a fascinating topic called the four color theorem (ref: Wikipedia).

The best ready-to-use solution I'm aware of is the Five Color Tool included in the ColorTools contributed by Mark Cederholm (pierssen). 

Additional ideas and algorithms may be found in this Esri Community thread and in this StackExchange thread. 

[Suzanne-Boden]

Hi Reno, I've often seen layers with an attribute for symbology. For example, a layer has a Symbol field with a set of values assigned (maybe 1-5). Features with a Symbol value of 1 are drawn with a certain color, value 2 draws with a different color, etc. The layer can then be symbolized with a Unique Values scheme. If you have a lot of features, this could be tedious to set up but there are likely code snippets or scripts out there that would randomly assign a Symbol value of 1-5 to your features. From there, you could edit Symbol values as needed to adjust adjacent feature colors.