A Quick Puzzle to Test Your Problem Solving

I&#x27;m curious to see more about the distribution of questions and answers people had, and how the HN population may differ from the NYT&#x27;s. There will certainly be self selection bias here, but if you&#x27;re willing to share how you did with others, please enter it here: <a href="https:&#x2F;&#x2F;docs.google.com&#x2F;forms&#x2F;d&#x2F;17e5BIL0lH8OHsGj89Zdtdl8GeCVLC8TbMxsPApGcSGg&#x2F;viewform" rel="nofollow">https:&#x2F;&#x2F;docs.google.com&#x2F;forms&#x2F;d&#x2F;17e5BIL0lH8OHsGj89Zdtdl8GeCV...</a><p>The result summary is visible here: <a href="https:&#x2F;&#x2F;docs.google.com&#x2F;forms&#x2F;d&#x2F;17e5BIL0lH8OHsGj89Zdtdl8GeCVLC8TbMxsPApGcSGg&#x2F;viewanalytics" rel="nofollow">https:&#x2F;&#x2F;docs.google.com&#x2F;forms&#x2F;d&#x2F;17e5BIL0lH8OHsGj89Zdtdl8GeCV...</a><p>The raw answers are visible here: <a href="https:&#x2F;&#x2F;docs.google.com&#x2F;spreadsheets&#x2F;d&#x2F;1ZxR2_eOUtNLXwgKfLO1JWhiXx-UQOxsYlKaBFe7f3m0&#x2F;" rel="nofollow">https:&#x2F;&#x2F;docs.google.com&#x2F;spreadsheets&#x2F;d&#x2F;1ZxR2_eOUtNLXwgKfLO1J...</a>

It responds &quot;No&quot; to (10000000000000000, 10000000000000001, 10000000000000002) so the rule is not so simple after all :)

I ran this experiment for a while (code at <a href="https:&#x2F;&#x2F;github.com&#x2F;darius&#x2F;wason" rel="nofollow">https:&#x2F;&#x2F;github.com&#x2F;darius&#x2F;wason</a>, derived from <a href="http:&#x2F;&#x2F;lesswrong.com&#x2F;lw&#x2F;g2&#x2F;positive_bias_test_c_program&#x2F;" rel="nofollow">http:&#x2F;&#x2F;lesswrong.com&#x2F;lw&#x2F;g2&#x2F;positive_bias_test_c_program&#x2F;</a>).<p>In my logs most people seem to have gotten it right, though presumably that&#x27;s because it was linked from LessWrong.<p>For an actually-fun game like this, see <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Zendo_%28game%29" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Zendo_%28game%29</a>.

Derek Muller of Veritasium has done this test over a year ago on people in one of his videos: <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=vKA4w2O61Xo" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=vKA4w2O61Xo</a><p>I&#x27;ve given the test to various people since then and never once came across someone who&#x27;d guess it right away, or within a short period of time. The breaking time came usually after a few minutes when they gave up and started throwing out random numbers that coincidentally did not meet the rule. Once you hit the first &quot;No&quot;, it took a very short time to figure out the rule for almost everyone.

More or less related: when I&#x27;m looking for constructive criticism from someone, I&#x27;ll ask them &quot;what do you dislike about this?&quot; or &quot;what&#x27;s wrong with this?&quot; instead of &quot;what do you think?&quot;<p>I tend to get much more interesting and useful feedback this way.

function judgeSentence(sentence, numNo)<p>var probablyWrong = [&quot;doubl&quot;, &quot;expon&quot;, &quot;multipl&quot;, &quot;^&quot;, &quot;<i></i>&quot;, &quot;power&quot;, &quot;two&quot;, &quot;2&quot;, &quot;twice&quot;, &quot;as big&quot;, &quot;nth&quot;, &quot;rais&quot;];<p>var seemsRight = [&quot;larger&quot;, &quot;increas&quot;, &quot;greater&quot;, &quot;small&quot;, &quot;less&quot;, &quot;big&quot;, &quot;&gt;&quot;, &quot;&lt;&quot;, &quot;go up&quot;, &quot;ascending&quot;], weaselWords = [&#x27;but &#x27;, &#x27;not &#x27;, &#x27;odd&#x27;];<p>Been expecting something more interesting than that

