On Friday I posted this puzzle….

The black lines in the diagram below represent matchsticks. Can you make the equation correct by moving only 1 match? Oh, and you can’t place one across the equals sign to make it ‘not equal to’!

If you have not tried to solve it, have a go now. For everyone else, the answer is after the break.


And the answer is all to do with pi…….

Did you solve it? Any other answers?

I have produced an ebook containing 101 of the previous Friday Puzzles! It is called PUZZLED and is available for the Kindle (UK here and USA here) and on the iBookstore (UK here in the USA here). You can try 101 of the puzzles for free here.

111 comments

    1. But that is the difference between 22/7 and pi to 8 decimal places and 22/7 is a repeating decimal, which pi is not. Pi is also irrational and 22/7 is rational. Another good approximation is 355/113.

    1. Agreed. I saw the pi thing, but I never liked that approximation, and an equal sign ought to mean equal. So I kept looking for another answer and didn’t find it.

  1. puzzles are best when they are clever. This is a clever puzzle. If you are disappointed in this presentation then you have totally missed the point and are missing out an a little bit of joy that everyone else if getting. The loss is yours, not ours.

    1. It’s clever all right, but there are certain hidden or explicit premises to all puzzles, in this case that the answer to the puzzle makes mathematical sense. It’s no fun trying to find an answer if no correct answer exists! Also, “everyone else”? I’d like to see this thread by the end of the day, then we’ll see if “everyone else” is getting joy out of this.

      The puzzle is cute, I’ll give you that. But it’s cute in the way that a toddler says, “that’s not a cow, cows have spots and that one doesn’t”.

    2. I’m one more of the “everyone else” who you claim to have on your side. To me, this puzzle is as joyful as a pub quiz where the quizmaster doesn’t know the answers to his own questions. I’m sure everyone else will be similarly frustrated that one of the answers they dismissed as being incorrect was the one the quizmaster wanted.

      If we’re not allowed to change the equals sign into an inequality sign then we shouldn’t be allowed to turn it into an “almost equal to” sign either.

    3. Jimbo, well put. I couldn’t put the finger on it, but the fact that ≠ was explicitly excluded makes the expected solution rather unpalatable.

  2. No no no. As a physicist I have to strongly object to this. pi is an irrational number and cannot be represented by a fraction.

    This is simply not a solution at all.

    22/7 is not even a good approximation. 355/113 is significantly better.

    1. Yes 355/113 is quite good. However, one does not get anything for free. It appears that the first few rational approximations of π give just about as many correct decimal digits as used in the integers. In that context, 355/113 is merely among the better rational approximations, and it still needs 6 digits for 6 + 1 decimals (∆ ≈ 10^-7).

    1. I like VVI, it’s as good as any other roman numeral, they’re only good for clock faces and puzzles. Give yourself the prize.

    1. Well, I suppose if we mix Roman numerals and a Greek letter, we could introduce Arabic with US handwriting interpretation for the heck of it.

      Your particular “canceling” technique, however, is just about o.t.t. Do you cancel summands and divisors too?

  3. Sorry, didn’t like this one at all. Like most of the other posters have said, 22/7 is merely an _approximation_ of pi. It’s not even a very good one being accurate to two decimal places only. I suspected this was the answer but was hoping it would something more clever.

  4. My answer was to take one of the “I”s on the top and use it to turn one of the “I”s on the bottom into a (lopsided) “V”.

    Thus the equation becomes:

    XXII over VVI equals II

    i.e. 22 over 11 equals 2

    1. Well VVI isn’t actually a valid number – that would always be written XI. However, at least the arithmetic is right – unlike the official answer.

      I’d worked out the PI approximation very quickly and tried to find an exact answer. You did better than I managed.

