I was curious what the best way to do this would be using constraints, and whether or not it can be done without scripts (I know this used to be doable).
Roblox did a short video series on making a door with constraints. The last one covers how to automatically make it close.
Making a Door: Vertical Hinges
Making a Door: Limits
Making a Door: Springs
Basically, you would both use HingeConstraints, for the ability to push it open while keeping the door in its frame and SpringConstraints, for it to pull the door shut automatically.
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