The comments here suggest people are missing the full significance of this problem. It&#x27;s not just a cute number puzzle - it demonstrates a profound human weakness that has a deep impact in everything we do.<p>1. People that think having a gun in the house makes it safer will not try to design an experiment designed to demonstrate the opposite.<p>2. People who think organic food is better for you than regular food will not try to look for evidence that the two types of foods are equally healthy.<p>3. An Israeli who believes the area where he lives was uninhabited before 1948 is not going to think about what kind of evidence would contradict that belief.<p>I&#x27;m not saying the views above are incorrect. It&#x27;s just that we are all guilty of falling in love with our beliefs when they should be mere acquaintances. Hence the quote, &quot;People don&#x27;t change their minds. They die, and are replaced by people with different opinions.&quot; [1]<p>[1] <a href="http:&#x2F;&#x2F;www.paulgraham.com&#x2F;quo.html" rel="nofollow">http:&#x2F;&#x2F;www.paulgraham.com&#x2F;quo.html</a>

Funnily enough, I notice confirmation bias quite a bit in a D&amp;D game I am currently DM of. I&#x27;m playing with a group of friends who are big into video games, and as a result they consistently seek resolutions to conflicts in D&amp;D by way of what they know from shooters: kill everything in sight. Yes, it&#x27;s at times a valid answer, but it&#x27;s not the only one and it&#x27;s certainly not the most interesting one. The best way that I&#x27;ve seen the confirmation bias dissipate from their thinking is to put them into situations where their bias just doesn&#x27;t help at all.

If anyone&#x27;s curious about the raw numbers, I found the counts here:<p><a href="http:&#x2F;&#x2F;int.nyt.com&#x2F;newsgraphics&#x2F;2015&#x2F;2015-06-26-rule-guessing-game&#x2F;numno.json" rel="nofollow">http:&#x2F;&#x2F;int.nyt.com&#x2F;newsgraphics&#x2F;2015&#x2F;2015-06-26-rule-guessin...</a><p><pre><code> {&quot;count&quot;: 27723, &quot;numNo&quot;: 0, &quot;share&quot;: 0.7716051100782098} {&quot;count&quot;: 2921, &quot;numNo&quot;: 1, &quot;share&quot;: 0.08129922903504133} {&quot;count&quot;: 1883, &quot;numNo&quot;: 2, &quot;share&quot;: 0.05240891758746417} {&quot;count&quot;: 1285, &quot;numNo&quot;: 3, &quot;share&quot;: 0.035764980934621056} {&quot;count&quot;: 880, &quot;numNo&quot;: 4, &quot;share&quot;: 0.024492749589468118} {&quot;count&quot;: 525, &quot;numNo&quot;: 5, &quot;share&quot;: 0.014612151743716774} {&quot;count&quot;: 288, &quot;numNo&quot;: 6, &quot;share&quot;: 0.008015808956553202} {&quot;count&quot;: 156, &quot;numNo&quot;: 7, &quot;share&quot;: 0.004341896518132985} {&quot;count&quot;: 108, &quot;numNo&quot;: 8, &quot;share&quot;: 0.0030059283587074506} {&quot;count&quot;: 56, &quot;numNo&quot;: 9, &quot;share&quot;: 0.0015586295193297892} {&quot;count&quot;: 45, &quot;numNo&quot;: 10, &quot;share&quot;: 0.001252470149461438} {&quot;count&quot;: 11, &quot;numNo&quot;: 11, &quot;share&quot;: 0.00030615936986835146} {&quot;count&quot;: 22, &quot;numNo&quot;: 12, &quot;share&quot;: 0.0006123187397367029} {&quot;count&quot;: 8, &quot;numNo&quot;: 13, &quot;share&quot;: 0.00022266135990425562} {&quot;count&quot;: 4, &quot;numNo&quot;: 14, &quot;share&quot;: 0.00011133067995212781} {&quot;count&quot;: 5, &quot;numNo&quot;: 15, &quot;share&quot;: 0.00013916334994015976} {&quot;count&quot;: 3, &quot;numNo&quot;: 17, &quot;share&quot;: 0.00008349800996409585} {&quot;count&quot;: 1, &quot;numNo&quot;: 18, &quot;share&quot;: 0.000027832669988031953} {&quot;count&quot;: 3, &quot;numNo&quot;: 20, &quot;share&quot;: 0.00008349800996409585} {&quot;count&quot;: 1, &quot;numNo&quot;: 21, &quot;share&quot;: 0.000027832669988031953} {&quot;count&quot;: 2, &quot;numNo&quot;: null, &quot;share&quot;: 0.000055665339976063906}</code></pre>

The puzzle is not nearly as interesting as the code being able to understand my answer!<p>My answer: <i>The numbers increase from left to right</i><p>Application response: <i>As you seem to have guessed, the answer was extremely basic</i>

Neat - as others have pointed out, I feel that being familiar with unit testing would help in this situation. Having negative test cases is just as important, if not moreso, than having &quot;happy path&quot; tests.

