You Can Solve This Maths Problem, But Can You Solve It Correctly?

It's never too early for maths sequence riddles. Veritasium's Derek Muller offered a selection of strangers a simple sequence of three numbers -- 2, 4, 8 -- and asked them to determine the rule governing the sequence. It's not what you think.

Actually, it is what you think, meaning the problem Muller presents here is meant to challenge how you approach problems. There is a standard way to work out the sequence, but how do people react when the standard way fails?

Can You Solve This? [YouTube via VVV]


    I can't watch the video while I'm at work but I'm going to hazard a guess and say this is that experiment where you give someone a sequence and ask them to create rules for that sequence, and what rules they come up with determines how they think.

    The sequence "2, 4, 8" can follow a number of rules. The most obvous is that the number doubles each time so to continue you could say it "16, 32, 64...". But if someone said the next number is 32 instead of 16 you'd get confused. You could create a more complex rule where you multiply the two previous numbers or something. 2x2 = 4, 2x4 = 8, 4x8 = 32, etc. But then maybe they will say the next number is something ridiculous like 1,017,984 and throw out your pattern completely.

    Few people will come up with the most simple rule that the sequence obeys which is just "ascending".

    Last edited 26/02/14 12:38 pm

      What if 'my rule' is 'there is no rule and you can have whatever numbers you want' :P

      Or the rule is they have to go up each time, so you can't have 7,9,2.

      EDIT: Haha, yeah it was exactly that! I should have watched the rest of the vid first.

      Last edited 26/02/14 12:53 pm

      No!! Maybe the simplest rule is just "radom".

    I know! All the things in this sequence are NUMBERS!

    I'm so damn smart.

    I fail to see the relevance this has for games.

    Everyone knows the only piece of mathematics that is involved with games is Tower of Hanoi.

      It's 100% relevant, but not because of numbers or math or what the answer may or may not be. It's all about patterns.

      Games (and life in general) are all about recognising patters, whether it's the sequencing of plot devices, boss-fight approaches, risk-reward of buying certain items over others, whether to pull the trigger or not, etc. As gamers we learn to recognise and react to patterns in various ways, which is why we tend to perform better than non-gamers in spatial reasoning tests a lot of the time; we're training constantly.

      The point of this example is precisely its low starting criteria, and the broad complexity it still allows if you apply some thought to it.

        There was no pattern here, his numbers were not adequate to define his rule in and of themselves which makes it fundamentally flawed. He is essentially tricking people (in an almost mocking manner) and setting them up to fail for no practical reason. The correct answer was and is x2, by trying to make them "guess" his particular rule it serves no real purpose. They have already solved it by already recognising the basic patterns and can not learn anything more from it.

        So i disagree with your conclusion, this is irrelevant. Everyone knows that to prove something you try to disprove it which often gives you more information, there was no inspired moment or light bulb conclusion/revelation to this video it was just a person giving pointless numbers then hand feeding them the information slowly until they got HIS "sequence". I can sum this entire video up as guy try's to teach scientific method in roundabout way to confuse random strangers.

        It has no point or purpose.

          It was supposed to be a lesson on the scientific method and confirmation bias; that it is at least as important to try to prove your theory wrong as it is to confirm it is right.
          I think of the question in more programmatic terms, however. I think it is important to test all possible variations of sequences, regardless of whether you think they will provide an affirmative answer, because it is not the wrong answers that define what is right, but the boundary cases on each side of right/wrong.

            Here's an interesting proposal: I propose that all palindromic numbers with 4 digits (1441, 9779, 5665, etc) are multiples of 11. Prove this true or false.

              I've done that one before, and is really easy to test given how few four digit palindromes there are (100), which is made simpler again because the increment between each in the same thousand block is 110, which reduces the number of required tests to 10. The number is reduced to 2 once you realise that the increment between each thousand block is 1001.
              So, test that 110 and 1001 are both divisible by 11, then the problem is solved.

              That said, you'd need to prove that these are the only four digit palindromes, so given how quick any vaguely modern computer can handle these calculations, it is probably easier and would not be noticeably slower to just test every number from 0000 to 9999 to see if it is a palindrome, and then check if it is divisible by eleven. A single false would prove the hypothesis false, but that won't happen.

              The moral of the story is, this is a case where it is easier to prove something on paper than with a computer, due to the eccentricities of most programming languages (that make it awkward to treat a number as a string).

    Math problems should never be reworded. Ever. English is ambiguous; mathematics is (generally) not.

    Your wording implies this is rule seeking based on one sequence: 2,4,8 - find any rule that validates that sequence and it's solved. His implies he has one rule in mind, which validates 2,4,8 (but doesn't define its elements, but only validates them), and encourages you to discover the rule he is using by applying it to different sequences.

    That said, I take issue with word problems in general. "I have three apples, and I take two away, how many do I have?" "Well, where did you put them? Did you give them away? Then you have one. Did you put them in your pocket? Then you still have three. Did you leave with the two apples, thereby leaving one behind? Then you have two, and I have one." Any wonder I failed probability in 3U maths... Give me conic sections and calculus any day.

    The rule is the numbers must appear in ascending order.

    The great thing about maths is that each problem can provide a definite answer. This goes against that, just like all those people on Facebook with those questions with brackets in them and then people get all high and mighty saying 'you lot are using the wrong kind of maths, you're all stoopid'

      It's like any word puzzle or lateral thinking problem that provides you with a scenario based around an already defined solution, and all the answers which could be correct are considered wrong solely because they're not the one you're supposed to think of.

      E.g.: "A man is hanging from a rafter above a poolpuddle of liquid"
      Sure, the "correct" answer is he hung himself by standing on a block of ice and waiting for it to melt. But another perfectly plausible scenario is that someone else hung him there and he voided his bladder post-mortem.

      Last edited 26/02/14 4:50 pm

        Pool is the wrong word, i think you meant puddle. Pool can be misconstrued as a large body of water and would rule out your first answer. :P Which is basically this entire article and video

        There was no maths problem it was basically some guy trying to trick people for no reason, by using words and terminology that was designed to mislead the individuals. IT was presented as a math's problem, it isn't, it was alleged to have a sequence, it didn't. Almost everything was used to put the person down the wrong path, the whole thing was asinine.

          Ha, yes! Pool presents an entirely different scenario to the one I intended!

          I guess the verbal equivalent of this is the words ending in "gry" thing, which XKCD does a perfect job of critcising, so I will just link you there for the sake of the reference being understood.

    I think the issue is more to do with the awful click bait article headline.

    For one, it's not a maths problem but a logic exercise.

    Two, it created an implied challenge to solve from that sequence disregarding the fact that wasn't really part of the challenge at all. Those numbers were near meaningless and a slight red herring, to compare to @os42's apple example those numbers are merely the apples. Meant to be disregarded by a critical thinker.

    It's a nice example of a way some of our internal biases play out and a decent share, but it isn't even close to being a maths problem.

      It actually seemed like a lateral thinking puzzle to me.

        I had meant to reply to @cufcfan616 and his comments about a definitive answer.

        I definitely agree about it being a lateral thinking puzzle though, just not maths.

    The rule is any increasing number. It is a study in confirmation bias

    It was a bit difficult to figure it out going purely by other people's guesses, but I had it about 30 seconds before they revealed it. I'd have been a bit disappointed if I didn't get it because my job involves a lot of investigation and testing which requires you to think of both the negative and positive cases.

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