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I've always glued the back of the puzzle, as I was leery about messing up the front. But I didn't use a lot of glue- just enough to secure it to posterboard before framing. Plain old Elmers watered down and painted on with a paintbrush. I also used glue sticks, which were even better- the only downside is that it uses up a lot of glue stick. I now have a large, non-rectangular puzzle that won't fit in a standard frame- so I'm going to hang that on its own. For that I'll probably have to coat both the front and back to seal all the pieces together.
Contact paper is a great idea! Just to hold the puzzle together until you can attach it to posterboard or foam board or whatever.