Two puzzles this week.

First, in what sense is this order of the numbers from 1 to 10 palindromic, (that is, reading the same from left to right as right to left)?

1   4   3   5   10   2   6   9   8   7

Second, if you rotate the number 6 by 180 degrees you get the number 9.  What is the largest increase possible by rotating a number by 90 degrees?

As ever, please do NOT post your answers, but feel free to say if you think you have the solutions and how long it took.

Answers on Monday.

75 comments

  1. It took about two to three minutes to get them both right and the pleasure was great, thanks! I’ll try these on my students.

  2. I haven’t seen these before and I think they are cute. The second one took about 30 seconds. The first one I sat and looked at for maybe 3-4 minutes then suddenly got it. Unlike some previous puzzles, I am sure my answerw are right.

  3. I’m normally scared by the sight of these number ones, but they required no mathematical skill so I got them pretty much straight away (otherwise I would have been screwed).

  4. Had my suspicions about the 1st one immediately, wrote out my initital thought and was proved right.

    I suspect the 2nd one is actually a trick question, that is if you’ve gone where I think you’ve gone with it.

  5. First- I did not even try.
    Second- I actually rotated the numbers by 90 dgrees. (both clockwise and anticlock wise. At first, nothing clicked. Then I think I got the answer. Though, not very sure if that is the right one.

  6. Second one is easy but I don’t like it as a puzzle anyway.
    First one I haven’t figured out after a couple of minutes.

  7. Will casually think the first one over whilst working.

    For, the second one my answer might be a bit cheaty, but it’s certainly the largest possible increase 🙂

  8. The second one is easy, but my english isn’t good enough to well understand the question!
    Am I suppose to reorder the number in a palindromic order?
    or
    Am I suppose to named the order of the numbers?
    or
    Am I suppose to do something else?

    1. They already are in palindromic order. You don’t really need to do anything except explain how the statement ‘They already are in palindromic order’ makes sense.

  9. Thought I had a brainwave for #1, but doesn’t quite fit- I’m probably overcomplicating, but it does look like it should be right. #2 no problem.

  10. My brain must be on strike lately, I seem to have lost my puzzle solving ability and am remaining unenlightened. Will have to have a coffee and try harder later!

  11. Got both of them pretty fast – second was less than a minute, the first came to me on first guess, only veryfying my answer took some time.

    Nice puzzles anyway and this time without any twisting of unmentioned rules 😉

  12. A further puzzle once you’ve solved part 1 – how many ways can the numbers 1 to 10 be arranged to make palindromes? Here’s a second way:
    2, 4, 1, 7, 9, 5, 10, 3, 6, 8

  13. A more interesting question for the first one would be to tell us the condition and then have us work out the palindromic sequence.

    Got the 2nd one immediately, and the first one after a few minutes thinking.

    1. As above – you can still find other palindromic arrangements of the numbers 1 to 10. Here’s another I’ve just found:
      3, 7, 5, 9, 1, 6, 10, 4, 2, 8

  14. Ah, I had the right idea but the wrong methodology for a while for the second one, but got it before too long.

    The first was tough, until I remembered tricks used on this blog before with numbers.

    Cute.

  15. This time I actually timed it. It took me 30 seconds to read it through and by then I knew the answer to the second puzzle and had an idea to check on the first.
    That idea didn’t work so then I did some thinking and scribbling and came up with a new idea which did work.
    In total 4 minutes.

  16. The concept for the first one in seconds but had to get a paper and pencil to confirm. The second one almost instantly but it requires a bit of ‘out of teh box’ thinking. Depends how you define ‘number’.

    1. Note that Richard doesn’t speak of a “number”, so in a sense, he circumvented that kind of objections. Anyway, your “thinking out of the box” teased me to conclude, there are two solutions!!!!

  17. I don’t seem to get the first one. The second one was very easy for me though, it took less than a second to figure it out.

  18. Clever, very Clever. The second one was instantaneous, but the first took more thought. Maybe one or two minutes for the total time, but with a gap where I “sleep” over the subject. Nice puzzle.

  19. Got the second one quite quickly, as for the first, I still did not get it yet and feel rather silly with myself that so many others have.

  20. The second one was pretty easy, took about a minute to think about it. Haven’t really tackled the first one yet since I’m horrible at number pattern recognition if I don’t see it immediately.

  21. The possible solution to the first one came instantly- but it took me a few minutes to actually check as to whether or not my hunch was right.

    My brain needs more random access memory.

  22. The first I got right away I just had to check it and the second I yet to have gotten….I cant really understand what it is asking…

  23. Ah, I thought I had the second one with 706006, then realised it was 90 degrees instead of 180. took a few seconds after that.

  24. Changing 8 to ‘infinity’ (with no context as to which infinity) does not necessarily give the largest increase. It could equally represent a decrease and so remove 8 from the running as a solution. I guess the rest depend on the font and your imagination.

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