Open book exams are exams that are taken in a classroom, with a limited amount of time, but where the student can consult notes, textbooks, and any kind of written material. They are usually meant to test problem-solving abilities and the capacity to apply the existing theory rather than memorization.
It seems natural to allow the use of e-books in these tests as well as their dead-tree equivalents, since a student should be able to use their preferred medium to study and may have bought the e-book version rather than the paper one. Also, ecology and save the forests.
However, many modern e-book readers have 3G or Wi-Fi networking, and this would make it easy to cheat by getting external help (which is, of course, not allowed). It is not simple to make sure that this connectivity stays off during the exam: you can't just remove the SIM card and everything is ok.
Is there a solution other than "live with the cheating" and "forbid e-book readers overall"?