    2. I don’t think “always” is applicable when talking about Roman numerals. They’ve been standardised in recent times, but Wikipedia has citations for things like IIII=4, IIIIX=6, LXL=90. No citation for VV=10, but I’m pretty sure an actual ancient Roman would have no trouble with it 🙂

  5. FWIW I like the answer but I’m glad I didn’t spend any time on the question as I don’t think it’s fair.

    This is a real problem in puzzles: Are there any cheap tricks?

    Have to say I think this was cheap. A good puzzle can be worth spending a long time on but you have to be confident it’s not, like I said, cheap.

  6. lol guess i was “wrong”

    my solution was to rotate one of the matchsticks making up the equals sign so that the equation would turn into a “greater than” sign, or something similar to or along those lines (i.e. greater than or equal to, and etc.)

    1. @Alocaly: I’d disagree. The puzzle said you had to ‘make the equation correct’, it didn’t say you had to make a ‘correct equation’. It seems to me that making anything which is correct would satisfy that, regardless of whether it’s still an equation or not.

  7. In the instructions we’re instructed that we may not change the equals sign to a not equals sign.

    So to find that in the solution it’s implicitly changed to an approximately equals sign is a disappointment.

  8. I took one of the I’s from the right hand side and used it to change ‘XXIII’ to ‘XX-III’. I guess it’s not a perfect solution though as there isn’t really space for the minus sign.

  9. The aim of the puzzle is to find the correct solution – 22/7 = pi is not correct. I worked it out but assumed the answer would’ve been correct.

  10. I removed a match from the second X of the top XXIII term to make XIIII and placed the moved match on the horizontal dividing line between XIIII and VII, resulting in this exactly correct equation:

    XIIII
    — = II
    VII

    1. This is the only solution I could come with. Though I knew it wouldn’t be the correct one as “X / I I I” wouldn’t be considered the same as “X I I I I”

    2. that was my answer! Just wasn’t sure if XIIII allowed or not as it should have been XIV but considering the anwer given is not exactly correct… I don’t think precision is important in these puzzles 🙂

  11. As ‘Pi’ is made up of two curved (splayed) lines topped with a ~ shaped ‘lid’, the symbol Richard used to equal 22/7 is not quite the ‘Pi’ symbol.

    As we all know, 22/7 is an approximation of the value of Pi, and the Matchstick-created symbol is an approximation of the symbol for Pi, therefore Richard is correct!

    Messy, I know, but these puzzles are meant to amuse and, sometimes, confuse.

    I suspect that the reactions above are exactly what Richard ecpected to see, but I’ve thought ‘outside the box’ for this comment.

    By the way, I don’t always agree with the ‘solutions’ to the Friday Puzzles, but this week I do.

  12. Well, as far as I am concerned it was a good puzzle, typical of Richard’s. If you expect mathematical precision then best you look elsewhere.
    You cannot have decimal Roman numbers so it IS as correct as it could be.
    Another approximate answer would be to change VII to XII giving
    XX!!! / X!! which is 23/12, also approx 2 !

    1. “Decimal” is not the point – in the convention of such puzzles, Roman numbers are accepted, and π sure is cute here but a cop-out. The entire mathematical notation employed is modern: the fraction, the equals sign, and the designation π, which came about only in the early 18th century – it is of course also neither Roman nor decimal, but Greek.

      The unhappiness of many commenters about the puzzle stems from “≠” being mentioned in the question, yet the solution is an inequality without being stated.

  13. I think it’s a surprisingly fun but wrong solution.

    I like it, because it’s the first puzzle that has pi in it and makes it a bit wicked. But I don’t like it either because I would never have thought of using pi in such a rational puzzle as it could never provide a correct solution.

  14. If you consider the second X as a multiplication sign, you can take a I from the top to make another division between V and II, so you’ll get :

    X x II / V / II = II
    ((10 x 2)/5)/2 = 2

    (Kudos goes to a colleague of mine)

  15. This “solution” was very disappointing. Worse, by implying that pi is a rational number, it actually propagates misinformation and is thus a disservice to mathematical education and the correct understanding of the world.

