cover Please do NOT post your answer, but do say if you think you have solved the puzzle and how long it took. Solution on Monday.

Create one side of an equation that uses the digit ‘3’ five times to create the number 31.

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.


    1. There are several answers, One is

      3+(33/33) where + is being used to join not add. There may be a special mathematical symbol for that.

      33 – 3 + (3/3) is not as simple as it uses three mathematical operators not the two in the above

      (3 + 3/3)! + 3 + 3 is more complex still

    2. Sorry, but (3 + 3/3)! + 3 + 3 = 30

      Also, the first thing it says in every Friday Puzzle is “Please do NOT post your answer. It’s a good thing that only one of your three attempts to break this rule was correct. 🙂

  1. Done in 10 seconds, after I’d struggled with the wording of “one side”…. I would have written “use five 3s to make an equation that = 31”.
    But I’m not a Professor!

    1. You mean “expression”, not “equation”. An equation has an equals sign in it somewhere. Each side of the equals sign is called an expression.

  2. Five seconds.
    Might have done it quicker if I had used digits other than 3 as well, which is not barred by the question.

  3. For once, I thought of an answer very quickly, less than 30 seconds.

    ****** WARNING for any newcomers *****
    Based on previous experience, someone will probably post an answer in the comments despite Richard’s request.

    1. I wonder if Richard’s intention that you only use 3 and no other digits, otherwise it’s ridiculously easy as someone has shown above

  4. I have a solution that uses only five 3s and nothing else, but as Eddie points out the puzzle is poorly worded.

  5. Not exactly precisely worded is it? Most obviously, there’s no constraint of only using 3s on one side of the equation (without which it’s a trivial problem with, literally, an infinite number of solutions). There’s also a question of what operators or functions might be used.

  6. Oddly – I chanced on the answer with my first guess… hopefully this is an indication that my brain i firing well today 🙂

  7. There are several answers, One is

    3+(33/33) where + is being used to join not add. There may be a special mathematical symbol for that.

    33 – 3 + (3/3) is not as simple as it uses three mathematical operators not the two in the above

    (3 + 3/3)! + 3 + 3 is more complex still

    1. And I see that my prediction earlier that some idiot would post an answer has been fulfilled.

      Barry – I’m genuinely curious: did you not see Richard’s request not to post the answer or did you decide you just weren’t going to abide by it?

    2. So now it must be Thursday. Anyway, nice to see some invention, even if the last one yields 30, not 31. If you want a concatenation operator, many computer languages have them. Both + and & are commonly used, but I’m not sure that mathematicians will accept the mixing of string and integer types.

    3. Bazza’s been a fairly regular visitor for a couple of months now. He knows the instructions.

    1. As MathMiles said, I do hope that some of the people who posted the answers would clarify why they did it. One possibility is that this particular puzzle was too easy, so maybe those posters gave the easy answers to challenge us to find the more interesting ones. If that’s why you did it, you should have said so when you posted it. But probably best is to not have revealed the answer or maybe to give a difficult to interpret hint,

    2. @Stephen Jones

      Thank you for your questions about whether I saw Richard’s admonitions.

      I believe it is better that we show kindness to others during our brief time on earth rather than say we are simply “obeying orders”.

      If a man was starving would you say “Please wait. Dinner is served at 8pm?”. Some people have cried out that they do not know the answers. Kindness permits us to respond.

      This is everso more true if we see others feeding poison to the starvers. (To follow my metaphor, poison here means incorrect answers). Evermore so we should step in and help in these cases. “I have been ordered to wait until Monday” is not a compassionate reply.

      The Internet is about knowledge and communication.Neither wants to wait.

    3. Barry – I’m with you on being kind for others, but frankly your justification is ridiculous. We’re talking here about the frustration of solving a puzzle that will be revealed on Monday, not a matter of life and death!

    4. Halley’s Comment!!!!!!!!! Booyakasha!!! That has got to be the BEST name I’ve ever seen on a forum. Well done.

    5. Stan, MathMiles,
      I don’t think of them as spoilers, more as a social service.
      Keep it up Bazza.

  8. Oh dear, you pedants with your ‘not precisely worded’ comments! You do all realise that that’s part of the test don’t you? Once you’ve worked out the word part, then you get to do some sums. This one is easy for the maths minded. It’s obvious there’s only one way for one to make the one using only 3’s. Then how does one make a number big enough with the remaining 3’s? There’s only one way as far as I can tell.
    One is hungry for a cube of cheese.
    Happy weekend everybody.

  9. let’s see if the ascii force is strong with me today:


  10. It was an instant-solve for me.

    @Barry Goddard: Your analogy is idiotic. If someone is so desperate for an answer, all of Richards puzzles are easily googleable (probably where he gets them from!).

  11. There are lots of ways – my first took about 3 seconds, most of that to conceptualize the values needed. Maybe the speed comes from once having solved a much more involved one – express every number from 1 to 100 with four 4’s.

