First, if you haven’t participated in the Saint or Sinner online survey please take part!

Second, here is the Friday puzzle.  Can you move one matchstick and still have an equation that is correct?  I think there are at least three answers – can you find all three?

As ever, please do NOT post your answers but feel free to say if you think you have solved it and how long it took.  See you all on Monday!

247 comments

    1. move one matchstick and have it STILL correct. The idea is to find other solutions which are correct or which there are at least 3.

      It should still be an equation with an equals sign following the correct mathematical conventions and using the characters a calculator or clock would use.

    2. thank you Clementine…… :} … and when the puzzle was first posted the “still” was left out and once the question was asked the “still” was added…… :}…..but Tortoriffic thanks I was wondering about the correct shape for the numbers…..that helped :}

    3. Got it – only took my about a minute because once you get the “second” one (which is a bit odd), the third one is quite easy 🙂

    4. Took me about 10 mins. The first two came within 2 minutes, but the last one took a bit longer. It helped to write the equation in normal figures (9-3=6) After that I had the solution very fast.

  1. The “following equation” is correct, but I can move a single match and make three additional correct equations, too.

  2. I can see two clearly legit answers pretty quickly, in addition to the trivial case of moving any match a tiny amount so as to leave the equation as is, and a class of at least three more that might be stretching the rules a bit.

  3. I got one right away. Still working on the other two. I may have to go back and watch Scam School. I believe this, or a very similar puzzle was on one episode.

  4. I’m clearly not able to focus but have come up with two besides the one he used as the puzzle and mt dyslexia{I transpose my numbers} isn’t helping me nor the late night / early am food ads on the TV…..I’m starving….lol…..I need water then I’ll maybe think better…….

  5. Water not helping me think more clearly……lol…question…..if I turned the {-} into {x} would that really be moving two match sticks and then not an acceptable answer? Anyone?

    1. well after a couple of minutes and getting the first two……I’m stuck….there are 20 matchsticks……maybe I’m not using the same/right shapes for my numbers….I wouldn’t use the bottom { _} on my 9 and such…… I’m going to try and give it a rest and come back later for a fresh look…….and if not able to think…..I’ll as Nick…….LOL…….

  6. Got 3 answers, but am i allowed to do somthing with the = sign? Then i might Get a few more. Please answer if anyone have an idea

    1. that’s what I’m wanting to know ….and if so doesn’t that then count as the one matchstick move? If you count the – and = as matchsticks giving you a total of 20 matchsticks……anyone else have some input?…. :}

  7. I can find 2 more correct equations after less than a minute, but will keep thinking.

    Was the word ‘still’ added to the line “Can you move one matchstick and still have an equation that is correct?” after people posted? I didn’t have a problem understanding that we were given a correct equation and were being asked to find more…

    1. I think so cause I haven’t re-read it til you just asked and I didn’t see the “still” in the puzzle and it was hard to fully understand….. :}

  8. Done… all three. Friday’s puzzles have been an excellent course of matchsticklogy, so it was not difficult nor long to find the solutions.

    1. After post my comment I went to look to others and came to those who claim to have found more than 3 answers so, I returned to the problem and… funny thing, not only I took much more time to find two of my previous answers but also, one of them is still missing. Since so many are saying a third exists, it is possible I found it and forgot, but I’m not so sure of that now.

      I’ll try again when more rested. I hope no one is confounding equations with inequalities (although being correct expressions) or writing 3 as a child would do… that’s cheating.

    2. Now that the puzzle has been rephrased to rule out inequalities, I have only the two definitely legitimate solutions that lots of people have posted, and the dodgy one where you move one of the matchsticks in the equals sign above or below the other. I’ll be interested to see Richard’s other solution.

    3. hmmm… I didn’t noticed the puzzle was rephrased. And why are you backing off at this point, Nick? While I been spinning off by yours more than three solutions, your remark about puzzle phrasing finally made its way to my mind: an equality and an equation is not the same thing!!!

