Imagine that you have to make the number 8 from the numbers 4, 7, 6 and 3.  The rules are simple.  You cannot join the numbers together (so 4 and 7 cannot become 47),  have to use each number once and only once, and are only allowed to add, subtract, multiply or divide them.  You might do something like this…..

4+7 = 11


and 5+3=8

So, here is the puzzle….can you make the number 24 with the number 5, 5, 5, and 1 (again, you cannot join the numbers together, have to use each number once and only once, and are only allowed to add, subtract, multiply or divide them)?

As ever, please do NOT post your answer, but feel free to say if you have a solution and how long it took.  Answer on Monday!  have a good weekend.


  1. It took a few seconds to find one solution, but only because I’ve seen a similar puzzle before. (Same pattern in the answer, with different numbers.) Now to look for another solution… 🙂

    1. Thinking about this some more, the versions I’ve seen before — e.g., make 24 with 1, 3, 4, and 6 — actually use a different pattern of operations in the answer. And a little trickier to spot, I think.

    2. hey nick, did the one with 5551 but not urs buddy. what’s the trick? or are u gonna reveal ur own version on monday?

  2. Trying to figure it out but not having much luck…. gonna take a break and come back to it, hopefully it’ll come to me.

  3. Seriously guys? Do you have to be like that? Really think of how it makes Wiseman feel. He spends good time out of every week coming up with these, and the only thing you have to say is “So simple. It took 10 seconds”? At least Nick has the decency to give a reason for finishing it quickly, but people like Todio and Niraj really bug me. Someone took time to make a puzzle somewhat challenging, and all you want to do is talk about how easy it is? How about a little respect?

    At least the people who post “first” on things aren’t defaming it in any way. All you people are doing is posting “first” but in a more derogatory way to the publisher, not to mention the people who don’t get it in “5 seconds.” (Which I highly doubt that is even possible to read all of that and come up with the solution in that short amount of time)

    Grow up. It’s ridiculous that people resort to such bull to make themselves seem smarter.

    1. It’s OK Matt I’m still working on it too! lol……but I am slightly dain bramaged and dyslexic also… least that’s my story and I’m sticking to it……. :}
      Malinari …… where did you find your Magic Beans? And do I need a cow to barter or would it cost me one of my children?

    2. Well said Matt.

      But have you considered that all these puzzles might be part of one of Prof. Wiseman’s intricate and sneaky psychological experiments to determine how many puffed-up self important people there are out there ?


    3. Its a bit rich having a go at people for saying how long they took when ‘the author’ asks people how long they took to answer the question. You’re not a Republican by any chance are you?!

      Calm down Matt; I haven’t got the answer yet either and there is nothing wrong with my brain. Sometimes I get these straight away sometimes I don’t get them at all but there is no point getting pissed at the people that solve it in seconds.

    4. The thing I find fascinating is that almost all of us fail in at least one part of the puzzle every week. Most of us ignore (myself included) the following: “As ever, please do NOT post your answer, but feel free to say if you have a solution and how long it took.”

      I take that to mean you can say that you got it (or not) and how long it took. Period. All of our clever hinting around it (so we can tell ourselves we didn’t post the answer) is breaking that rule. It’s like being a little pregnant.

      And nobody seems to mention that point very often.

      I don’t know what to make of it, but I suspect it is evidence of a lack of maturity and self-control. At least that is what I feel for my part of it.

      If I were not so impulsive, I would honor his request and keep my mouth shut until Monday…

      God, I need a vacation.

    5. Dear Matt,
      I don’t see why you are upset by my post (I’m saying “my post” since you quoted that one). It took me 10 seconds to solve this problem and I haven’t seen similar questions before. Richard Wiseman asks for feedback about the questions, thus my feedback. It’s a feedback about the question, it’s not a feedback about my cleverness or a disrespect to Richard Wiseman’s efforts, or it’s about being the first one to solve this. BTW, there were many questions here which I could not solve at all, if that makes you more happy to hear it.