This phenomenon has had a profound effect on the history and philosophy of science. There have been entire schools of thought based on verification of hypotheses, and entire movements based on refuting those schools. The most effective strategy in this puzzle(and the one that is unintuitive for many) is to systematically generate alternative hypotheses and falsify them. Karl Popper claimed that this method is actually at the core of how we gain scientific knowledge, and his brand of philosophy of science is the most popular and arguably the most successful today.

I think that the &quot;quick&quot; adjective in the title is purposeful misleading. You are supposed to learn quickly the most general rule, but that is not so easy because there are many possible rules that could fit such a pattern. It seems that you should be rewarded for solving the puzzle quickly and then you fall in the trap. I propose to change the title to &quot;A puzzle to test your Generalization Abilities&quot;, and state clearly that you should try to find the most general rule that satisfies all patterns you can think of. In that case, I would expect the conclusion and results of the experiment to be completely different. So to summarize: the so &quot;quick&quot; adjective in the title has a very strong anchor effect.<p>Edit: changed for grammar and to express more clearly what I think.

Cool. The funny thing is I inserted a constraint of my own invention without even realizing it: &quot;Use the fewest number of examples possible.&quot; Of course, this meant failing miserably, and was nowhere in the problem statement.<p>Perhaps that&#x27;s an additional factor - not exactly confirmation bias, but not unrelated.

Wonder how many people here immediately knew what the rule was?<p>This is the standard example of to right way to test a hypothesis&#x2F;theory and the power of Confirmation Bias, testing sequences that are invalid under the theory instead of testing what you think is correct.

While the HN crowd mostly gets this right when framed as a math puzzle, my guess is that confirmation bias is alive and well in high tech just like in any other field. One example:<p>Young 20s entrepreneur vs. early 50s entrepreneur. Without knowing anything about either person, which startup is more likely to succeed? Even if you have the business plans for both, and you meet both - which one are you going to be more skeptical about as you evaluate which one of them gets funding?

Reminds me of the game mastermind which I loved playing as a kid.<p>Here&#x27;s a javscript version: <a href="http:&#x2F;&#x2F;www.archimedes-lab.org&#x2F;mastermind.html" rel="nofollow">http:&#x2F;&#x2F;www.archimedes-lab.org&#x2F;mastermind.html</a>

I&#x27;ve heard of intelligence failures to explain the Iraq war, now this author says it was confirmation bias which caused a completely erroneous justification for the invasion of Iraq. I think the author has confirmation bias in too easily using the term to explain government and corporate policy choices which have been based on false justifications.

Math person here. I&#x27;m curious to know if anyone used decimal numbers in their tests and if negative numbers were used. The rule is increasing real numbers and one can guess that the rule is increasing numbers without realizing this includes all real numbers and not just integers.<p>In addition to getting it right did you use an exhaustive set of tests?

Does laziness have anything to do with the responses? You get a rule that seems to work and so you seek the reward early. It takes effort to prove yourself wrong.<p>I was trapped by this and guessed it was exponential series n^1,n^2 etc for n starting at greater than 2. While technically true this was not the rule they had in mind.

People try to make the fit be as tight as possible to the sample data -- the explanation is that simple. I don&#x27;t buy the explanation provided in the article.

I got 7 yes, 5 no, and was still wrong. Maybe I&#x27;m just dumb.

The &quot;Check&quot; buttons weren&#x27;t enough of a hint for me and I jumped into &quot;This is a numerical reasoning problem&quot; mode. I&#x27;d argue that this kind of situational bias is as much a factor here as confirmation bias.

