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From: Jamie Holly

On a computer you would still need a transparency or each time you paste something it's going to cover the states next to it, considering our states aren't rectangular.

But if cut and paste is an option, then there is even a much simpler option. How about a map like this:

http://blogs.glnd.k12.va.us/teachers/pbrook/files/2011/08/usa_blank.jpg

Bucket fill tool on Photoshop fills each state fine.