    Just as there are no ghosts and homeopathy does not work, pi is not 22/7.

  16. Yup, very disappointed here too. I send the puzzle round work on a Friday and had many people say 22/7 = Pi… My answer to all of them was ‘is 22/7 equal to pi?’ which, of course, it isn’t. By it’s very nature, Pi can’t be represented by a fraction.

    At least last time Pi was part of the solution Richard incldued that the answer was correct to 6dp (though of course this would have made this puzzle a fair bit easier).

    I was much more satisifed with the XXII/VVI = II solution, it doesn’t stick strictly to Roman Numeral conventions, but everyone understood it.

  17. Wow, smug mode. I found A technically correct answer without resorting to pi.

    The equation is made of matchsticks. Take the horizontal matchstick from the division line beneath the second X and put it vertically after the II on the bottom.

    That gives
    (X/V) x (III/III) = II

  18. I didn’t resolve the puzzle, but reading for the solution I was not so disappointed as others.
    Here in Italy they teach us to use 3,14 as an approximation of Pgreek.
    So when we calculate c=(2 Pgreek r) for the circumference we just put in the calcolator 3,14.
    A friend of mine from Taiwan told me they use instead 22/7.
    I’ve never heard of that approximation before she told me.
    Knowing that I guess my friend from Taiwan would be able to get the puzzle as she is used to see 22/7 as Pgreek.
    Cheers,
    Stefano

  19. On the one hand….I feel sorry for Richard who gives us a new puzzle each week for free. Must be hard coming up with something original and puzzling and correct every week. So I can accept this puzzle as being “not quite” (for the “not equals” reasons given) and wait for next week.

    But on the other hand….if I had paid out good money for it, I would have a much higher expectation. So I therefore agree with the previous poster that puzzles like this put me right off shelling out for a bookful. What if all of them were as “flawed” as this one?

  20. Before coming up with the pi answer I found a different cute answer:

    Take an I from the numerator and use it to “cross out” the V in the denominator. This leaves XXII / II = II Interpret the right side of the equation as eleven.

    If Richard can use pi I can mz Roman and Arabic.

  21. I didn’t solve the puzzle. But I did manage to predict that the solution was going to be controversial when I saw the number of replies.

  22. I’m dissapointing with this. If this is a valid solution you can find a lot of approximations:

    XXIII / XII = II
    XXII / VII = III

    Curtis Frye, Cybergibbons, Andi, … provide real solutions with a valid equal.

  23. Unlike a lot of other people on this thread I don’t take this too seriously and enjoy it for the Friday afternoon/Saturday morning fun that it is.

    Whilst not being absolutely, totally, 100% accurate the solution brought a smile to my face which was as satisfying, if not more so, than the feeling I’d have got if I was correct.

  24. Glad to see there’s disagreement about this puzzle, as there should be. As approximations go, 22/7 is one of my favorites, but it remains an approximation.

    By the terms of the puzzle, the equals sign is not made of matchsticks, but if it were you could conceivably allow for bending them into a sign for “approximately equal to.”

    Seems to me that part of a puzzle’s appeal is the contrast between the non-obvious nature of the solution and it’s obvious correctness once you’ve seen it. The only obvious thing about this “solution” is the flaw in it.

  25. Okay, here’s my mathematically correct, but somewhat slanted answer:

    / X|| | / | V| | = || or |12| / |6| =2

    Hey, its just as easy to imagine a slanted line is vertical as it is to imagine a straight line is squiggly. Plus pi is never equal to 22/7.

  26. It also works if you remove one of the matchsticks from the second X, and stab it into a nearby block of cheese.
    Then you have “XIIII / VII = II”

    It didn’t specify where the matchstick had to be moved to.

