PuzzleUp 2013 season

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PuzzleUp 2013 season
http://www.puzzleup.com/
This problem solving contest is very good indeed, and I think many here would enjoy it.
The 2013 contest starts tomorrow am (Wed 24/7/13 at 11:00 GMT)
You can see what types of puzzle to expect by checking the archives: http://www.puzzleup.com/2012/archive/ (change year in url to see previous years)
[Edit. I've just realised it is a few years since I last participated!]
This problem solving contest is very good indeed, and I think many here would enjoy it.
The 2013 contest starts tomorrow am (Wed 24/7/13 at 11:00 GMT)
You can see what types of puzzle to expect by checking the archives: http://www.puzzleup.com/2012/archive/ (change year in url to see previous years)
[Edit. I've just realised it is a few years since I last participated!]
Re: PuzzleUp 2013 season
Interesting.
So just checking I understand (?):
There's one question given per week (on Wednesdays) for 20 weeks.
And you get the maximum points for it if you answer it correctly between noon Thursday and noon Friday (BST).
So just checking I understand (?):
There's one question given per week (on Wednesdays) for 20 weeks.
And you get the maximum points for it if you answer it correctly between noon Thursday and noon Friday (BST).

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Re: PuzzleUp 2013 season
Yup, that's about it. However, it's far more important that you get it right first time than have to make a correction at some later date.
There are often corrections/clarifications (eg, about the definition of 'scales'), so it isn't wise to enter too early.
(you can make corrections right up until the end of the 20th week)
Taking the clock away levels the playing field somewhat. Is that a gauntlet I see before me?
There are often corrections/clarifications (eg, about the definition of 'scales'), so it isn't wise to enter too early.
(you can make corrections right up until the end of the 20th week)
Taking the clock away levels the playing field somewhat. Is that a gauntlet I see before me?
Re: PuzzleUp 2013 season
You missed the maximum marks by one in a few thousand. How did you manage that most frustrating feat!

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Re: PuzzleUp 2013 season
Ken, I don't think that was the maximum possible. I'm fairly sure I was late for a few, and may even have had a correction or 2 in there.
So yes, it was a surprising result to say the least.
So yes, it was a surprising result to say the least.
Re: PuzzleUp 2013 season
Oh, just a note if anyone tries to register with a hotmail.com or outlook.com address, you need to add "puzzleup.com" to your Safe Senders list otherwise you can't get the login details...
Re: PuzzleUp 2013 season
So I'm giving this a go too. The submissions for Puzzle 1 seem to be over, is it safe to discuss now?
Re: PuzzleUp 2013 season
I don't think it's really safe to discuss until the whole season is over.detuned wrote:So I'm giving this a go too. The submissions for Puzzle 1 seem to be over, is it safe to discuss now?
You can still earn points for answers entered late, and you can change your answers later on if you realize you screwed up.
Also, while the puzzle community is basically a helpful, cooperative, friendly sort of group, it should be pointed out
that helping other people get the right answer screws up your bonus points for getting a puzzle right that
a lot of other people missed.
Re: PuzzleUp 2013 season
yeah fair enough  radio silence from now on, not that the first two puzzles have been particularly difficult.
I'm curious about the popularity/difficulty %'s. I guess they must have something to do with proportions of correct submissions or something...
I'm curious about the popularity/difficulty %'s. I guess they must have something to do with proportions of correct submissions or something...
Re: PuzzleUp 2013 season
I thought that too. But when I tried validating last years scores it didn't add up. The actual correct percentage is lower than I expected.detuned wrote:yeah fair enough  radio silence from now on, not that the first two puzzles have been particularly difficult.
I'm curious about the popularity/difficulty %'s. I guess they must have something to do with proportions of correct submissions or something...
The answer can be found if you click "Add A Comment", where you rate the popularity and difficulty (between 0% and 100% each), and optionally leave a comment.
Re: PuzzleUp 2013 season
I can't see us commenting after six months unless there was a really spectacular puzzle (or two...). I know that we are not allowed to discuss but if we wrote and said that all UK puzzle members would submit no later than two weeks (deadline plus one week to allow for emergencies), then it would be policed and we could share comments. I have read his philosophy, yet to me a novel puzzle is only closed when it has been admired and dissected. Thoughts?
Re: PuzzleUp 2013 season
After 5 weeks, I see a progression.
Week 1 I did in my head.
Week 2 I worked out in a couple of minutes.
Week 3 Took me an hour or so, I also wrote a program to doublecheck my answer.
Week 4 I couldn't solve, but knew how to write a program that would get it easily enough.
