This is a pretty cool example of confirmation bias. I was 100% sure the rule was a sequence of numbers that were all powers of some base... (2, 4, 8 - 16, 32, 64 - 3, 9, 27 - 5, 25, 125 - all got a "yes"), but it turned out to be something much simpler/different. It's like if you turn into a certain news channel every day and always see stories about [group of people] doing [thing you disapprove of], you might think that there was something wrong or inferior about [group of people] that causes them to do [thing you disapprove of], rather than something more subtle.
I was of the same opinion. But I was worse than you. I believed that the rule was "each nth number is the nth power of the first one, with n=[1,2,3]". Hence, 2^1, 2^2=4, 2^3=8. I tried several. 3,9,27; 5;25;125; 128; 16384; 2097152. All yeses. Then I tried 1,1,1. I got a "no". But the amount of positive evidence toward my hypothesis was overwhelming. I thought that was a bug.
I have no way to prove this, so you'll have to believe me on this one-- My "Theory of Knowledge" class in high school did this puzzle, and the first two to get the answer confidently both ended up in college for computer science. Pretty interesting-- you've learned with computer science, and others who have it, whether "it" is talent or whatever, appear drawn to fields where it's applicable.
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!
A little off-topic, but... most of the discussion here seems to be focusing on the fallacy presented, but I would just like to point out how amazing it is that, with such a small number of data points, we as humans can latch on to an entirely plausible pattern. More data may show that pattern to be incorrect, but, with surprising frequency, human intuition can come up with a rule that fits at least partially. In my experience as a programmer, trying to get a computer to achieve the same result typically involves pre-programming different patterns to check for. There are, of course, numerous strategies that can be employed, but the complexity of the program appears to quickly surpass that of a simple glance.
Confirmation Bias! Interesting. I learned a lesson! The rules of that test might need to be rephrased to be completely fair, however. I assumed there was a game aspect to it--that, you were penalized in some way for each guess, or that there was a penalty for guessing one that didn't fit the sequence (a "no" answer). I might have approached that differently being made to feel comfortable for guessing wrong. As a teacher, I go out of my way to make sure my students know it's okay to be wrong.
I wish they had chosen 2, 4, and 7. That would have made it more challenging for me. I thought the answer was the previous output x2 for sure, but since that also works and is not incredibly a difficult math problem, I feel the test doesn't really prove much about how I think.
Maybe I'm the one who misunderstood the puzzle, but isn't that basically the point? They are trying to trick you into thinking that the rule is "each number must be double the last", when it's actually much simpler. That way, if you don't try numbers that doesn't obey the rule, you won't realize that you've got the wrong theory. I can't think of any obvious incorrect rule the sequence 2, 4, 7 would fit, so people may have stumbled across the correct answer only by verifying correct sequences.
I see your point. However, I don't think that leading someone down a certain path just to pull the rug out from under their feet is the best way to prove a point. There's not a lot of self-discovery going on here. It's just that the creators would rather lead you to where they want you to go than have you lead yourself.
Maybe I'm trying to make it more complicated than it needs to be. FWIW, it was an interesting exercise and completing it made me think more critically about the project. Mission accomplished!
Except that neither 0, 0, 0 nor -1, -2, -4 worked.
That was pretty fun. I'd never done anything like that (at least that I remember). At first I though they were all powers of two, but since every sequence I was trying was passing the test I started putting really random sequences until I found some that failed the test.
Same. I guessed 1-1-1 to see if it was addition or exponentiation.
I wish there was another test besides this one that people always use. Hearing about it once means my brain immediately goes to the correct solution I've heard before when you say match the pattern and start with 2 4 8. It's not exactly testing if I've gotten the concept down at that point.