If the hands are indistinguishable isn't the time is always ambiguous?
No. At 3 o'clock, the minute hand is pointing vertically (on a bearing of 0° if you like) while the hour hand is pointing due east (bearing of 90°). There is no corresponding time where the hour hand is at 0° and the minute hand is at 90° (12:15 doesn't quite work because the hour hand has moved beyond 0°). So if one hand is pointing due north and the other is due east, you know it must be 3 o'clock.
However there are times when you can't tell.
Good luck with the GCSE teaching by the way - can't be an easy task for you. I did my GCSEs in 1996.
Nice try, but no.
Take 3 o'clock say. On a clock where the two hands are identical, 3 o'clock will look like 12:15, but not quite because at 12:15 the hour hand has moved a bit beyond the vertical. The trick is to find pairs of times where the hands *are* in exactly the same positions.
I hope that helps. Note also that I said a 12-hour period, so we don't need to worry about AM and PM.
Here's a clock-related puzzle I found out about yesterday:
Imagine a two-handed analogue clock (hour and minute hands) where the two hands are indistinguishable, i.e. they are the same size, shape, colour, depth and so on.
During any 12-hour period, at how many different times is the time shown by the clock ambiguous?
NB: 12 o'clock doesn't count.
Well done. I wonder if the constructor deliberately designed that clue so that people would immediately think "ITALIAN".
If you're interested, I've made a cryptic crossword of my own (my first serious attempt at this) and you can see it on my website. It's called the Cryptic Colossus. I'd like to know what you think of it. Cryptic crossword construction is something of an art - I'm not sure I'm quite cut out for it.
Looks good. What program did you use to make it? I've got a puzzle website and it would be useful to know how I could make it interactive.
A couple of features you could add which would be nice:
A timer so people could complete it against the clock (and maybe even a leaderboard showing the top ten times or whatever)
A way of selecting levels of difficulty (about five different levels would be perfect).
But overall, good work.
I've finally got around to doing Little Pigley Farm! Great puzzle! I wish I could be that inventive. Makes my puzzles, with their clues like A = 2B, seem rather dull.
Anyway, Little Pigley Farm was a thoroughly enjoyable puzzle. Took me a while to get started. The first 20% of the puzzle took 80% of the time! Anyone else had a go at it?
I tackled this puzzle a year or two ago. I successfully completed it but it certainly wasn't a 5-minute job.
Regarding duplicate answers, well I compile cross-number puzzles from time to time and it's definitely something I'd try to avoid, but not at all costs (unlike crosswords where they're a total no-no).
I can't remember off hand whether this one had duplicate answers.
Man is that one crazy quiz! To have any hope, I'd have to print it out first before even thinking of attempting it online. It reminds me of real exam questions I've had to do where there are three statements (X, Y and Z) and the possible answers are along the lines of:
A: X and Y are correct but Z is incorrect
B: X and Z are correct but Y is incorrect
C: Y and Z are correct but X is incorrect
D: X is correct but Y and Z are incorrect.
Well I made a sneaky alteration to number 4 in the end, forcing a unique solution to the puzzle.
There are now nine Maelstrom puzzles on my site (which should keep you going for a while). For one that's slightly different, have a go at this one.
Any feedback would be appreciated. Also, feel free to have a go at some of the other puzzles on my site. Good luck!
Yep, you've got me there with number 4. That's probably the hardest thing for me - making sure I haven't overlooked any possible solutions. Multiple solutions don't invalidate the puzzle (there's nothing in the rules stipulating a single solution) but people tend to prefer a unique solution. I remember for instance in 2005 there was some controversy in the UK when Sudoku puzzles appeared in (I think) the Telegraph with multiple solutions. Maybe if my puzzles provoke controversy that's no bad thing (!), but I'll certainly be aiming for a unique solution in future.
Anyway, I'd agree puzzle 5 is at the tricky end of the spectrum, and I'm pretty sure that one does have a unique solution; it looks like you've found it, so well done!
John: firstly these puzzles aren't meant to be easy. There are subtle hints to that effect on the Maelstrom web page. I try to make the puzzles as elegant as possible, which generally means that you'll need to use all the clues to arrive at the solution. However, I will try to vary the difficulty level, so that some puzzles are considerably easier than number 5! I also hope to produce puzzles with clues like "A is prime", "(B+C) is a cube" in future.
Mathsyperson (and whoever else might be interested),
I've just uploaded another couple of Maelstrom puzzles (nos. 4 and 5) to my web page:
If it was up to me, I'd be spending far more time creating new puzzles than I currently am. Still, I hope to update the site with new puzzles more frequently from now on, so keep checking!
Some great responses here. In fact the US Open is the only Grand Slam that does play a tie-break in the fifth set - the others all require a two-game margin when the score reaches 6-6. Indeed Federer was taken to 10-8 in the final set in the Aussie Open a few days ago.
You've pretty much covered all bases now. If there's no tie-break in the fifth, the points difference can be potentially infinite. I like the way NullRoot put it: "scores are both equal and infinitely different".
And if there is a fifth-set tie-break, -78 is the magic number as Mathsyperson explained. Retiring from the match did cross my mind, but retiring at 0-5, 0-40 in the fifth set to give a difference of -91 never occurred to me, so well done Jane!
It might also be interesting to look at the lowest percentage of points you can win while still winning the match. I guess (for the 5th-set tie-break case) you'd do that by making the total number of points as small as possible while keeping the difference at -78. So all the games our player wins (except the tie-breaks) would have 6 points, all the opponent's games would have 4, and all the tie-breaks would have 12. I make that a total of 264 points, of which our player wins just 93, or 35.23%.
For the 'no tie-break' rule, I reckon you'd need a 6-4 final set, meaning our player would win 86 out of 244 points, or 35.25%.
Anyone want to check these figures or my reasoning? The fact that it's possible (though extremely unlikely) to win a tennis match with barely a third of the points shows that not all points are equal. I suppose that's part of the beauty of the tennis scoring system.
And NullRoot, what's P and R ?
I was lucky enough last week to be in Melbourne (what an amazing place) and see some of the incredible tennis there. So here's a tennis question:
Unlike in most sports, you can win a tennis match despite winning fewer points than your opponent. What's the *biggest* negative points difference you can have, and still win the match?
I realise there is more than one answer here, but that makes the question more interesting, doesn't it?
I'd definitely put myself in the recreational maths category. I spend a fair bit of my spare time creating word, number and logic puzzles, a selection of which you can see on my new website.
I used to do maths a bit more seriously and by looking at some of the topics in this forum I'm alarmed by how much I've already forgotten. I'm impressed by how much debate there is over the 0.999... = 1 issue!
There seems to be a healthy interest in maths (and other) puzzles here, so you might see me lurking in that vicinity from time to time.
Well done! Glad you enjoyed the puzzle. The intention was that it could be solved with logic and perseverance rather than just trial and error.
In fact making a grid that works isn't that easy. As well as making it rotationallly symmetrical (like crosswords you see in newspapers) I also have to ensure that there are 26 answers in the grid (one for each letter of the alphabet) and that there are no ambiguous across/down answers.
No there aren't any negative numbers in the solution! That would be particularly sneaky, and didn't actually cross my mind when I wrote these puzzles.
Yes, 251 is certainly a good place to start. Had a look that Wikipedia article - can't say I'd ever heard of sexy primes before!