I understand the power of confirmation bias. I believe it to be natural for anyone. It&#x27;s perfectly normal to seek an explanation that fits the already built cognitive structures, developed through experience. It&#x27;s unreasonable to simply jump into new paradigms everytime we encounter a new fact. It takes time to prove that it doesn&#x27;t fit, and then we start looking for new explanations.<p>However, the test simply required a possible solution. There are plenty solutions and it&#x27;s absurd to think they have the simplest one. The simplicity of the rule is subjective, in that is evaluated differently by different people. The famous &#x27;simple but no simpler&#x27; is relevant here. As long as we were not told to look for the simplest solution, ALL solutions are equally probable. That being the case, I started to with the first solution that popped into my mind. I sticked with that because of my psychological state. Some searched for other solutions.<p>I don&#x27;t think that getting an YES was the main driving force. Of course it feels good to get an yes. This is fundamental in human relations. But it&#x27;s not the whole story. People do not disbelief globar warming because they want to get an YES. The reason is much deeper. Just as many, so many people go to the wave of climate change because it&#x27;s fashionable, it makes them feel good, accepted , part of the mainstream. Being a climate change denier is being a disident this day (not my flavor of disidentism), and being a disident is not for everyone. And perhaps disidents picking their fight have complicated reasons for doing so.<p>I went with the doubles.

I remembered this puzzle from HPMOR, but either way this is just writing a unit test.

This looked like a puzzle I had seen before, so I assumed this was the case (testing a few sequences just to verify) and turned out right.<p>I guess the conclusion is that if a problem looks suspiciously like one you&#x27;ve encountered before, there&#x27;s a good chance that they are the same or similar. The world is self-organizing, not completely random where you must obsessively second-guess your accumulated wisdom.

Anyone played Monkey Island 2?<p>There&#x27;s a puzzle with a doorman, there&#x27;s a few distracting clues where the answer is actually very simple.<p>It doesn&#x27;t offer confirmation bias though, and it took some time to figure it out.<p>I consider it a very similar test.<p>So one could actually construct such a test without the confirmation bias part, and then look at how long it takes for people to realize the simple model.

&gt; A mere 8 percent heard at least three nos<p>I guessed correctly with only 2 nos. Since there is no penalty for guessing incorrectly here, I felt safe enough with my theory. I might have checked for more nos, if I had to announce my theory publicly (Twitter, comment, etc). However, I also knew about Confirmation Bias beforehand.

For a more extensive version of this article, see &quot;Mistakes Were Made (But Not by Me)&quot;:<p><a href="http:&#x2F;&#x2F;www.amazon.com&#x2F;Mistakes-Were-Made-But-Not&#x2F;dp&#x2F;1491514132" rel="nofollow">http:&#x2F;&#x2F;www.amazon.com&#x2F;Mistakes-Were-Made-But-Not&#x2F;dp&#x2F;14915141...</a>

Seems busted now - clicking the &quot;I think I know&quot; button does nothing. I thought the answer was:<p>Let the first number be x. If x is 0, then the second number is 1. Otherwise, the second number is two times the absolute value of x. The third number is 2 times the value of the second number.

Veritasium covered this classic puzzle &#x2F; bias test nicely, last year. <a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=vKA4w2O61Xo" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=vKA4w2O61Xo</a>

So, am I supposed to feel bad if I assumed it was some tricky, hard to figure out function? It just reminded me of those questions on the ACT or whatever and I froze up and got frustrated.<p>Am I a dim bulb?

I&#x27;m a data scientist, and it relieved me no end that I got this one right: <a href="http:&#x2F;&#x2F;i.imgur.com&#x2F;V5oJ4i4.png" rel="nofollow">http:&#x2F;&#x2F;i.imgur.com&#x2F;V5oJ4i4.png</a> I would have had second thoughts about my career choice if I got this wrong :)<p>The correct approach for any data modeling problem is to think in terms of entropy. Each subsequent approach should minimize entropy, until you reach diminishing returns.

I guess I&#x27;m the opposite: I got more No&#x27;s than Yes&#x27;s. My immediate sense was to find No&#x27;s. I guess that&#x27;s why I like 1 star reviews.

My explanation to the scarcity of &quot;No&quot;s: people are used to seeing in these puzzles mostly sub-types of increasing series: exponential, linear, etc. By the time they had ruled out these sub-types, and had resorted to guessing &quot;ascending&quot;, they wouldn&#x27;t have encountered even a single No.<p>I predict that if the rule was narrower, like &quot;exponential&quot;, much more guesses would have yielded No&#x27;s.

Wish I could have done this with no previous knowledge of the puzzle, I knew it right away because I saw the exact same problem in a Veritasium video.

I think the first-known matching pattern plays a huge role. The original 2,4,8 sequence, for example, locked me in immediately to doubles of the previous number (causing me to test 1,2,4 and 7,14,28 and such). Had it been a different starting sequence (like 3,9,27), I might&#x27;ve based my guesses differently. Same for 1,2,3.<p>In other words, first impressions really <i>are</i> important.

<i>They don’t want to hear the answer “no.” In fact, it may not occur to them to ask a question that may yield a no.</i><p>So the author&#x27;s obviously never heard of sanity checking, in fact that&#x27;s the second thing that I always do once I confirm a solution is to confirm it&#x27;s not a fallacy.<p>Having said that, my solutions were -10 -20 -40 -10 -8 -4 1024 1026 1030<p>and I said it was +2, +4 and got it wrong!

Veritasium video on the same thing<p><a href="https:&#x2F;&#x2F;youtu.be&#x2F;vKA4w2O61Xo" rel="nofollow">https:&#x2F;&#x2F;youtu.be&#x2F;vKA4w2O61Xo</a>

Reminiscent of the folding table libertarians with their questionnaire and that political cartesian coordinate chart. &quot;You answered that &#x27;it&#x27;s wrong to steal&#x27;, [...psychobabble...], on this science graph it appears you&#x27;ve always secretly been a libertarian, we meet at the cinnabon on sundays&quot;.

My process was [1, 2, 3], and then I guessed each number is greater than the last.<p>It was totally a possibility that they wouldn&#x27;t apply the simplest rule, but I felt it highly unlikely. This &quot;rule&quot; is a meme of the rationality community, especially given the example, so it seemed pretty likely that it was sequential numbers.

did anyone else only try even numbers? guess &quot;increasing even numbers&quot;<p>pretty interesting how in-the-box my thought process was

Umm... Not sure what&#x27;s so special about it. Isn&#x27;t that what all programmers and science people do all day?

Veritasium, a pretty interesting youtube channel, posted a video on this experiment a while back. I found the discussion afterwards to be more thought-provoking than this article.<p><a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=vKA4w2O61Xo" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=vKA4w2O61Xo</a>

Constraints allow for only integers &lt;= 9999999999999999 and &gt;= -9999999999999999 which is interesting considering (-)10000000000000000 through (-)9223372036854775807 are also within the bounds of a 64 bit integer.<p>It&#x27;s ironic that these facts are not mentioned considering the article is about confirmation bias.

The attached reading material is interesting, but this question is too similar to problems where you guess the next one in the sequence and none are missing.<p>A rule where the numbers are increasing does not explain why 3 or 5 or 6 is missing from the sequence in that version of the question that is much more common.

I failed it again... Every time I take a test like this I ended being fooled by the confirmation bias.

My mathematical logic is rusty, but if I recall correctly, Gödel&#x27;s incompleteness theorem basically states that it is impossible to solve this kind of question. No matter how many tests you run, there will always be an uncertainty.<p>An incredibly stupid example is that the rule could be &quot;yes for strictly increasing, OR if one of the numbers is -18273192783127897981.&quot; You&#x27;ll never know.<p>I understand this is contrived, especially when the test subject doesn&#x27;t know. But if you do realize this while doing it, it makes the test a little frustrating..<p>EDIT: I see people are making a connection with unit testing, and the irony is poetic. This is precisely the problem Dijkstra was talking about when he said that &quot;Testing shows the presence, not the absence of bugs.&quot;

There is no penalty to being told &quot;no&quot;. That <i>also</i> applies to &quot;I think I know the answer&quot;. There is no penalty for being told &quot;no&quot; there as well, so once you have a reasonable guess why not check it? Disagree with their analysis.

I don&#x27;t seem to be able to submit my answer or follow the link to see the answer for &quot;just tell me the answer&quot; is this supposed to be a trick or is my browser just not capable of properly following those links? Using Chromebook.

Anyone tried entering letters in the boxes? I didn&#x27;t. I think <i>that</i> would have been an unexpected twist.<p>So, after all, I think I fall in the trap of confirmation bias that the sequence must consist of numbers only.

After total of 13 answers including 6 &quot;no&quot;, I guessed it right :)

the questions is somewhat ambiguous. it would be more interesting to see what happens of people really understood the question and if they had a real motivation to get it correct.

