Consider the set of northwestern states or provinces
{Montana, Washington, Idaho, Oregon, Alaska, British
Columbia, Alberta}. If a person chooses one element,
show that in three yes or no questions, we can determine
the element.
You need to use "bit" (binary digit) theory. Ask the three questions that will each divide the number of alternatives in half. (2^3 = 8)
For example, is the area in the first half of the list? Is the area in the first half of the remainder? Is the area the first of the remaining two? Regardless of whether the answers are "yes" or "no," you have your answer.
This is a good method for playing "20 questions."