Three number related ones this week…..

First, what is the largest number you can get using only 2 digits?

Second, can you make 1000 using eight 8’s? Oh, and you can only use addition.

Third, can you place a mathematical symbol between 3 and 7 to get a number which is greater than 3 but lesser than 7?

As ever, please do NOT post your answers, but do say if you think you have solved them and how long it took. Solutions on Monday.


  1. The problem with the first one is that one can intrepret the question in different ways, giving different answers. So in place of an answer, I have instead the realisation that the multiplicity of answers exists. Given that I came here to solve puzzles and not practise telepathy, that is the best I can do.

    For the second one, the correct answer was the second candidate solution I tried.

    The third one is too simple to be in any way satisfying.

    Altogether, it probably took me about a minute or so. Less than a minute for each one, I’m quite sure.

    1. The second one should be very simple using deductive reasoning. The third is probably playing on a thought trend that the bran picks when solving the first two… did you jumped on the solution immediately or did you tried other things first? The first can only have several solutions if they produce the same number… I’m not really sure that happens here. “the largest NUMBER you can get using ONLY 2 digits”… I think this excludes entities that are not numbers, and the use of anything else to represent them, except two digits.

      PS.: It is a sad, rainy day outside and I got an irresistible need to be a math troll with someone… sorry, it was you. To compensate, let me share with you an incredible finding: Yes, that’s right, the US secrete services has a site to recruit talented children in solving puzzles. It has brain teasers too. 🙂

  2. Yes, this time I got all of them in short order. For the first one, to get a meaningful answer I assumed no operation that could be repeated indefinitely without adding more digits.

  3. There are indeed a few possibilities for the first one. If we can’t use any symbols or operations in our answer, then there’s one possible answer (this is what I assume the question is most likely asking). If we are allowed to do symbols, then not only is there a larger answer, but there’s no single largest answer.

    The second one was pretty easy, took just about a minute to find an answer.

    The third one, I have one answer that satisfies it, though I’m not sure if what I used counts as a mathematical symbol.

  4. First: This one is interpretation dependent. I can get a value up to 1307674368000 using only two digits, but I don’t know if that is within the rules. As other stated: it is dependend on wether you are alowed to use symbols or not. If not, then I would not call it a puzzle.

    Second: Easy, about 15 seconds.

    Third: I got an answer, but I would not call it a “mathematical” symbol. So I am not sure if this is the answer.

    1. I got another answer for the first one using only two digits which are not mathemetical symbols, and that also gives a very large number. It is comparable to the puzzle of two weeks ago…

      I can get 5 answers using different rules. One of the answers is even higher than the one I stated in my previous post.

  5. 1. I don’t know whether mathematical symbols are allowed.
    2. Too easy to bother timing.
    3. Are the numbers allowed to be in either order?

  6. Subject to correct understanding, I’m quick on this one: seconds to arrive at concepte, the rest of a couple of minutes on implementation.

  7. Yay! Last week left me sad as I didn’t get it at all. This week I am clever Ish. Got them all, I think, in not very long. Many thanks to the hubby for being clevererer than I with the last one. X

  8. Surely the answer to the 1st one depends on how big a pencil you can use 😉

    I got answers to all 3 in a few mins, but can only be certain the 2nd is ‘right’

  9. Got the last two whilst reading them but the first one took a couple of minutes.

    At first I did get a very very large number then, after looking at that answer for a few seconds realised that I could make a number massively larger than that one.

    No maths or additional symbols involved.

  10. I’ve got answers for all three of them. Not entirely sure about the third one, but it works for me. And I think I have a better answer for the first one than Richard, because it’s unimaginably HUGE (and no, no actual symbols are used, just a specific notation of the two digits)..

  11. I have a nine-digit number answer for the first – using only two numbers (no extra symbols).

    The second was the first thing I thought of – not sure how else I could have approached this one?

    The last took a moment, but what I’ve used is a mathematical operation – though not so much a “symbol”.

  12. It took me about 5 minutes.

    1.- I assumed that no symbol is allowed, other than the two digits.
    2.- I had to fiddle with a calculator.
    3.- I am not sure if what I used can be classified as a mathematical symbol.

    Regarding the first puzzle, I just thought of a way of representing a incredibly large number with just one digit! Kind of cheating, though.

    1. jh, I had the same thought about 3. you could even use it twice to satisfy the requirements of the puzzle, but it would make no difference to the answer!

    2. I’m pretty sure that the “number” you are thinking, is not a “number” in the conventional mathematical sense. There are math systems (non-standard analysis, hyperreal fields, transfinite numbers, etc…), where that is considered a fair game number but here?…

      Anyway, yours (in the two digit version) were my contingent solutions too… in case the solutions Monday became to funny. It is always good to have an atomic weapon at hand.

  13. Unfortunately I am incredibly busy today. I suspect it is going to take all day to solve this, simply for lack of trying.
    I may even wait until Sunday, as I have to work tomorrow as well.
    I quite fancy a little trio of puzzles on a Sunday morning actually.
    I shall post my thoughts (or lack thereof) when I have any. No spoilers or hints this week.

