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.

Read your course syllabus. If you still have questions, ask your instructor.

There is no single standard set of rules for "open book exam", nor even any universal definition. Your instructor could have decided that some resources are allowed and others are not. You need to obey the rules determined for your particular course by your particular instructor. "What is considered cheating" is "any violation of the rules announced by your instructor".

It's irrelevant what anybody else says "open book exam" means or what they might say you can or cannot use. If someone on Stack Exchange says "it's fine to use resource X", and your instructor says it's not, I assure you that using resource X can lead to you being charged with cheating, and saying "some random person on Stack Exchange said it was fine" will not be a good defense.

I routinely run open book exams. I allow students to bring: books about any topic they need or wish; notes of any kind, especially course notes; solutions of all the exercises solved during the lessons, those of past exams and those given as homework; programmable calculators (but no computers with connectivity).

(Of course, I warn them that all of the above are useless if they haven't studied)

So, for me, cheating means:

1. Trying to find a solution from external resources by means of cell phones, computers, radios or whatever.
2. Copying a solution from a course mate.
3. Asking for advice to a course mate.