      I solved it in 10 seconds thus found the question easy and said so in the comments as requested by the author. What would you suggest? Should have I waited 8 hours to post my comment and say “It took me 8 hours” just to be seen nicer to people? You are assuming too much and “adding” too much meaning to my simple post. So indeed; grow up. Maybe a psychologist can explain why humans tend to read too much between the lines and put more meaning to simple comments.

      Any psychologists around? :o)

    6. You gotta be kidding!

      As ever, please do NOT post your answer, but feel free to say if you have a solution and how long it took.

  4. I have an answer, but it involves the liberal use of use of Magic Beans. it took a lot longer than a few seconds to arrive at this answer – do you know how hard it is to get hold of Magic Beans these days…….?


    1. lilabyrd any mammal can be used for bartering for Magic Beans, It’s left to you’re own moral judgement to decide whether this should be a small child, or something more bovine.

    2. lol…..well…hummm a cow, a child or a cat/dog…..hummm….this is going to be tough…….as I do believe I am going to need them… bad case of brain freeze……

    1. komincents, I don’t think Richard leaving out the word “basic” is a problem at all. He says you are, “only allowed to add, subtract, multiply or divide” the numbers. What could be clearer than listing the only allowable operations?

      Regarding your other points below, Richard’s form of words rules out negation, exponentiation, roots, logs, sine, cosine, tangent, factorial, and any other operation you can think of that is not among the four listed! Factorial can be defined *in terms of* multiplication, as can exponentiation, but neither *is* multiplication.

      As far as I can see, there are no “shenanigans” whatsoever in this week’s puzzle? 🙂

    2. OK, I guess…but why does he change it? Why make it a question? Why did the original author feel the need to include the word basic if the other operations were not a subset? If multiplication does not include the other “in terms of” types of multiplication, then why is the concept of “basic” even needed? Not sure I agree, but I see you are a very educated man, so I place a lot of weight on your opinion…

    3. I don’t know where Richard got this puzzle from, but it’s a simple idea that goes back a long time, probably at least to the 19th century. The page you cited does indeed refer to “the four basic arithmetical operations”, but maybe it goes on to exclude factorials, powers, roots and so on precisely because it doesn’t explicitly state what those four basic operations are! Nowhere does that page say that you can only use addition, subtraction, multiplication, and division, so I find Richard’s form of words to be much clearer.

    4. Thanks…interesting…but I was thinking while on my walk with the dogs…

      Not all multiplication is factorial, but all factorials are multiplication, so does that not make factorials multiplication? Is there any time factorials are not multiplication?

      Why is it that if you do it ten times it stops being multiplication?

      In other words, what is the difference between 10 to the third power and 10 times ten times ten times ten?

      Each time you multiply something by itself, it is still multiplication. So why if you do that three times is it not multiplication.

      Not trying to be argumentative…sincerely curious.

    5. Honestly, I didn’t notice that the four operations were not spelled out on the other one.

      Interesting how I missed that.

      But, not to be stubborn, I’m still thinking the following:

      The fact that the other puzzle’s author assumes we know what the four basic operations are (as he did not feel it was important to list them), added to the fact that he then goes on to specifically exclude various parts of those four basic operations proves to me they exist as part of and not separate from the operations.

      And, if those parts of those operations are excluded there and not here, it is evidence these items might be important.

      Not to mention it seems like this is further evidence that there is a pattern of ambiguous language in all of these puzzles, right?

      I’m sure there are many who think I am off the scale into ridiculous. I’m not mad at them. Believe me, they aren’t the first. I can’t tell you I like the way I think…but I don’t not like it enough to change.

      Don’t know if I could, anyway.

      So don’t hate, friends.

      Be happy!