      I was too distracted to note that until saw your comment. And being that true, there is indeed more than three solutions. Actually, besides the two solutions I found (Is nagging me the third solution I though I found but forgot… how convenient to forget it before finding it faulty… that’s my conviction), if indeed a “correct equation” is what we usually think it is, I find at least TWENTY more solutions to the puzzle (11 is with the puzzle rotated 180º).

      PS.: After come to this conclusion, I went to hunt other commentaries and saw that Joshua beat me to expose that aspect of the puzzle. However, I don’t agree with his arguments. If I remember correctly, an equation is simply the statement of an equality between two expressions. And now that I’m counter-arguing him, the two expressions don’t need to really be equal to lead to a correct equation: if I give the following equation to someone, x^2+1=0, no one is going to complain it is an incorrect equation, instead he will say it is an impossible equation. In this reasoning, 9-2=6 but also 5-3=6 or 5-3=9 are valid solutions to the puzzle. What constitutes an incorrect equation would be 5–3=5 or 5-3+9 because these either don’t make sense or are not equations. So to my 22 earlier solutions I’ll have to add much much more. I’ll stop here because this is not clearly the intended result for the puzzle… so my freedom to talk about it: I’m not spoiling any solution.

    4. It’s a math-off!

      You are right that “an equation is simply the statement of an equality between two expressions.” But what differentiates a CORRECT equation from an INCORRECT equation is whether the two sides is whether those two sides are equal independent of condition. 9-2=6 and 5-3=6 are absolutely incorrect. Let’s not get heady about everything. We don’t have to define base-10, we don’t have to argue the semantics of “incorrect.” The puzzle was clear in its intent, so an answer that flouts basic math like the two above are just not appropriate.

      x^2+1=0 is not incorrect, you are right, but not because it is “impossible.” That equation does have a solution: the solution is i, the imaginary number, equal to the square root of -1. That being said, my point stands that even that equation cannot be correct; it is simply VALID for x=i.

      The definition of a “correct equation” is one in which the two expressions on opposite sides of the equals sign are, in fact, equal in every possible scenario. For the sake of this puzzle (and quite honestly, for the sake of mathematics not devolving into meaninglessness), that’s not a matter of philosophy or linguistics or interpretation. That’s just what a “correct equation” entails.

      I appreciate your argument, I just don’t agree with it! 🙂

    5. Joshua,

      where are you getting your definition of a “correct equation?” I can’t find your version anywhere! In fact, the closest I get is when I look at rules for math competitions, but even there the equations are merely “valid” – just that they are also the equation the judges were looking for as a solution to a problem.

      I think you have chosen to create a definition to support your argument rather than rely on one that existed previously.

  9. You had me there for half a minute 😀 In answer to the above, yes it’s right now, but you can also move a matchstick to significantly alter it, creating another equation that’s also correct.

  10. Ok, I was just misleading. Didn’t read correctly the statement. In term of equations, I found only three (he he he…). The 14 I managed to find out were mostly non-equalities, which unfortunately are not equations.
    Sorry to have talked big.

    1. By the way… Cracking only eleven matches in eighty equal parts, can you prove the Tarski’s undefinability theorem ? o_O?

    2. Please don’t think my big willy was aim at you specifically. 😀 (Besides, check the time stamps.)

      I was just cracking wise. I can only get one solution.

    1. thank you Mr. Wiseman for removing the spoiler posts, now more will be able to enjoy through the week end….I see you are on the home page!

    2. Anywho got the three normal ones is about a minute, and 3 others that I do not think they were looking for but are correct none the less.

    3. I found 3…

      It took me one frikkin day! I feel stupid now…

      Actually i tried for an entire minute, and gave up (which i do pretty often), and now, when i wanted to show it to my girl one day later, the answer just appeared in my head…

      But the official time is one day.

  11. Sort of got an answer in hexadecimal but not sure where to put my spare match. Do we have to use the match?
    Also stood on head to do it but don’t think that’s cheating.

