ixYesterday I posted a puzzle and promised the solution today. If you didn’t try it, take a few moments now to give it a go before looking at the answer. For everyone else, read on….

So, the image above shows the number 9 in Roman numerals. Your task was to draw one single continuous line and turn this into a 6. I originally thought that there was only one solution, but it turns out that there are (at least) two.

Solution 1 is rather elegant:

9to6_2

Solution 2 was suggested by Bugs Man and is somewhat more involved:

9to6

The puzzle is here, but does not appear to be very well known, and that site only gives the first solution.

My thanks to Bugs Man for the graphics, and the second solution.

So, how did you get on? Did you come up with Solution 1 or Solution 2?

Update: The way in which you tackled the problem might give you some insight into you thinking style. Solution 1 is all about mental set. The puzzle is created to make you think about Roman Numerals, but the obvious solution requires you to think of the image as ‘ix’ rather than ‘IX”. Solution 2 is harder work but, in a way, more logical. So, people who produced Solution 1 first might be more likely to be lateral thinkers whereas those who produced Solution 2 might be more likely to be logical thinkers.

54 comments

  1. Wow, I love Solution 2 (which means of course, that I gave Solution 1).

    Wonder if Prof Wiseman can draw any conclusions as to the thought processes behind each solution? Would be cool if we could draw some inference (if there was any) from a particular choice of answer.

  2. Well, Solution 1 is all about mental set. The puzzle is created to make you think about Roman Numerals, when the obvious solution is to think of the image as ‘ix’ rather than ‘IX”. Solution 2 is harder work but, in a way, more logical. So I would say that people who produced Solution 1 first were more lateral thinkers and those who produced Solution 2 more logical.

    The fact that most people don’t look for a second solution having found the first is a good example of the Einstellung effect in action.

    http://en.wikipedia.org/wiki/Einstellung_effect

  3. I thought it was fairly odd how you originally wrote ‘Turn it into a 6’.

    Which lead me to wonder ‘why didn’t you write “six”?’

    Then I realised why. You didn’t say the line couldn’t be curvy.

    My husband came up with a solution similar to the second. He wasn’t impressed with my reasoning for the first solution. :p He is, by the way, a computer scientist.

  4. Having come up with solution 2 first, and then being inform by RW that there was an alternative, I then had another go. Version 2 took me literally seconds, but version 1 took me a good 4 minutes.

    This logical v lateral preferred thinking style is, I suspect, as a result of my science background before moving into marketing and business improvement consultancy (which often needs lateral thinking). Conclusion: Old habits die hard!

  5. I thought of solution 2 first (basically straight away after viewing it), then right after thought of solution 1, thinking that the first solution I came up with was stupid and having it as SIX made way more sense.

    Then I read this, and now think, oh, so the first one I came up with was a valid answer.

    Funny how things are…

  6. I immediately thought of the second solution.

    I’m German and we have a proverb: “to pass off an X for a U”, meaining “to fool someone”. It is based on the same principle: With Roman numbers it’s easy to change V to an X and vice versa, so that was what many innkeepers and fraudsters did. The letter V became the U in our alphabet.

    Knowing this story, it was quite easy to find soolution 2!

  7. Thought of solution 2 immediately, never thought of solution 1. Which kind of disappoints me, because I fancied myself a lateral thinker (as a subtitler, I do need to come up with creative solutions!).

  8. Like most of the other people who commented, I came up with solution 2 pretty quickly. I completely missed solution 1, even when I knew that there where two ways to answer the puzzle.

  9. Solution 1. Solution 2 very clever though. Not sure I would have come up with it no matter how long I spent thinking. Sometimes when one solution seems so obvious it is difficult to get past that even when you know there are more solutions.

  10. Wow I’m impressed with myself I did solution 1 in 1 second I hadn’t even finished reading the question! I’ll put Lateral Thinker on my soon to be jobless design student CV, thank you Dr. Wiseman!

  11. Just showed the puzzle to my dad, and he came up with an entirely different solution! He used his line to draw a ‘6’ after the X, making it IX6, or 1×6=6.

    Though I just realized I didn’t give him the puzzle as shown here — I didn’t say ‘turn it into a 6’, but rather wrote IX=6 and asked him to solve that. So it’s a solution that doesn’t entirely fit the puzzle… but it hit me as being pretty lateral as well.