Week 5 Is a postgraduate level maths problem (see it below). If it had a symmetric solution you could easily publish a paper on it. But the numbers have been chosen so that is not possible. We're just looking for an optimal solution to a complicated problem. Worse, we need to find a solution for N and also prove that N1 is impossible to know when we have the correct answer. But there's no reward for being 'close' or the 'best', you're either right or wrong.
And as far as computer checking goes, the number of options to check is a 200digit number, which isn't even close to possible.
And I'm not enjoying the "never give an answer", "never discuss the problems" aspect either. If I knew that at the end we would see the answers, and some nice maths proofs that make me go "ooooh" (I usually like this kind of maths), then maybe. But as far as I can tell we'll never even be told what the answer is, or if we got it right.
So for me, the fun is starting to die away. Maybe nobody will get the answer? Maybe we should just have an educated guess? If someone guesses correctly they'll have a decent advantage...
Are there going to be more like this, or worse? Should I spend a day of my life on it?
@Alan: It's hard for me to estimate the difficulty of previous years' problems just from glancing through them. How do this year's set so far compare, do you think?
OK, that's enough moaning. How are you others finding the season?
I've submitted an answer to all of them if anyone wants to discuss the earlier questions.
Oh, and for the rest of you, if you're curious:
Q5:
"Using a pool of problems, 20 tests will be formed.
Every test should have the same number of problems.
Any problem should be included in at most 10 tests.
For every 5 tests, there should be at least 2 problems common to all of them.
What can be the minimum number of problems in this pool?"
The answer is over 100.
Week 1 I did in my head.
Week 2 I worked out in a couple of minutes.
Week 3 Took me an hour or so, I also wrote a program to doublecheck my answer.
Week 4 I couldn't solve, but knew how to write a program that would get it easily enough.
Week 5 Is a postgraduate level maths problem (see it below). If it had a symmetric solution you could easily publish a paper on it. But the numbers have been chosen so that is not possible. We're just looking for an optimal solution to a complicated problem. Worse, we need to find a solution for N and also prove that N1 is impossible to know when we have the correct answer. But there's no reward for being 'close' or the 'best', you're either right or wrong.
And as far as computer checking goes, the number of options to check is a 200digit number, which isn't even close to possible.
And I'm not enjoying the "never give an answer", "never discuss the problems" aspect either. If I knew that at the end we would see the answers, and some nice maths proofs that make me go "ooooh" (I usually like this kind of maths), then maybe. But as far as I can tell we'll never even be told what the answer is, or if we got it right.
So for me, the fun is starting to die away. Maybe nobody will get the answer? Maybe we should just have an educated guess? If someone guesses correctly they'll have a decent advantage...
Are there going to be more like this, or worse? Should I spend a day of my life on it?
@Alan: It's hard for me to estimate the difficulty of previous years' problems just from glancing through them. How do this year's set so far compare, do you think?
OK, that's enough moaning. How are you others finding the season?
I've submitted an answer to all of them if anyone wants to discuss the earlier questions.
Oh, and for the rest of you, if you're curious:
Q5:
"Using a pool of problems, 20 tests will be formed.
Every test should have the same number of problems.
Any problem should be included in at most 10 tests.
For every 5 tests, there should be at least 2 problems common to all of them.
What can be the minimum number of problems in this pool?"
The answer is over 100.
Re: PuzzleUp 2013 season
I was pretty annoyed with the "six kings" problem because it's a real pain to compute, but the answer is easily available if you know the usual places to find answers to tricky combinatorics questions. So it felt like sort of an honesty check on the participants. I know why the folks running the competition don't want to deal with it, but I think it's hard to run this sort of competition when the answers are just numbers. Having a contest where you had to supply a proof would be a pain to grade, but would somehow feel more satisfying and less easy to cheat on. Even in the first (easy) week, I knew what the answer had to be without working out how to do it. In that case, it didn't take me that long to figure out how to actually make the solution happen and verify that it was correct, but it was very guessable.
As far as the discussion/solution aspect, yes it bothers me.
One thing I've always said coaching a Math Team is that a lot of the best math in any tournament happens in the bus on the way home. The problems you solve during the tournament are the ones you already pretty much know how to do. The discussion afterwards is where you learn new mathematics, learn new ways of looking at problems that you thought you understood, and so on.
I also agree that this week would be "nicer" if it were symmetric. It would probably boil down to something geometric, which would be very satisfying.
As far as the discussion/solution aspect, yes it bothers me.