  12. Now I’m up to 5 but one is a bit bogus 🙂 The other four are certainly valid. I wonder if there are more!

  13. Got three in about 30 seconds.

    What amazes me are the number of people who continue to post answers, hints, etc. Do you people not read the instructions, or are you just simply rude?
    Read:
    [b]As ever, please do NOT post your answers but feel free to say if you think you have solved it and how long it took.[/b]

  14. I got two (the same two which some people later gave away) – still struggling to find the rest…

    Hmm…are we allowed inequalities (i.e. equations using the sign “≠”, as in A – B ≠ C) ? 🙂

    1. Don’t think so mittfh. Then it stops being an equation and the question states ‘still have an equation that is correct’.

      I am still stuck looking for the third if I have to use the match I have moved in the equation.

  15. I want to have inequalities – then I can find several more, but have just checked: equations must have an equals bah humbug!

    1. ..and the other two, but of course you won’t post those cos posting the answers is naughty!

      I’m still stunned how some now have got five solutions.

    2. Thanks Ji, thanks so much. I hadn’t seen that one yet, and now since you went ahead and broke the rules and posted the solution I don’t have to bother working my brain to try to find that solution. Except that working my brain is the whole reason I read the puzzle in the first place, and I never would have read your answer if it hadn’t happened to be right above my post after I found my first solution. So yeah, thanks for the spoiler and for reducing the amount of fun I can have with this puzzle.

  16. I’ve got one, took me forever because I kept looking for something harder or trickier. Still haven’t found any more and I feel rather dumb about it.

  17. Argggh, got the first two in under a minute but have been struggling with the third for some time now! I will succeed…eventually! 😉

  18. I DO like puzzles with multiple levels of solutions – that way they are exactly as hard as you want them to be!

    I came up with a few more than twenty, but the others cheat. Twenty seems to be my max.

  19. Hello,
    I do some math puzzle as well in my blog,
    I used to hold comments for moderation with 24 hours…
    the question is, many give up…
    those who claim they got it, are you sure?
    later, I let them see the solutions, and still, many got wrong…
    there are people before them who got it correct, but they still get their own wrong ones…

    thus,
    it is a hard issue to handle…

    Belly Laughs

    http://jingleyanqiu.wordpress.com/2010/03/03/belly-laughs/

    Doggone Funny

    http://jingleyanqiu.wordpress.com/2010/03/01/doggone-funny/

    Feline Fun

    http://jingleyanqiu.wordpress.com/2010/02/28/feline-fun/

    Guess what Am I

    http://jingleyanqiu.wordpress.com/2010/02/25/guess-what-am-i-side-splitters/

    check out these,
    you will see
    they are wrong all the way even I let the answer open!

  20. You take off the bottom part of the 9 or the top part of the 6. Took all of a few seconds. : ) I can’t figure out the 3rd answer though.

    1. Ooh, I didn’t get those!

      Where do you put the stick from there? Or are you interpreting “move” to mean “take off” and not “move to another part of the puzzle?”

  21. Reading some of the comments makes me think I have answers that are totally different from the ones some other people have. For example, I have no idea how the comment “the first two were the easiest” or something like “once you figure out the first two the third is easy” could possibly relate to the answers I got. This leads me to believe there are maybe at least 5 legit answers.

  22. I got the first one in a couple of seconds then the other two within a minute.

    That was fun (and my first (of many) Friday puzzles)!

  23. there are the 2 obvious answers, maybe a third, but there are several if you think outside the box (i.e. the not-equal-to sign).

    was that a spoiler? I don’t know.

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  25. It will be more fun using real matches. I just played on the image of this site. It’s not about being pround of how fast and easily solved. I think many people may agree it was fun doing this kind of puzzle at 6 years old…especially with your father or your uncle…

  26. I don’t know what you people are talking about. I think that there are only two solutions. That is, if you don’t count inequalities. There are many ones with greater than/less than or “doesn’t equal”. And changing the styling of letters is no good either. Those ideas would allow for more than 3 obvious solutions, I don’t think Richard Wiseman would have missed them

    I also don’t consider “E” to be the same as “3”, and I don’t think picking up a stick and putting it back down where it was constitutes “a move”.

