It is known that in a certain city there are a significant number of witches, even though this practice is forbidden. The problem is that nobody knows who these witches are, since a witch is very careful to appear to others as a perfectly normal person.
You are appointed by the Mayor to establish (as accurately as possible) how many witches are in the city. You are allowed to do a single phone call to every family in the town. In general, you can expect a sincere response to your questions, excepting of course the case when a truthful answer would cause a witch to disclose herself.
How would you carry on your job?
[updated – more specifics]
Let’s assume that you must determine the number only through phone calls. The only thing you have is the list of phone numbers to every family in the town (no credit card information, you cannot hire private investigators, etc).
Also, let’s assume that witches are pretty good to appear as “innocent” people. Psychological tricks won’t work, or even if they do, you cannot use them as a reliable source of information.
Finally, let’s assume that witches don’t really know each other, although assuming the contrary would be an interesting variation of the original problem.