    6. komincents, “multiplication” is usually thought of as a binary operation between *two* numbers. So 10 × 10 is an example of multiplication. You can write 10³ = 10 × 10 × 10, but the right hand side is really two multiplications: either (10 × 10) × 10 or 10 × (10 × 10), both of which evaluate to the same number: 1000. Similarly, the factorial of a positive integer can be thought of as repeated multiplication: 5! = 5 × 4 × 3 × 2 × 1, where we have four multiplications, which can be done in any order and always yield 120. So exponentiation and factorial can be defined in terms of repeated multiplication. (At least for positive integers.) But they are not the same as multiplication, and aren’t considered to be “part of” it.

      In a similar sense, multiplication can be thought of as repeated addition, at least for positive integers. And multiplication is not the same as addition and isn’t considered to be “part of” it.

      So I’m sure that in excluding exponentiation and factorial the puzzle’s author didn’t mean to imply that those operations are “part of” the basic four operations. Any more than multiplication is “part of” addition. He probably just wanted to make it extra clear that any other operations than the basic four were forbidden, though it was really overkill to say so.

      Factorial can be extended to non-integers — see the wikipedia entry — in which case it’s no longer defined in terms of repeated multiplication.

    7. OK, got it. That does explain it well. Although I don’t know if I totally understand. In any case, I appreciate the time you took to try. Raising my beer in your direction.

    8. To complement what Nick said, most of non-basic operations or functions can be translated in successive basic operations. If the function is analytical, formulas like Taylor’s series do that. If we accept “operations” other than the basic, just because they can be translate on them, we open a door for many more alternative solutions without need.

      I suppose that an alternative approach to the puzzle would be to get 24 making an expression here with the symbols 5, 5, 5, 1 and any of the set {+,*,-,/,),(}. Exponentiation would be no problem since we cannot use here positional notation (we have to use symbols like ^ to represent it). If the pretended result was 26, we could have dropped out the symbols ‘(‘ and ‘)’ using instead the naive approach used by Richard in his example (I’m saying that, in the moment we already know the answer to the puzzle).

  5. D’oh! Didn’t think to measure how long it took. I would estimate it having taken under 5 minutes, possibly more like 3 or 4? I’ve never seen a puzzle like this. After approaching it in my head I pretty quickly pulled out a pencil and paper and opened up the calculator program to help, heh. Thanks for the deliciously distracting mental entertainment! 😀

  6. Doh, stuck on this one…oooo no I’m not…. but an I allowed to use the maths operation that I have. It is sort of the form of one of the 4 alloweds. Hopefully I’ve solved it in about five mins. If not put down hours cos otherwise I’m stuck.

  7. I believe I have a solution but if Mr. Wiseman’s preferred solution turns out to be the one I came up with I will have to claim foul!

  8. I think that there’s only one correct solution (considering all the 5’s as indistinguishable). The real trick would be to prove it!

    Is there a general approach to such questions or do they just require educated guessing (eliminating the impossible, checking the rest)?

  9. I have a solution which I hope is OK, it uses only the given operations. If I’m right there is a related general proof I’d like to see. Took 20 mins to get a solution, but still need to think on (there could be a red face here). Fun, thanks.

  10. Yeah this is the kind with the really goofy solution. Good luck folks! Remember your distributive rules! Once again, the shenanigans entail Richard neglecting to inform us we may use parentheses, presenting it in a way such that we can only assume we have to do it one step at a time.

  11. A few seconds to find a solution with exponentiation. Then discovering that was cheating, a few minutes to find the correct solution, after disbelieving there could be any solution for a while. I’d probably have given up entirely if it wasn’t for Nick’s encouragements.

    If there were 4 different numbers, there would be a lot of options. With 3 numbers the same, there aren’t really very many options at all. So why did it take a long time to find the route when there are so few options? I can’t really say without giving too much of a hint.

  12. about 10 minutes including the time it took to read all of the comments. Somehow I hardly ever manage to solve these puzzles without reading other people’s comments first.

  13. You get great selection bias in these comments. No one ever posts when they can’t do it. (I couldn’t do it bye the way)

    1. The only solution I’ve found so far involves me cheating by adding a 2 & a 4 into the mix & breaking that rule about not being able to just splice them together.

