This Simple Maths Puzzle Will Melt Your Brain

Adding and subtracting ones sounds simple, right? Not according to the old Italian mathematician Grandi — who showed that a simple addition of 1's and -1's can give three different answers.

Wait, what? If that sounds like it makes no sense that's because... well, it doesn't really. But better let Dr James Grime explain it to you rather than me. Prepare to scratch your head. [YouTube]


    When did Martin Short dye his hair blonde?

    why did he not mention BIDMAS? Adding brackets changes the equation, that's why he gets 3 different answers.

      B[IO]DMAS is only relevant if the equation includes operations that otherwise have different orderings; e.g. is a mix of addition and multiplication. For example (1+3)+5 = 1+(3+5), 1*(3*5) = (1*3)*5 but (1*3)+5 != 1*(3+5)

    The problem is we're trying to seek a definitive answer, but it depends on what definitions you accept. Do you accept partial sums? Do you accept the averaged sums? All the answers are technically correct, they just depend on what version you accept.

    OK. Now to think of something incredibly clever to say...
    I got nothin'.

    Adding brackets where ever you like changes the equation, but in this case it highlights the two different answers by moving the last element in the infinite series to the front.

    It's an infinitely varying series, so it really depends on then you stop, which doesn't make it seem infinite anymore. It's like saying "what's the last digit in the result of 9 divided by 11?".

      Yep. Technically, this is a non-convergent series, so talking about an infinite sum is completely ridiculous. Any finite sum is equal to either 0 or 1 depending on if the amount of terms is odd or even.

    This video is embedded in the page on an image of a Samsung Smart TV. Now I can't watch it because I feel the TV is quietly judging me.

      It is. Korean TVs always do better at maths and science than Aussie TVs you know.

    It looks like he stuffed up in his second possible placing of the brackets:
    The extra addition symbol between 1 and the first set of brackets [as in: 1+(-1+1)... ] changes the equation [the extra addition symbol in there makes zero sense].
    It should really be: 1-(1+1)-(1+1)...
    Almost everything past this first error is just mathematical waffling.

    Last edited 27/06/13 7:09 pm

      Mmmm, pretty sure he did it right - his demo is about grouping them not changing them. The additional + symbol changes nothing. Your placement of the brackets in "1-(1+1)-(1+1)" actually changes the sign of the second 1 in each of the bracket sets (you're making it negative). You could write out the same series like this:
      (+1) + (-1) + (+1) + (-1) ...
      Now try grouping them. Do you see my point?

    If that particular equation has no end then there is no answer

    Ok, I'm no math expert... but these (Grandi's series and Thomson's Lamp) are Infinite series.
    In the case of Grandi's series where the number of terms (n) is even the answer is zero, where n is odd the answer is one (as the starting point is 1), that's great, but as it is an infinite series (n=infinity) and infinity is neither odd nor even, there is no answer, end of story. The same aplies to Thompson's Lamp. It's not really a puzzle as a puzzle has an answer.

    If you want some fun try to convice people that point nine recurring (.999....) equals one (1). It is true, but most people refuse to beleive it even it you give half a dozen provable explanations.

    This is the single stupidest thing I have ever seen... You have changed the equation by adding in brackets wherever you please, thus it is 3 separate equations. Why in the actual f--- would you make a video on this? Why would you legitimately post this as "news".

    The only thing that has caused my brain to melt is the blinding fury at how stupid this is


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