On Friday I posted this puzzle…..

If you turn this number upside down or reflect it left-to-right you get 11 either way, but the original number is not 11.  What is it?

If you have not tried to solve it, have a go now.  For everyone else, the answer is after the break.

The answer is the Roman numeral IX – did you solve it?  Any other answers?

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. That’s also the answer I got as well, along with anything else that starts with 11 and has as many zeros as you like afterwards. I think it’s a perfectly valid answer, providing upside-down refers to a rotation, not a reflection.

    2. @XRayA4T

      I also got 11/100 or .11 which I think is a more apt answer than delving into the Roman numerals as poster Matryn implies something “turned” upside down can be turned towards/away from oneself rendering Richard’s IX as IX and not 11, so it is incorrect.

      Actually .11 upside down is 11′ or ’11 (using ‘ for lack of decimal pt.) so it appears even more incorrect……hmmm, ok Richard you win!

    1. I had the same problem at first because I thought of “turn upside down” as turning in 3d, with the top coming towards me and the bottom going away from me, resulting in a top/bottom reflection.

      But then I realised that another way to “turn upside down” is to turn it like a clock. I didn’t end up with IX though. I chose 111 (binary for 11), which is wrong because it’s always translated to 11, unless you add zeros.

    1. Anne,

      That doesn’t quite fit the problem. In order for your solution to work, you’re simply choosing to call II Roman numerals to start with and then calling them 11 at the end. If you can do that, then you can call it 11 to start with and that violates one of the conditions.


      Imagine that you had to write IX on a piece of paper and then flip in by moving the paper. You will have to rotate it 180 degrees to make it happen instead of flipping it front to back.

  1. Yes, I got IX as one possible answer. Another is the number 13 in binary, which is 1101 – when turned upside-down or reflected left-to-right you get 1011, which is binary for 11.

  2. I got the answer because one prat (as seems normal these days) thought it was clever to post it in the comments last friday.

  3. Ditto. Got the Roman after 5 minutes of wondering about typography and/or handwriting styles.

    And here is another solution in one more encoding, not unheard of here – Morse. Its symbols obey the same symmetry, namely that turned upside down = reflected left-right

    Original: – – – – . , – – – – . = 99
    Transformed: . – – – – , . – – – – = 11

    1. Hey, that works-binary to start, binary in the end, not eleven, then eleven, as long as you don’t turn it forward(same as in Richard’s sol’n) when turning upside down it’s perfect!

      A better answer to Richard’s because we get to use the much cooler binary numbers rather than silly out-dated Roman numerals!

      Good Job rcomian!

    1. pardon me for voicing an ans that some people do not like, but it is a number when reversed, it is a number spelled in letters not numbers so that is a good trick. also if it is not a num how can Lazy Z use it as 1?

    1. That’s not a solution at all because it starts out as eleven and finishes(no matter how you turn/flip it upside down) as eleven. Does not meet requirements at all

  4. Given that every Friday some plonker either supplies the solution or a heavy tip, perhaps there is a case for not allowing comments when the puzzle is posted – after all, most of them either take the smug form of declaring “I did it in so-many seconds”, or cries of “which bit of ‘as ever, don’t post the answer’ did you not understand?”. You can’t really have a meaningful discussion, and it just gives scope for those idiots who spoil it for the rest. I hope Richard reads this and considers the idea.

    1. I agree, Tom, but a simple solution is to just not read the comments on a Friday. It’s a shame, as there is sometimes some useful discussion, but unfortunately people like Dave’sNeighbour think it is funny/clever to annoy everyone by deliberately giving it away week after week. There’s obviously something missing from his life.

  5. I got IX and 1101 and think 0.11 is just as valid but they all rely on 180 rotation rather than vertical reflection for the ‘upside-downing’ so none are really satisfactory.

  6. My answer was 11, assuming the first time richard 11 he used base 10 and the second time base 2. I am almost willing to accept being wrong…

  7. I came up with the binary solution first, then the Roman numeral II solution. That led me to the Roman Numeral IX solution. Then I came up with the 110 solution (infinite by adding zeroes if you don’t use thousands separators), and that also led me to one other solution:

    Richard is British, and I’ve seen the British use the middot “·” as a decimal point (although I’ve seen them use the full stop as well). So, the number could also be ·11, since rotating or reflecting it puts the dot on the other side.

  8. For the first time in several weeks, I didn’t get it at all this time. I was thinking of “upside-down” as meaning a vertical reflection rather than a 180 degree rotation, but even so I don’t think I would have got it.

  9. I beg to differ. IX on paper is 9, as seen in the mirror it is XI and means 11, and visa versa. Clearly not equal. The answer must be II, which is 2 and it is 2 (or II) whether it is seen in a mirror or upside down.

  10. My daughter figured it out quickly after I asked her, “What trick do number puzzles almost always seem to use in cases like this?” “Roman numerals? Oh, it has to be IX since XI is eleven.” The binary solution 1101 is equally good. I’d quibble that the various 1100 and 0.11 type solutions are correct technically, but not in spirit since you’d use the word “eleven” to say them … “eleven hundred” … “eleven tenths.”

  11. I thought maybe (01 + 1) … although this is merely an expression which can be evaluated into a number.. 🙂 Steve, St Albans.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )


Connecting to %s