    1. Btw, Krypto shows some really interesting quirks about the people playing. I usually prefer to multiply and divide, my wife to add and subtract. So while my wife would likely have solved the example with 3,4,6,7 -> 8 like Richard shows, my spontaneous solution was (7-3) x (6-4) = 8 …

  14. Bored in a computer lab session, so I wrote some a program to solve the problem using random permutations of all the numbers and operators.

    1. :-S

      Why write a program that solves it using random permutations?! Why not something that was non-random? Using random permutations opens you up to checking the same result multiple times, leading to an inefficiency in the algorithym.

      Whatever would your computer lab teacher says?! If you’re going to be naughty in a computer lab session, surely you should at least produce an elegant, efficient algorithym? tut tut tut!!

  15. Well, it took me about 5 minutes to figure out the shenanigans here. (It wasn’t hard to find the original.) Yup, he left out part of the wording again. He was clever, though, and chose a set of numbers for which there is only one possible answer (providing one ignores the part of the puzzle he left out). But I found the trick anyway. He tried to make us think that because there is only one answer to this “puzzle” it must be legit. (Some of these “24” questions have no solutions, others have many, still others only one.) In this case, however, his puzzle is missing crucial information. He gives a list of acceptable operations, but that list is different from the one in the original. Shenani-effing-gans! 🙂 (Yes, I’m marching to the beat of a much, much different drummer…) Technically, the answer is that using only the operations allowed by his rules, there is no possible solution. Yes, I got the answer he was looking for…does that mean I have a mind? shrug

    1. I don’t know what you are going on about. I got the answer using only the allowed operations and didn’t see any shenanigans at all.

    2. Steven, thanks for the chuckle. I’m guessing you are British by the use of that phrase. Yes, I sometimes do “go on”, don’t I? Time for my medication…

    3. OK, took my pills…now I am doubting myself again. I still have some questions. I mean, go look at the rules for the puzzle on the page I linked to above. They seem to be much more specific than the rules presented here.

      However, I think that the one difference that I saw at first (and thought it might be another case of shenanigans) may or may not be important.

      Now I see more differences…but I haven’t figured out if they matter either.

      The jury is out on this one.

      Which just makes me question his intentions for the whole exercise.

      Is it just that he does a poor job of recreating a familiar puzzle and he has no ulterior motive? Or, is he intentionally presenting puzzles with various changes, making the puzzle unsolveable at times and solveable at others for no good reason? Do I continue to look at the future Friday Puzzles in order to collect more data, hoping the pattern will be revealed? Or, is there a point here that is unknowable to all but him, and more data will never be enough?

      The problem I have is how much time do I spend deciding if it is a pattern that can be figured out or not. It is important to me to be able to leave something alone if there is no chance to solve it, but then I wonder if I gave up too early.

      Ya, I know, there I go again, going on…

      Time to walk the dogs.

  16. Got it. Took me a few minutes. Probably could’ve done it faster but I just woke up and I was distracted by a Quirks and Quarks podcast. Yeah. That’s it. 😀

  17. Well, crap…I’m wrong. Nick is correct. There is something missing, but it doesn’t matter. It can be solved without the missing piece. I’m wrong this time. It is solvable. At least, I can’t spot the shenanigans. Again, I take it back. (hanging head, spanking myself…) Thanks a lot Richard…I almost figured you would do that this time. I’m standing by the last few times, but this time, he got me. No fair, no fair, no fair. Make me look like an idiot by throwing one in that is not ambiguous. Just when I thought I had it ALLLLL fingered out.

    1. Go to the link I posted…compare Richard’s instructions with the original. You will see the difference. But, this time, Richard left out a part that was not required to solve it. I really don’t know if I am chasing my tail, or he really is an evil genius. Kudos to him (or not). Now, where did I put that bottle of Valium?

    2. OK komincents… relaxed now? This is the one my son just told me.
      A man leaves home and makes three left turns and returns home and meets a person in a mask. What is the man doing? …….. :}

  18. These puzzles are getting too easy these days, only took a couple of seconds.

    Would be nice to have some that you spend half of the day thinking of.

