Oh man! I took a course this last semester called "Evidence Based Medicine" in which we explored some of the common biases and discussed how to avoid them. One of the online homeworks included a program that generated tests like this one. Unfortunately, I've just tried messing around with it and it requires access to our school's account-protected website (University of Arizona, D2L) to work. Sorry I can't get a link here.
A few guiding rules that we determined:
1. Once you've established a theory or hypothesis, validate it by making it return a negative. If your hypothesis is "ascending even numbers," throw an odd in there to make sure it fails. If it doesn't, your hypothesis is incomplete.
2. Eliminate other possible hypotheses. For example, the series could accept all numbers under 1000. Try throwing some super-high numbers in and see if it fails. Do this for each plausible hypothesis.
3. Be efficient by testing two or three hypotheses at a time. You can check to see if the rule is "numbers under 1000" or "even numbers" at the same time by entering 1001, 1002, 1003. If this fails, you can break the test into its individual parts and test them one at a time.
It was neat to see this applied to real life. In addition to the government and business examples given in the article, you also see this in medicine. Just as an example, a doctor might unfairly conclude that nausea is a sign of appendicitis. He may do this because he takes the time to ask each appendicitis candidate about nausea/ vomiting/ diarrhea, while he neglects to ask those questions about patients with ear pain. Perhaps almost everybody has nausea, but since he only asks the patients with abdominal pain, he never does the test to prove his hypothesis wrong.
Thanks for taking the time to link!