  12. OK – it’s all got a bit heated about the issue of posting the solution in the comments. Some see it as a service to others that overrides Richard’s request not to. So to be constructive, I’d genuinely like to know:

    Are you happy seeing solutions posted in the comments?
    Reply to this post with either Yes or No.

    1. Good luck with this, MathMiles, but I fear you’re on a sticky wicket. There’s a pack of twats who do it just to wind others up every week — because they know they’ll get a reaction. It’s throwing cheeseballs at a dog (Greg Davies). To be honest, when I first came here, a year or so ago, I used to find it annoying as well and I would join in with the rebukes, but I quickly realised that it’s all part of the game. Even that Hugh Janus cancer doesn’t bother me much anymore.

    2. And to add, it’s a NO from me, although I admit it’s nice to find hints in the comments, when I can’t work out a solution.

    3. Slange – fair point, and I’m not really that upset about it, but as some have argued that they are serving society by posting the solution, I thought I’d ask “society” if that’s what they want.

    4. I also sometimes wonder if it’s all just a long-term psychology experiment by RW to see how people react on the internet to instructions and those who ignore them…

    5. MathMiles: Yeah, I read that one earlier on (the one about doing society a favour) and I had to laugh. I don’t know if Bazza is a created character or if he’s for real, but he does make me smile, I must admit.

    6. MathMiles: Yes, I’m sure that Richard is recording all of this. I know I’ve got some decent stuff out of it myself (about cyberbullying mainly).

    7. Anyway, “Democracy is so over-rated” looks about right – the turnout on this poll is worse than a European Parliament election. Two votes and one of those is mine! I’m laughing too.

    8. I think the right answer is “yes”. At least that means people won’t stumble into spoilers. Unless Richard introduces a moderator, I don’t see any way of avoiding it. There’s always somebody who wants to spoil the party.

    9. @Stephen Jones

      Your comment about programming languages may inadvertently exclude some solvers whose only experience of equations is with programming.

      From work with star charts (very mathematical and intuitive) I for example have great experience in programming with Excel and other spreadsheets. Thus a solution such as this is easy for me:

      round(sqrt(3!!)) + 3 + 3 – (3/3)

      (round is the round down command. sqrt is the sqrt command).

      We should not exclude such solutions without offering alternatives, Many younger people today will not have experienced mathematics but they will have great experience in programming such as above.

      It is easy to lay down the law on what is and is not permitted on someone else’s blog. Yet it is harder to be an exemplar of what is truely good online communication. Let us all try harder to encourage interaction and creative responses rather than say we should say nothing because google has all the answers.

      I have not lost heart despite being criticised here and elsewhere. Lets not others too,

    10. When you’re in somebody else’s space, e.g. their blog, “to be an exemplar of what is truely good online communication” is to be considerate of the guidelines for being in that space. The benefit in doing puzzles lies in figuring something out for yourself, not in having somebody feed you the answer. (especially if that answer is wrong, as at least one of yours was) You’re not helping anybody; you’re spoiling their experience. That’s why it called a spoiler. Please don’t do it.

    11. @Rod Kimball

      Thank you for your kind support. As you say when invited into someones space be advised of their rules. Richard has invited us into his space but that is only possible because Sir Rim Bernard Lee has invited all of us (Richard included) into HIS space.

      The Internet is a place for free exchange of information. It be at our peril that we work to prevent that. Richard may have good intentions to prevent information at weekends – perhaps his parents are 7th Day Adventists. But we need not mindlessly follow his rules if we can help add to the greater good of humanity.

      As some others and Mr Jones have pointed out: often Richard is posting AFTER the answer is already available by a Search Engine. It then is rather as if he wants his horse after the stable has bolted,

      We should not allow those who want rules to have their way unthinkingly. Rules may be good but care action after thought is surely better.

  13. Slange Navarr, FYI both my parents died of cancer, so your use of the word ‘cancer’ is a little unwarranted.

  14. So how many solutions are there? So far I can think of five solutions (using + – * / ^ () and !) . Three of them I found on my own, then another from the comments, and then I used that idea to generate a fifth answer. Anyone have anymore?

    1. Of course, no correct answer is really better than any other, but yours is my favourite so far. However, I completely agree with all the folks (Richard included) who ask that you not post your answer before Monday. There’s a reason it’s called a spoiler.

  15. About 5 seconds. The equation essentially wrote itself as the obvious solution without even thinking about it.

  16. If you don’t want to be annoyed by the self-important booliaks who write answers in their comments (despite being asked by Richard not to do so), DON’T READ THE THREAD until after you have already worked out your own answer. The pompous booliaks who come here every week to complain about the people writing spoilers are infinitely more booliakterous than the booliaks who write spoilers.

    1. And then there’s the people who complain about the people who complain about the people who post solutions…

    2. … not to mention the people who complain about the people who complain about the people who complain about the people who post solutions…

  17. I solved it in less than a minute, with the same answer as Halley’s.
    Then I wasted 15 minutes of my life reading the comments.
    I am now wasting a further 1-2 minutes writing this comment.
    Hopefully, I will not waste any more time returning vainly to this thread to check if anyone has responded to my lame comment.

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