  12. Hmmm best i could think was to put a big blue line through it to make equal marks like on a die. Oh well one day ill get one of these right!

  13. Thanks for the insight and explanation as to possible thinking style!

    …and I’m such a victim of the Einstellung effect 😛

    Berber Anna – that is a fantastic solution your dad came up with!

  14. I turned the box 90deg to the right and drew my line from the left side of the now-sideways I, connecting the leftside of the sideways open X, and then looped down to the bottom of the X, and looped up to the right hand side of the X, connecting it into a rather odd looking 6.

    I’m not sure what kind of thinker that makes me. Maybe a drawing obsessed one?

  15. Berba Anna,

    I congratulate your father.

    That makes at least 3 solutions. I wonder if there are any more (climbing out of Einstellung mode!) ?

  16. My second speedy solution, after getting solution no. 1 in a few secs, involves a liberal interpretation of Roman numerals and some economy with scale. I mentally drew a small ‘v’ in the space between the I and the X. This makes IV (four) before X (ten), i.e. six. I think I must be so lateral I’m positively polygonal!

  17. Mine was similar to solution 2, but not quite the same. I drew a blue V over the top part of the X, then turned it upside down.

  18. I basically got solution 2, but instead of “very thick line” I crossed out the bottom part of the X. I always considered myself a logical person…

  19. Got solution 1 in about 15 seconds. Not sure I think solution 2, albeit ingenious, really complies with the rules of the game. It’s none the worse for that of course, but does blocking out actually equate to drawing a single line?

  20. I got Solution 1 in about 10 minutes. I was looking at creating either a Roman or regular numeral 6 out of IX’s forms and/or negative space, but it took some staring and doodling before the written word “six” popped into my head. I have been editing/formatting text all day long so was definitely more in the mood for pictures than words. (I dunno if this indicates lateral or logical.)

  21. My first solution was to draw a really big 6 with a very thick line through the figures, totally obliterating them, which I decided was cheating a bit. Then I came up with solution 1. Oddly though, I can remember seeing that puzzle before with solution 2 as the answer – I just couldn’t quite remember how to get there.

  22. Solution 2 seemed sort of obvious to me, but I think the fact that the IX was framed very neatly in a box precluded my rather linear and logical mind from seeking any kind of solution “out of the box”. Well done to those that saw the bigger picture and weren’t limited by artificial boundaries.

  23. Got solution two after a few seconds of concentration, then went straight to the answer and discovered that it was considered solution two. It wasn’t that I hadn’t thought about curvy or non-curvy lines; I had assumed that since the question used Roman numerals, what was sought was a solution in Roman numerals. I did think (before checking, that is) that my solution should be allowed, as the thickness of the line had not been specified.

  24. Someone showed this to me and my solution was none of those above, but was to put l X 6 (which could also have been the other way up as 6 X l)

  25. Just found this website and the puzzles today, and I came to a different solution, which is somehow similar to solution 2.
    I drew a long horizontal line through the middle of both numbers, making it a “VI” that is mirrored by that line. I considered rotating the page 180° optional and think this is a valid solution.

    Since English isn’t my native language, it doesn’t bother me that I couldn’t come up with solution 1. I don’t think you can distinguish logical/lateral thinkers using tests in a non-native language.

    BTW: Really interesting website, congratulations!

  26. I hate these since its always a trick answer.
    An ‘S’ is not a line (geometry) , its a curve.
    And a thick line, isn’t one either.
    You altered the definition of a line to suit the puzzle.

  27. You said; ” …. draw one single continuous line and turn this into a 6. ”
    So I assumed you meant draw one continuous line and turn this ( the one continuous line) into the number 6 !?
    I thought it must have been a trick question as it was so obvious.
    What does that response come under then? Lateral, logical or just plain stupid ?

  28. I would think solution one is more logical because solution two definitely shows some creativity where logic is precise and reasoning.

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  31. The rules are by drawing a contiguous line. Rotating the image, while creative, it is arguably against the rules. Orientation is not arbitrary.

  32. SIMPLE LOGIC:
    In numeral number there’s IX for #09,,

    Da question is, wat should u add for it will become 6?

    N need da explanation, just answer it,I lyk of dus have a ryt answer

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