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

A puzzle via Tod B this week. ย Can you figure out the secret of this sequence and so discover what numbers should replace the question marks?

111 = 13

112 = 24

113 = 35

114= 46

115= 57

117= ??

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. Depends on whether the post before it is 117 or 118.
      At least, in my answer that’s important.

  1. Hmmmm,
    Why is there no 116=xx ?
    And if my answer is correct then this is not a sequence that can be continued …….very unsatisfactory.

    1. Not really if you do it by multiplication then addition instead of just digit manipulation. Same answer as adding xx.

  2. Worked out a rule for first example, checked it against others. Solved final case. Total time, 30 seconds.

    If I’m right, it’s a really easy puzzle. If I’m wrong, it’s a really vague bad puzzle!

  3. It is not clear to me why 116 is missing from the sequence.
    The puzzle is either very hard (my time is then – not done yet and not counting) or trivial (my time then is 5 seconds).
    In that a post consistent with the trivial version of the question has been pulled from the site I have to assume that it is a very trivial question.

    TMT has now left the building.

    1. To trick you into coming up with the wrong answer by not really paying full attention.

  4. not even a microsecond

    you should try to keep the level of the site a bit better

    better post at irregular intervals and when having nothing interesting not posting at all than posting useless things at regular intervals

  5. I think I’ve seen this one before – at least something very similar, so it only took a couple of seconds.

  6. 15 seconds or less, depending on whether or not you want me to count my inner voice saying that I can’t do these maths puzzles…

  7. As for all the people who post answers when asked not to do, this is why I don’t read past the break until I’ve solved it or given up. /shrug

  8. There’s an easy solution and a slightly more difficult solution that I think the puzzle designer was shooting for.

    1. For those who solved it in seconds, what would your answer be for “231 = ??” ?

    2. I see what you did there but I don’t think that’s the solution the puzzle designer wants (it’s hard to know because the first to digits in the examples are all 1s).

  9. I’m sort of confident got it, but can’t be that easy, I’ll wait until Monday then probably have to groan!

  10. Hm, I see at least two solutions and both seem equally good.
    1. Linear progression. If this is the answer, then why choose 111 as the first element – beyond me. In this case each pair will be unique.
    2. A little bit more convoluted, involves some arithmetic and rearrangement. In this case 111 will no be different from 21.

  11. The “obvious” answer seems so trivial that it hardly seems worthy of calling this a puzzle. If there’s a more interesting answer, it’s too bad a case that doesn’t fit the obvious one wasn’t given.

  12. For those who need a hint, think of first grade addition when you solve this. For those who know the answer, what would this be: 1000: ??

  13. I get three answers. First obvious one starts with 7 which most people will have. Other answers both start with a 6

    1. If you apply the principle of Occam’s Razor, the obvious one is the right one. I suspect an infinity of possible answers exist, but in this case they will all be more complicated than the immediately obvious one.

  14. The way it is presented there are two ways to go about answering it that both come to the same conclusion for 117. What would the answer for 1234 be? If you approach it from a computer generated logical point of view (which I assume you aren’t) then the answer is 12366. If you approach it from from the a symbolic point of view then it shares an answer with one of the examples you were showing already (I preferably don’t want to say since I’m guessing this is the solution that was intended).

  15. It took me 20 seconds. This is this easiest one I’ve seen, but a good one. Keep these awesome mind bending puzzles coming!

  16. I identified 2 patterns both work. One you had to be clever when 116 is missing the other one it doesn’t matters. Anyone else?

  17. I got 79 and 117
    116 was missing it would be 68
    your adding by 11

  18. but if you do
    111= 1+1+1=3*13=39
    112= 1+1+2=4*13=52
    113= 1+1+3=5*13=65
    114= 1+1+4=6*13=78
    115= 1+1+5=7*13=91
    116= 1+1+6=8*13=104
    117= 1+1+7=9*13=117
    there for it would be 117=117
    so which one is right
    79 or 117

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