One thing I've always said coaching a Math Team is that a lot of the best math in any tournament happens in the bus on the way home. The problems you solve during the tournament are the ones you already pretty much know how to do. The discussion afterwards is where you learn new mathematics, learn new ways of looking at problems that you thought you understood, and so on.
I also agree that this week would be "nicer" if it were symmetric. It would probably boil down to something geometric, which would be very satisfying.

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Re: PuzzleUp 2013 season
I found a value N where I could prove N1 was not possible, but couldn't prove whether N is possible or not, so just went with that as I won't find anything better. Not very satisfying or satisfactory.kiwijam wrote:We're just looking for an optimal solution to a complicated problem. Worse, we need to find a solution for N and also prove that N1 is impossible to know when we have the correct answer.
I too think at the end, all accepted answers should be available. I may be wrong, but at the very end I seem to recall you are shown all your answers with points against them.kiwijam wrote:And I'm not enjoying the "never give an answer", "never discuss the problems" aspect either. If I knew that at the end we would see the answers, and some nice maths proofs that make me go "ooooh" (I usually like this kind of maths), then maybe. But as far as I can tell we'll never even be told what the answer is, or if we got it right.
I might ponder them occasionally throughout a day, but never spend serious time on them. They're meant to be fun and challenging, but the latest is neither. Those types are not common. It's a few years since I last took part, but feel this is similar to previous years so far (present puzzle excepted). There have been many deeply satisfying problems with elegant solutions (like the 8 coins), but by no means do they all fall into that category. For me, it's worth sticking with it for when those appear.kiwijam wrote:Are there going to be more like this, or worse? Should I spend a day of my life on it?
@Alan: It's hard for me to estimate the difficulty of previous years' problems just from glancing through them. How do this year's set so far compare, do you think?
Re: PuzzleUp 2013 season
I did the first two weeks and then found i didn't have enough time to have a look at the problems.
There's lots of number crunching for this one, but I think there ought to be a pleasing symmetric solution. I have an approach that will yield a number which works, and with a little bit of bookkeeping will be minimal. Given the format of the overall competition, i can't say i care about it all that much so i'd be willing to discuss in private (email/facebook/whatever) if anyone wants to collaborate
There's lots of number crunching for this one, but I think there ought to be a pleasing symmetric solution. I have an approach that will yield a number which works, and with a little bit of bookkeeping will be minimal. Given the format of the overall competition, i can't say i care about it all that much so i'd be willing to discuss in private (email/facebook/whatever) if anyone wants to collaborate
Re: PuzzleUp 2013 season
Well, after getting hard there around weeks 4  5, the last two have been steadily easier. This week's in particular seems like a snap.
Re: PuzzleUp 2013 season
It's just lulling you, then BAM!
Re: PuzzleUp 2013 season
Sigh.
So this week's competition is roughly the same as a famous historical question that Isaac Newton argued over.
Newton couldn't actually come up with a good proof, although his conjecture was eventually proven correct.
I say "roughly the same", because its actually a slightly harder variation on the same question
(for those who have read the question, the separation for Newton's points was pi/3 or about 1.05 instead of 1,
and using 1 makes the proof of the conjecture harder, not easier...).
So we are left with the people who don't know much about famous conjectures and spherical geometry, who are
straight up being asked to solve a math problem that was too tough for Isaac Bleeping Newton, and those who
do know a bit of Math history who already know the answer.
(This coming off a super easy problem last week that would be the sort of thing
you'd see on any basic test on binomial probability)
This whole thing just feels badly broken at this point.
So this week's competition is roughly the same as a famous historical question that Isaac Newton argued over.
Newton couldn't actually come up with a good proof, although his conjecture was eventually proven correct.
I say "roughly the same", because its actually a slightly harder variation on the same question
(for those who have read the question, the separation for Newton's points was pi/3 or about 1.05 instead of 1,
and using 1 makes the proof of the conjecture harder, not easier...).
So we are left with the people who don't know much about famous conjectures and spherical geometry, who are
straight up being asked to solve a math problem that was too tough for Isaac Bleeping Newton, and those who
do know a bit of Math history who already know the answer.
(This coming off a super easy problem last week that would be the sort of thing
you'd see on any basic test on binomial probability)
This whole thing just feels badly broken at this point.

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Re: PuzzleUp 2013 season
So you're saying the problems are either too easy or too hard for you, so the contest must be 'broken'?
Enjoy the ones you enjoy, and dismiss the rest  that's the easy answer...
The nonmathematical way of doing this week's is simply to mark dots on a ball!
The mathematical way is to guess, then calculate if that value is possible.
