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.

1. garrett says:

that wasnt too bad. 3 minutes. good puzzle though

2. The second was easy… The first though… Have to think about that one for a while I think.

1. M says:

same here

2. Gus Snarp says:

Is the second one really that easy, or am I missing something?

3. 6 minutes for both. Took a little bit of thinking for the first one.
Nice pair, though. I”ll use them in tomorrow’s math class!

4. Israel Girón says:

Second one was easy…not sure if I got the firsts one though…

5. Second one easy, one minute. First one – thinking, thinking…..

1. Bernhard says:

Same here.. as i expect that what i found for the first is not what is searched

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.

7. About 30s. My first impression was correct for both so no need to explore alternatives.

8. Morgan says:

Second one instantly. First, not sure I even understand it…

9. allegoricus says:

A few seconds for the second one, but the first, … 😦

10. Charlotte says:

Wow I actually got the first one straight away! I think I’ve got the second one too 🙂

11. mR pSYcHo says:

I think these have been the easiest puzzles so far.

12. florayG says:

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.

13. Gareth says:

Got them both instantly. It’s good to finally have a couple of puzzles that my tiny mind can solve! 😀

14. 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).

15. Al says:

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.

1. Julia says:

same for puzzle #1.
I had to write #2 down too, then it was obvious.

16. rmb says:

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.

1. rmb says:

Oh, right now suddenly even the first one clicked. Liked it. A clever one.

17. moopet says:

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.

18. JimC says:

1 – 2 minutes for both. Second one gave me a bit of a chuckle when I figured it out.

19. Dave H says:

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 🙂

20. MiniKeb says:

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. Julia says:

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.

21. Jo says:

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.

22. I got the second half (the 90º rotation bit) in seconds. Still puzzled by the first bit, though.

23. Marion says:

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!

24. Andy Thelwell says:

Part 2, 3 seconds.

Part 1… thinking…

25. Nic says:

About 1 minute to get both. Simple!

26. Both were fairly simple…not more than half a minute each. Must try with students too! Thanks!

27. Daniel says:

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 😉

28. Ed says:

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

29. Carl says:

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. Ed says:

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

30. Shell says:

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.

31. DeepField says:

Contrary to most of the comments above, the first one was immediate. Haven’t solved the second one…

1. DeepField says:

Just realized it was 90°, not 180°!

32. it took me sometime to understand it, after that just couple of seconds to find the answer i like this one.

33. Janne says:

Few seconds for both… these were easy

34. 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.

35. Cosmin Romania says:

I got the second one immediately.
The first one was finally cracked after a few HOURS.

36. Todio says:

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. Joao Pedro Afonso says:

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!!!!

37. Juan says:

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.

38. Joao Pedro Afonso says:

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.

39. Mitch says:

The solution for #1 seems so easy that I barely believe it’s what the author meant.

40. Kieran says:

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.

41. 3 seconds for the 2nd one; 2 weeks for the 1st, give or take a week

42. Marc says:

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.

43. Ed says:

2nd one was easy. The first one took 2 tries and a pencil and paper.

44. Lindamp says:

Easy but nice!

45. 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.

46. Didn’t time it exactly but definitely under 5 mins. Nice puzzles.

47. Jenny says:

I got both immediately, which is unusual but sure felt nice.

48. Eddie says:

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…

1. Eddie says:

Nevermind I got it….

49. Bob says:

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.

50. Hyanur says:

second one really easy, if there’s no clue 😉

the first one took me some minutes, but got it, too…

51. Pedge says:

Got them both instantly, took about 30 seconds to check myself for the first one.

52. Patari says:

I got the 2nd part in a few seconds, but the 1st part only after looking at it again a few days later.

53. mr tompkins says:

I got the answers before the puzzles were posted, I’m that good.

54. cliffette says:

The first one has me flummoxed. I really hope I won’t slap my forehead too hard when the answer is revealed…

55. cliffette says:

Arrrrrrghhh! Never mind, I got it now. Feel like slapping my forehead anyway.

56. nelson says:

I can’t understand the first question at all, can anyone explain to me what I have to do?
The second is too simple.

1. cliffette says:

The number sequence is palindromic. Your job is to explain how it is palindromic.

57. Chris says:

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.

1. Bob says: