What is considered cheating in an open book exam?

In my experience, I've seen three versions of open book exam:

1. You can bring in a set of notes.
2. You can use any textbooks and notes you want, but no electronic assistance.
3. You can use any reference you want local or remote, except for asking other people to solve your problem for you.

As personal electronics become smaller and more pervasive, these are all effectively converging together: if you allow students any open book, then you have to allow the whole internet, and impose an honor code that requires students to not outsource their problems.

In this environment, my feeling is that the only way to run an open book exam is to be testing for mastery of material, rather than problem solving. In other words: open book works only when the answers cannot be readily extracted from the book (or other resources), but only from the synthesis of all of the knowledge within. There must be no single "right answer", but a range of possibilities requiring creativity. Thus, cheating can be detected in the same way that plagiarism can, because every student should be producing their own unique answer.

The best and fiercest open book exam I have ever taken was in an algorithms class as an undergraduate. The exam was six questions, each asking us to develop the best possible algorithm that we could to solve some curious problem based on the principles we had learned in the class. We were handed the exam to take home and given 48 hours, in which we were allowed and encouraged to use any resource we wanted, except not to talk to anybody else about the problem. It was brutal, it was terrifyingly hard, and it was the most fun I've ever had on an exam. That, I think, is a standard to aspire to.