  19. Took me around 10 minutes to solve it. Great puzzle indeed.

    I kept getting stuck since I had a hard time thinking outside the box, experimenting. My hint to all of you who cant solve it is – use a calculator and/or a sheet of paper.

  20. It took me about a millisecond to get the incorrect solution involving only three figures, then all the time it took to eat my lunch to not figure it out in my head, and then a couple of minutes with a piece of paper to find a solution that worked. Any longer and I’d have gone for the brute force programming method of solution too.

    I can’t work things out in my head.

    Neat puzzle.

  21. though i worked it out in seconds then realised i didn’t, then i followed a theory and i have the answer, whether its the correct way i don’t know but i did all the things a was allowed and none i wasnt. I am normally unable so really chuffed, sure i will be disappointed when i find out i did it wrong

  22. It took me 10 or 15 minutes, but to be fair I was watching Carpool at the same time. This is my favorite puzzle of recent weeks. Thanks for doing this, Richard!

  23. As of right now (about 5 minutes after first reading the question) I have no idea. I’m hoping inspiration will strike in the next few minutes.

    1. I thought I had it once when I thought you didn’t need to use all the numbers, but it seemed too simple so I reread the puzzle to check that I had the rules right, when I realised that I needed to use all the numbers. Once I tried to use all of them there seemed an intuitive way of dealing with it and after a few seconds of thought I managed to arrange the operations and my operands in the right order. I then felt a wave of satisfaction throughout my body. All credit to my intuition and the mathematical education that has fuelled it over all these years.

  24. No idea. I can’t seem to do it without leaving one of the numbers out, or using one as an exponent. If there weren’t people reporting that they got it, I’d say it was impossible. Of course you guys could be in on it, too. Hmm…

  25. hmmm… I’m tottally in the dark here. There is a way but is far fetch and allows two different solutions… must not be it. I’ll wait eagerly for Monday, I suppose.

    1. Okay, I got it. Stupid: the solution I got was one I entertained Friday, but must have botched when I did the math in the head… 😦

  26. It’s a fairly straight-forward solution. When you find it you’ll be mad at yourself for not getting it sooner. It’s not out-of-box thinking, I would say, and it’s nothing fancy. If you have a far fetched solution, it’s wrong.

  27. Err, got two solutions. One is definitely cheating and the other looks suspicious. Can’t help thinking I’ve been hoodwinked.

  28. I came really close to solving it after about 10 minutes of trying, and then I read the comments. The “too simple!” comments made me think I was on the wrong tack, so I cheated and went here:

    I was actually extremely close and should not have been discouraged by those extra-clever folks!

  29. Took me and the other guy in the office about 3 minutes to come up with 2 answers one which isn’t valid because it uses a factorial but pretty fun none the less. The other I am pretty sure is correct.

  30. Great puzzle. I’ve got the answer (I think the only one). It took one hour, pencil and a piece of paper.

    Looking forward to the next one.

    1. Got it, about an hour for my subconscious.
      No dirty tricks here, look deep enough and you will get the point too 🙂

  31. I do these 24 puzzles a lot, and this took me a while the first time I saw it. It’s not the usual way of thinking about these puzzles. One of my students posed it to me last year, so to say that I got in a few seconds isn’t truthful. I answered it in a few seconds… this time.

  32. I find these puzzles rather easy, out of practice. I challenge my daugthers once in a while to, say, produce 100 using all the digits, or producing all numbers from 1 to 10 with five 1’s…

    1. That is until I realized I had misread the problem: I had a couple solutions for a different puzzle: 25 instead of 24.

  33. Took me 15-30 minutes, I think. (Too engrossed to check the time.)

    My solution feels tricksy, but I think it technically conforms to the rules. I’m pretty sure some people are approaching it a different way, though. Seconds? I don’t see how someone could solve it my way that fast.

    Well done, Richard.

    I’ll wait for Monday before consulting the oracle of Google.