The same experiment: <a href="https:&#x2F;&#x2F;m.youtube.com&#x2F;watch?v=vKA4w2O61Xo" rel="nofollow">https:&#x2F;&#x2F;m.youtube.com&#x2F;watch?v=vKA4w2O61Xo</a>

Decimals and negative numbers still get you a &quot;yes&quot; as long as you obey the rule. However, the button to submit your answer didn&#x27;t work for me.

My first assumption was x,2x,2(2x) - then I tested 0,0,0 and got a NO which disproved my first assumption... the answer is obvious after.<p>Did anyone else test 0,0,0?

I got it, but it took a bunch of guesses before I had the pattern. It&#x27;s a good example of how our preconceptions shape our answers.

We should all be doing good on this one if we have been practicing making our test cases are red first before turning them green :D

Confirmation bias affects Corporate America and Government Policy, but not science? Talk about confirmation bias :)

Have large numbers of HN people really not seen this riddle before? Maybe I read weird things.

After programming daily for more than a decade, I question my assumptions annoyingly often.

This doesn&#x27;t seem to work right for negative numbers. The article says the rule is &quot;each number must be larger than the one before it&quot;, but if you try -2 -4 -6 it says that pattern doesn&#x27;t match the rule.<p>Maybe I&#x27;m just being pedantic here, but last I checked -6 was larger than -4.

for anyone who hasn&#x27;t seen it Veritasium did a video on it.<p><a href="https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=vKA4w2O61Xo" rel="nofollow">https:&#x2F;&#x2F;www.youtube.com&#x2F;watch?v=vKA4w2O61Xo</a>

Sadly ive already seen Veritasiums test. so i was biased.

Nice game, got it right after 7 yes and 7 no

I thought..<p><pre><code> F(n + 1) = n * 2</code></pre>

Got it right with 7 nos.

Yup - Dick Cheney!

-10, 0, 0.01

That page prints the nyt logo in the javacript console (will probably look messed up here):<p><pre><code> 0000000 000 0000000 111111111 11111111100 000 111111111 00000 111111111111111111 00000 000000 000 1111111111111111111111111100000 000 000 1111 1111111111111111100 000 000 11 0 1111111100 000 000 1 00 1 000 000 00 00 1 000 000 000 00000 1 000 00000 0000 00000000 1 00000 11111 000 00 000000 000 11111 00000 0000 000000 00000 00000 000 10000 000000 000 0000 000 00000 000000 1 000 000 000000 10000 1 0 000 000 1000000 00 1 00 000 000 1111111 1 0000 000 000 1111111100 000000 000 0000 111111111111111110000000 0000 111111111 111111111111100000 111111111 0000000 00000000 0000000 </code></pre> NYTimes.com: All the code that&#x27;s fit to printf() We&#x27;re hiring: developers.nytimes.com&#x2F;careers

&quot;We’ve chosen a rule that some sequences of three numbers obey — and some do not. Your job is to guess what the rule is.&quot;<p>My mistake was to assume that choosing the first number uniquely defines the next ones in the sequence. Since, you know, like all the sequence puzzles I&#x27;ve seen before worked like that, and I didn&#x27;t read it rigorously enough. Oh, by the way, the doubling thing is wrong if you use negative numbers (wrong as in it gives false positives, instead of just false negatives). But the problem definition doesn&#x27;t even tell what set of numbers we&#x27;re operating on.<p>Finding the rule the sequences obey is impossible since it could be that all cases follow a simple rule except for one triplet which you&#x27;re unlikely to find. It&#x27;s trivially easy to fool the user into finding a wrong rule.

I got this wrong, but oddly enough my first attempt <i>was</i> a No. I tried, &quot;6, 1, 8&quot;<p>After that, I went with doubling and it worked 3 times with various sizes of number, so I went with that.<p>Double bonus points if you can guess what I was testing with the first sequence (which the given numbers do satisfy).

I liked this puzzle. It got me. I am thankful for it.

The official answer to this puzzle makes a huge assumption: that there is one correct answer. There is not one correct answer. (x, 2x, 4x) gives you a &quot;yes&quot; every time, therefore it is a correct answer, at least as automatically checkable, and there&#x27;s an infinite number of such tuples. To find a &quot;no&quot; you&#x27;re reduced to random guessing. That&#x27;s not a puzzle, that&#x27;s crap. The confirmation bias material might be true, but the puzzle does not illustrate it.