  27. as others have pointed out, 22/7 does not equal pi, and the puzzle specifically said to “make the equation correct.”

    the best solution that retains using only roman numerals and does not add any special operators is:

    (X / III) / (X II) = II

    I.e., 24/12=2. but it is inelegant because (1) one of the I’s on the first row is crooked, and (2) XIIII is a permissible but non-standard roman numeral.

  28. When I realized the solution, I knew that Richard had studied enough higher math at university to think that using 22/7 as an approximation for pi would be acceptable, and I’ll bet he also knew it would be controversial, which for him is no doubt part of the fun.

  29. I had this solution in mind:
    Move the second(!) straight I from XXIII to the right side, thus getting:

    XXI I
    ——- = III
    VII

    interpreting XXI I as (XXI)(I), or 21 times 1. After all, no sign is a multiplication sign , as in “2x” or “3y” 😉

  30. Just came to check how Mr. Wiseman had messed up a math puzzle yet again this week. I was not disappointed. He’s a magician with a layman’s interest in puzzle-math, but with no respect for precision or his audience.

  31. I have an alternative answer… U can move any match and put it diagonally over the equal sign to say that eg 22/7 does not equal 2:)

  32. But don’t you see, people? We’re all a part of one of Richard’s mind control experiments! By arguing about the puzzle we’re playing straight into his hands. Don’t fall for it!

  33. Come on all you nitpicks! Did you really think there was a price for exhibiting ecxellence in mathematical trivia that few of you even use daily. It’s a puzzle meant to be fun and therefore is slightly off the rockers.

    I once was taught there is such a thing as good enough. This puzzle exemplifies the definition of good enough.

    Hey, there is no prize. No winner. Why don’t you just enjoy the feeling of being decieved. This is a safe environment – try not being a know-it-all.

    Oh, did I tell you that possibly, just possibly, Prof. Wiseman may use your comments as input to som psycologyl study? Maybe that’s the point of the puzzles?

    Naeh, that can’t be! Can it?

    Lighten up you nitpicks and enjoy the spirit of the puzzles. I’m sure it will help you get laid if nothing else.

  34. Ah, the cynic speaks. Must be terrible living with a paranoid mind… You’re always being surveyed- even when you buy milk at your supermarket. That’s just the world we live in. If that makes you nervous, I suggest disconnecting yourself from the internet and living in a basement in the middle of a secluded mountain range… Big Brother is coming for you *cackles* in that environment you can hunt and get rid of all the tension in your psyche instead of blasting it at people that really don’t care about your opinion.
    And since your so worried about being surveyed, don’t comment on these blog posts… Everything can be dissected. Silly, silly you…

    1. Yes, and Jonathan Swift really wanted the Irish to eat babies.

      You do however provide an excellent example of things that are not equal – cynicism is not equal to irony.

      The former anyone can indulge in simply by being plain and blunt, the latter is a difficult art – both to perform and to understand,

      And admittedly I am merely dabbling in this art.

  35. Well the puzzle tell us that we can move only one match but does’not put limit on number of times we can re-position the matchstick at it’s place. Hence my soln:

    1.) Re-position upper matchstick to form XXIV
    2.) Move the below matchstick to right and reposition it to make IV

    Final eq: XXIV / XI = IV

  36. there is a sulution: take a one bottom stick (so there is VI left at the bottom) and use the stick to cross off upper XI (so there is only XII left on top). And here we are: XII divided by VI

  37. XII / VI = II (12/6=2) Can work if you move the one line from XIII to lay on top of the II and one line from VII to underline it. Many roman numerals are written that way.

  38. A trick is only good when the audience is drawn in and believes both the possibility of the trick and the outcome. Here the outcome is just plain wrong as 22/7 is NOT equal to pi. Hence you just lost your audience. And you cannot say it is a close approximation AFTER you have presented your “solution” because, once again, you have lost your audience in a deceitful statement of the puzzle (in that you asked to be proven correct, not to approximate it). Equal is equal, it cannot be “a little” equal or approximate.

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