I don't know of any conjectures, and didn't need any spherical trig to solve this.
Enjoy the ones you enjoy, and dismiss the rest  that's the easy answer...
The nonmathematical way of doing this week's is simply to mark dots on a ball!
The mathematical way is to guess, then calculate if that value is possible.
I don't know of any conjectures, and didn't need any spherical trig to solve this.
Re: PuzzleUp 2013 season
I've been following the problems for a while without actually submitting them. I thought this one was quite interesting  I did use some spherical trig together with some combinatorics to get an upper bound, and then have a fairly handwavey proof (ie not mathematically rigorous) of a reasonably natural answer.
It's been my impression that this contest isn't solely about beautifully neat mathematical answers. Within private discussions it's become quite apparent how different approaches have led to the same answers...
It's been my impression that this contest isn't solely about beautifully neat mathematical answers. Within private discussions it's become quite apparent how different approaches have led to the same answers...
Re: PuzzleUp 2013 season
PuzzleScot wrote:So you're saying the problems are either too easy or too hard for you, so the contest must be 'broken'?
Enjoy the ones you enjoy, and dismiss the rest  that's the easy answer...
The nonmathematical way of doing this week's is simply to mark dots on a ball!
The mathematical way is to guess, then calculate if that value is possible.
I don't know of any conjectures, and didn't need any spherical trig to solve this.
It's a little like if the puzzleup question were "what's the smallest integer that can be written in two different ways as the sum of two perfect cubes".
All the people who know something about Ramanujan immediately answer 1729, and the rest have a lot of work to do. I don't really think historically
famous questions with widely discussed answers and their own pages on Wikipedia and Mathworld are really a good idea.
And the other point I was making is yeah, "guess and calculate if that value is possible" is fine, except that the calculation in this case is silly.
Without giving too much away, there's a fairly nice, easy to spot, satisfying way to fit "N" points on the sphere, but there's just about enough
wiggle room to fit "N+1" points. And by just enough I mean that the optimal solution for N+1 points is within .005 of a distance of 1, so you have
to be very precise to know if it works or not, because it either almost works or barely works. And the optimal solution for N+1 points is not obvious,
and is so difficult to prove one way or the other that even though Newton thought hard about it in about 1700, nobody proved it was
actually optimal until the 1950's. If this puzzleup question had been asked in 1940, nobody would know for sure what the correct answer was.
Re: PuzzleUp 2013 season
I recognise the frustration in Jackson's voice. I had a similar moment 6 weeks ago.
It's not the variable difficulty that's the problem, it's the choice of problems.
For this week, I did my handwaving proof like Tom mentioned, and felt that would be enough. I've learnt that these problems are often not provable, which slightly disappoints the mathematician in me.
I had absolutely no idea the cutoff between N and N+1 was so close though. And now I'm quite disappointed with the question too. People that spend 5 minutes will get the same answer as those that spend 10 hours on it doing it properly, and will never be aware that the problem was much more interesting than it looked. If he'd chosen a version such that N+1 was the answer, then there is a real reward for those that put all that effort in. But then you have the handful that know or google the answer, and so avoid all the trouble. And we don't just want a quiz on who knows the most about mathematical history...
It's not the variable difficulty that's the problem, it's the choice of problems.
For this week, I did my handwaving proof like Tom mentioned, and felt that would be enough. I've learnt that these problems are often not provable, which slightly disappoints the mathematician in me.
I had absolutely no idea the cutoff between N and N+1 was so close though. And now I'm quite disappointed with the question too. People that spend 5 minutes will get the same answer as those that spend 10 hours on it doing it properly, and will never be aware that the problem was much more interesting than it looked. If he'd chosen a version such that N+1 was the answer, then there is a real reward for those that put all that effort in. But then you have the handful that know or google the answer, and so avoid all the trouble. And we don't just want a quiz on who knows the most about mathematical history...
Re: PuzzleUp 2013 season
However, it's far more important that you get it right first time than have to make a correction at some later date.

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Re: PuzzleUp 2013 season
This contest is nearly over now. Contestants can now examine their score per puzzle on the website.
A little unsatisfactory that 2 puzzles have been withdrawn due to (as suspected for at least one of them) not having a definitive solution! Another has been announced as having two valid solutions (depending on the puzzler's interpretation of the problem). Hmmm...
It's not over until the fat lady sings...
A little unsatisfactory that 2 puzzles have been withdrawn due to (as suspected for at least one of them) not having a definitive solution! Another has been announced as having two valid solutions (depending on the puzzler's interpretation of the problem). Hmmm...
It's not over until the fat lady sings...