    So are there really three solutions that avoid all these (or other) silly tricks?

    1. hey G I agree with you and I freely admit I’ve been looking at this for about 24 hours off and on now and still only find two that are in the same fashion as the equation Richard gave us with which to work. Maybe something will hit me and I’ll see the light….lol….

    2. I’m also only finding two solutions. The worst part is, when I first tried to solve the problem, I become convinced I had found the 3. I didn’t wrote them, I wrote here I had found it, I read some had found more, try again, discover I could get only 2 his time… what was the third I forgot? It’s frustrating. Maybe that’s what happened with the wonderful demonstration of the last Fermat theorem. He never wrote it despite the notes in the book margin saying he had found one, because he was never able to recall it again. Or more likely, the proof was flawed but having tried to seriously got it, it became convinced he has forgot it. That is what more likely happened to me. Or perhaps for a small amount of time, I lived on an universe with a different set valid math axioms (Greg Egan has a nice short story about that).

      My “childish 3” I said I was not going to accept, is the E of @The G. I see that he has also play with different angles. Another thing I’ll not accept as answer is to move a matchstich of the equal sign, to a paralel position above or below. Is it possible I’m wrongly interpreting the problem? Maybe is not solutions with one move after the original problem, but successive solutions where the equation is changed with one move, keeping always a legal form.

      Well, Monday is not too far.

    1. easy to fix Jerryfel just light up one of the other matchsticks to look for the dropped one….just watch your fingers the matchsticks burn fast….hehehe….

  27. Got 5 in about 10 minutes while watching the live Burton Toyota Pro webcast. What kind of handicap does that give me? Wait, don’t answer that.

  28. Solved it.
    Took about 10 seconds. Really.

    I wish I had skills that were actually useful in the real world. D’oh!

  29. I found a single method that will generate *tons* of solutions to this, although I’m not sure if it’d be considered “cheap” or not.

  30. Mmmh… Instead, it’d be funny to find the number of equations you can do that aren’t true.
    9=3-6
    9+3=E
    -93=6

    😀

  31. I got one answer in a couple of minutes. I have at least one second answer, but it’s kinda sneaky– I’m not sure it counts, although it’s literally true and only involves moving one piece.

  32. I only found two, and though many people claim to have found many more, the only answers anybody has posted have been those two. I also found this problem on YouTube, and many people posted illegitimate answers (see my earlier post for some description).

    My conclusion: there are only two legitimate solutions. The fact that nobody has posted a third solution means that the people who claim to have found more know that their solutions are stretching/breaking the rules.

    A guess: The problem was posted as having three solutions because either the “no change” answer is one of the three, the original poster can’t tell the difference between E and 3, or we’re subjects in an experiment to test our honesty… (cue imposing musics…)

    1. Hey G,

      before you assume no one has a correct answer you couldn’t come up with, perhaps you should check your assumptions.

      For instance, there are whole branches of mathematics that don’t use just numbers in equations and, hey, what do you know! you can change that 9 into a ‘y’ (that would be known as a variable). Given that, all you have to figure out is some valid places to put that matchstick you just removed and you have another set of equations to use as solutions!

      Oh, and that “e” can be considered a variable too! People use all sorts of letters for varibles these days!

      Finally, you might consider checking the home pages of one or more of those people who claim more than two solutions.

    2. Hey G I’m with ya! AND I also found 365 answers!!!! All sorts of ways…..one for everyday …..all day long…..AND they dance and sing….but the really cool thing……no one can see them but me cause I’m special too! …………. :}

    3. Well heck nolo promittere, there might be infinite solutions; since you could move a matchstick anywhere and consider any arrangement of matchsticks to be a variable or function, you could claim a valid solution! Who says “8” is the number 8, rather than a variable that could be 6 or 2 or 347?

      But this type of brain teaser must assume certain rules, or else it’s pointless. In which case there are two solutions (the non-move solution with keeping 9-6=3 ~might~ be ok).