  14. 1. I’d say if no rules are given, anything is permitted. a nine-digit number is the best I can muster for now, but I’ll probably dwell on it for a while.
    2. The concept and the answer were simple to get, but still a nice puzzle.
    3. 7.937ish is the nearest I can get so far. Must be overlooking something obvious.

  15. Got all three in about two minutes. I had 1 and 3 as soon as I finished reading them, and 2 took just over a minute with pen and paper.

  16. 1) Easy – unfortunately any hint would give the solution away.

    2) Once I realised you could place multiple 8s physically together, the solution was arrived at in a few seconds.

    3) Depends whether the three is to the left of seven or not…

  17. In total about 3 minutes.

    Two of them were a little tricky but one of them seems so straight forward that I wonder what the puzzle is. (Which means I probably misinterpreted it, ey?)

    1. Yup, I missed a word.
      But since I put in an extra minute to make my first answer neater anyway, I already had the real answer on paper when I realized my mistake. (took me maybe half a minute extra)

  18. For the first one, a 9 digit answer is trivial, there must be more to it than that. If we’re allowed to use symbols, there is no upper limit to the answer. To infinity and beyond

    The second and third ones were rather simple I thought. On those I spent about two minutes, most of which went to verifying my answer to the second.

    1. Oh, I just thought of another number with just 2 digits (with an implicit operation) with no extra symbols, which has in the region of 40 million digits when written out

      Also, “digit” has multiple meanings, doesn’t it. Hm…

    2. “If we’re allowed to use symbols, there is no upper limit to the answer.”
      True. It follows we aren’t allowed to. So it is really pretty easy.

  19. After my total failure last week (not a very fair classification because I didn’t really try… but it worries me I didn’t had the motivation to try it anyway), these puzzles are very nice and light… just what I needed. About a minute for all three.

    My bet is, there is going to be some discussion about the answer of the first, Monday.

  20. The first one took me about 20 seconds. Although I assume I couldn’t use mathematical symbols, there’s no saying I can’t use (implicit) mathematical operations. There’s a little hint for those of you who are still stuck.

    The second one took me a little longer, about a full minute while playing around with my calculator to be absolutely sure. It’s easier than you think.

    As for the third one, it took me about 30 seconds, but only if I’m on the right train of thought. It does say mathematical *symbol* – it doesn’t say that it *has* to be a mathematical operator.

  21. Got 1 and 3 no problem. Actually I think I’ve got two potential answers for 3 but, I think one of them may not be allowed.

    As for two. I can make 1000 no problem using one eight… Trying to work it out using eight 8s. I’ll get back to you on that!

  22. I have answers to all 3. I am certain of #2. I may have bent the rules on 1 and 3, however. My answer to #1 is so big that I have no way of easily calculating it. #3 feels like a cheat but we will see on Monday, I guess!

    None of my solutions have any relationship to each other

  23. Facile in the extreme. Got them all in under 45 milliseconds. Don’t know why I bothered, quite frankly. They are all irritatingly ambiguous, and not even proper ‘questions’ – more like exercises in reading the mind of a lesser organism. I really should charge you for my time, which would doubtless be much better spent contemplating how incredibly clever I am.

    Which is a roundabout way of saying that you don’t half get some humourless berks responding to your Friday Problems. They may – some of these people – be good at maths (although perhaps not quite as brilliant as they’d like to think), but that’s no excuse for such pompous assery.

    Maths can be beautiful and fun, as many of the other respondents demonstrate. However, when Maths attracts so many personality bypass recipients to trail in its wake, it’s little surprise that it frequently gets such a bad press.

  24. ivan Says:
    “If we’re allowed to use symbols, there is no upper limit to the answer.”
    True. It follows we aren’t allowed to. So it is really pretty easy.

    It took me a while to get past the trivial 9-digit answer. I wonder if anyone here has my ~40 million digits beaten (no symbols used – implicit operation with standard notation only)

    1. Color me skeptical. Putting two digits (numerals) on paper without any other symbol leaves very few degrees of freedom for placement and meaning (2 standard, 3 if stretching it). I’m with the “trivial” 9-digit solution.

    2. Michael Says: (2 standard, 3 if stretching it). I’m with the “trivial” 9-digit solution

      There is another way of arranging two numbers to give a defined, standard meaning. It’s not common, but in maths it is well known and well defined. I could tell you, but I’m not supposed to until Monday

    3. Ah – I found a reference to *a* standard notation new to me (not sure if same as yours), and a resulting solution that is *incalculably* larger than 40 million digits. Certainly uncommon, intersting, frightening, and strangely beautiful.

  25. Re Q1 – Just joined some stars in the sky to get a VERY large 77 couldn’t begin to count how many light years big it is.

    Seriously, confident all three solved in 20mins. After finding the answers, realised there was no ambiguity in the question wording after all. Defo no symbols in Q1.

  26. First of all Thanks for the Riddles…

    However, question 1 depends on diferent variables .. leaving the good old decimal system makes upper limits futile…

    Question 2 took a few seconds to have th idea and a bit longer to be interested enoufh to chek if it was right

    mathematical symbol….hmm took some time to see the right solution…

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