  34. I solved it in a second or two, but I may have seen this puzzle before, and if not this one then the almost-identical puzzle with 3, 3, 7, 7 to make 24.

  35. Well I worked on it until my lap top finished it’s security scan and still didn’t get it… gave up and went to bed{6am my time- EST} then worked on it for an hour and got mad and called my oldest son…..math whiz… it from his father…..not me….lol….he gave me a few hints and told me to think about it……then I came up with an answer and I think it followed all the rules….so we shall see……. then he told me a word puzzle and I felt better……. :}

  36. Should rotate left and right brain to find the answers. A good article for thought, and allow me to duplicate the above work. thank you, greetings D3pd …

  37. I admit I’m very slow, it took me over an hour to figure this out and only by gaining a clue from some of the other comments- didn’t do a google search though! Ooops ! 🙂

    Thanks for that!

  38. After multiple attempts, I got it. My friend called me up at 2.30 in the morning saying she got it.. which she didn’t because she used an exponent. But she said something that gave me an idea…. and I got it. I actually still can’t believe I figured it out. Altogether, maybe an hour? Great puzzle.

  39. Took me about 5 minutes on my 2nd attempt. Took my son a lot less time … but then he is studying for a Maths degree!

  40. Ok – almost every Friday, I see this Richard’s Wiseman’s Blog Puzzle ad on the WP Front page – and almost every Friday, I check it out. I read the puzzle and the responses, don’t understand either, don’t have the slightest urge to take a mo’ or two to do so, and I move along – to my own vanitylog.

    This morning I have some time and, thrills and chills, I’ve decided to respond – but not to the puzzle.

    With a little time, I found that most, (don’t read that as anything else but MOST/MAINLY/FOR THE MOST PART), responders are male. (You can probably use a factorial to prove it – but I went to the websites.) That’s probably, (don’t read that as anything else but MOST LIKELY), got something to do w/that right-brained, visual, spatial stuff. “Stuff” being the operative word to clue you in, that I’m “probably” a left-brained, verbose female. (DYK – one of the responders above has a blog site about verbosity.) But, then again, it took me a while to decipher KOMINCENTS.

    Oh well, it’s time to quit the shenanigans of the exponentiation of SQRT’s, Quirk’s, and Quark’s – shoes are on sale at Nord’s!

    I believe that the only puzzle is who RESPONDS first – 5 seconds, 10 seconds, 5 minutes – all without answers – since Richard, as a magician, only asks: “As ever, please do NOT post your answer, but feel free to say if you have a solution and how long it took.” A classic misdirection – eh, Richard?

    Yesterday, Nick won by responding 8 minutes after Richard posted. However, did it really take Nick “only a few seconds” as he purports, or the ENTIRE eight minutes ? Ha!

    So – Yes, Richard, I have a solution and it didn’t take long. Ciao!

  41. Got it in seconds. I used to play this game when I was a counselor in Chinese School! Brings back such good memories =)

  42. Spent a while trying to get it and couldn’t, then a couple of hours later it came to me while I was having a shower. It does require a little leap of imagination, especially having read the example at the start of the puzzle.


  43. I can’t believe I worked out the solution at my first attempt–just a few seconds. I must be wrong. But it works. It answers the question. Can it be? I saw the Gestalt of this puzzle and realized it was not one to be labored over. If I’m dead wrong, I will feel like a fool.

  44. found what i think is a solution after about 5 minutes, but i have a question: must each number be the second number in the operation? In other words, if I start with 1 – 5 = -4, can I follow with 5 / -4 = -1.25? Or must I start with the answer to the previous operation (-4/5 = -.8)?

  45. So, I have a few questions. Here are the rules as written by the original author of this puzzle (found here: ):

    “MAKE 24 is a simple game. Four figures in the range of the natural numbers 1 to 9 are chosen randomly. Your task is to combine them in order to obtain the result 24 – but you may only use the four basic arithmetical operations and brackets. No ploys! Not allowed are factorials, powers, roots etc. Furthermore, you must not combine two or three of the four numbers to a two- resp. three-digit number (e.g., with 1, 3, 4, 8 given, 38 – 14 = 24 is no correct solution).”