      I looked at your home page, and it’s a nice creative exercise that has little to do with valid solutions to the puzzle. And what about 93?… at least two more “solutions” there. Also, you don’t seem to have considered rotating the equation 180°… many solutions there!

      I guess it comes down to what constitutes a correct solution. My strict interpretation allows 2 solutions. Your broader interpretation allows many more. A very broad interpretation allows infinite solutions. I wonder what the puzzle creator(s) had in mind…

    4. What you call a “non-move” solution might also be a “take the upper match of = and put it beneath the other match” answer. In other words, you moved something but the result appears the same.

    5. Please explain why an equation that solves to a simple integer is not considered a valid solution. I understand why creating an equation that leads to an impossibility would not work (e.g. one that reduces to something obviously false like x = x + 2, which reduces to 0 = 2, or 9 = 3 – 6, which reduces to 9 = -3), but why ignore a solution that uses a perfectly valid, simple and solvable equation?

  33. Ok, those 3 were inequalities…

    I take them back, but i found 22 solutions.

    And to Hell with anyone who says it doesn’t count! Grrrrrrrrrr!

  34. Just because I wonder what answers some people are counting, I wanted to clarify something. The question reads:
    “Can you move one matchstick and still have an EQUATION that is CORRECT?” (emphasis added by me, obviously)

    That means two things. First, each of your answers must be an equation, NOT an inequality. So, you can’t change the equals sign into a does-not-equal sign and still have an EQUATION.

    Second, your answers can’t contain a variable, unless the equation is an identity (x=x, x+0=x, 4x-x=3x, etc.) Otherwise, variable equations cannot be CORRECT, they can only be valid for a given solution set.

    Oh, and “e” is not a variable, it’s a constant (the natural logarithm base). “E” could be a variable, though.

    Just make sure your answers fit the rules!

    1. Joshua, in answering to a Nick’s comment, I ended commenting your post (basically, I noted his comment, prepared my answer with some fresh insights and then I discover some of those insides in your post, although with a different conclusion). You might want to give them a look, since I’m counter-arguing you.

  35. I am pleased to say that after looking at the puzzle for about 10 seconds I saw the match stick to move and where to place it to make it a correct equation.

  36. Sir. I Love all your puzzle. I acknowledge with the tweet. I got all three equation. First Two around 5 to 10 minutes and later on the last one. I start around 01:22H until 02:08H approximately 46minutes. Maybe if i concentrate more, it will be less. I love puzzle. Do you have any puzzle that I can win some prize or any certificate that you can send by email.
    Thanks

  37. When I was solving the puzzle, I assumed that 9 was defined by having that particular configuration of sticks, i.e., removing the bottom stick from the 9 creates nonsense, not a ‘different’ 9. The same for the 6. This also meant that any 6 or 9 created had to have the same configuration. Adding to that the rule that inequalities don’t count (matchstick over equals sign) I was still able to find 3 new equations which I believe are the indended answers, and 1 which is a stretch and possibly invalid.
    For spoilers, which I will not post here in deference to the rules, I will respond to emails bsr1 ‘at’ zips.uakron.edu

    1. That would be ‘intended’ answers. Not ‘indended’

      Dammit, Jim, I’m a Chemist, not a speller!

  38. Scratched my head a little bit. Came back about five minutes later and found two correct solutions.

    About another twenty minutes to find maybe six others using two different techniques.

    Will wait until tomorrow to find out if any of my answers are valid. The discussion will be entertaining.

  39. Okay, didn’t try this until I noticed that the answer was posted. Haven’t read the answer, and I got 3 correct answers and 3 answers that are “true” but don’t technically fit the specifications.

    About 10-15 minutes.

  40. One more thing Richard,!Very good your personal photos on the blog !…. What is the picture that most people choose? My favorite the first and last…

  41. if i move one match from 9 and place it on “=” it becomes “not equal to”

    then … 5 – 3 not equal to 6, 9-2 not equal to 6
    and so on … can these be correct answers??

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  43. Pingback: Math Dyslexia

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