This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
No, the interface may have default (package) access. This isn't a problem. However, inside an interface, all methods are implicitly public (i.e. even though they may not be declared as public). Thus when you implement the methods in a class, the implementing methods must be public as well. And inside a class, you must explicitly declare a method to be public, in order to make it so.