    Why does Richard leave out the part about factorials, etc?
    Why does Richard leave out the part about brackets? (Even though Nick is correct in that the “answer” can be shown without brackets…)
    Why does Richard leave out vital (?) parts of the question every week’s Friday Puzzle?
    Why does he change it at all?

    I just can’t ignore these red flags. Some may think that my inability to get past these unknowable issues is an indication that I have an inferior mind…(maybe I am impossibly stupid…)

  46. The rules here in this puzzle don’t seem to specifically allow or deny the use of other than whole numbers in the equations, but it also doesn’t seem to allow or deny the use of “…factorials, powers, roots etc…” either.

    Is it that the original puzzle has redundant instructions, left out by Richard as unnecessary?

    Is it that powers and factorials and roots are operations and therefore excluded by the specific four that are allowed?

    I’m just saying…every friggin week he presents a puzzle. Elsewhere on the web can be found examples of the very same puzzle with very different instructions. One can compare the puzzles as they are presented, and mostly, they all are the same. The only time you see clearly different instructions is when Richard posts it.

    Why does he change it, friends?

    Why, why, why?


  47. So, if Richard does not specifically prohibit factorials, then is that allowed?

    He does say we can use multiplication…is that not considered a factorial?

    From Wikipedia:

    “In mathematics, the factorial of a positive integer n, denoted by n!, is the product of all positive integers less than or equal to n.”


    “In mathematics, a product is the result of multiplying, or an expression that identifies factors to be multiplied.”

    So, if multiplying is allowed, why not factorials?

    The original puzzle’s instructions prohibit factorials…Richard’s version does not.


  48. “There are known knowns. These are things we know that we know. There are known unknowns. That is to say, there are things that we know we don’t know. But there are also unknown unknowns. There are things we don’t know we don’t know.” ~ Donald Rumsfeld

  49. By the way, I didn’t say that using a factorial would produce a correct answer…I didn’t bother to think about that part…mainly because I saw that some had already come up with answers using factorials, about which they either were unsure if it was allowed, or assumed it was not allowed.


    (slowly spinning the cylinder on my wheel gun…one bullet in there…one out of six chances…holding the barrel to my temple…slowly squeezing the trigger…closing eyes…listening for the click…a bead of sweat running past my left eye…)

  50. I mean, look carefully…the original puzzle says “…you may only use the four basic arithmetical operations…”

    Look at the word “basic”.

    Richard does not specify basic operations…he just says “only allowed to add, subtract, multiply or divide “.

    So, here in this puzzle, the multiplication function is NOT limited to the basic form, therefore including factorials.

    Explain where I am missing something here, please?

  51. I’m not sure what’s more amusing – the puzzle or the grumbling over tiny details.

    I did get sidetracked by the form used in the example, that being to take one of the supplied operands as the first partial solution, then repeatedly apply one of the allowed operators and one more of the operands to form the next partial. I’m pretty sure I exhaustively proved this one can’t be done that way.

    But I did find a good and clearly accurate solution using a modified sequence (i.e. parentheses)

    I don’t know, and really don’t care, how long that took. Well over an hour, including some programming.

    Personally I’m a little concerned over the emphasis many clearly place on something they see as “winning” over just learning and having fun.

  52. People are getting sidetracked by all kinds of weird thinking. The puzzle starts with an example showing how you may use the four numbers provided. Use the same methodology to get to 24 from the second set of four numbers. However the initial example does steer you down what later turns out to be an artificial barrier to thinking, which is why it’s a great little puzzle.

  53. PathemTM is a word puzzle innovation that captures components of all-time favorite games such as Sudoku, Boggle, Scrabble, and Crossword and twists them inside out and sideways. PathemTM has been validated by puzzle experts, published in puzzle books available on, and is poised to release interactive game applications for iphone, android, and facebook.

    Feedback is welcome.

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