Reviving Math Challenges: Can You Solve These Tricky Problems?

[fresh_42]

We, a small group of currently four members, want to try a new version of the math-challenges-threads once a month. It turned out to be not as easy as we thought, to find good problems. So what we've gathered are ten questions on "B" level and ten on "I" level for May, and plan to do the same each month.

They are a mixture of tricky calculations and/or some ordinary exercises. I admit, that I still find it a good idea to provide - in opposition of just to answer - good homeworky questions to settle students' understanding of concepts. That's where our new rule comes into play:

We want to give students a head start, because some problems might be easy for professionals but still difficult for students. This means that everybody with a title on PF (advisor, homework helper, mentor) is kindly requested not to post answers before 16th of each month. We think that's fair, so that high school kids and undergraduates can take their chance before someone with a greater experience reveals the solution. Of course you can still solve them, just wait until the 16th to publish your solution.

It also means, that we welcome everybody's good problems to help us prepare next month's challenges. So if you have one, please send it to me per PM and - please - with the solution and a note, whether you commit yourself to moderate its answers in the thread, i.e. decide whether a solution can be accepted or hints are necessary. I'm unfortunately no genius, as most of you will probably already have recognized.

The first two threads ("B" and "I") will be posted within the next hours.

 

[Greg Bernhardt]

Yay! I'm going to out the members on the challenges team because they've worked really hard @fresh_42, @QuantumQuest, @StoneTemplePython, @Charles Link

 

[Greg Bernhardt]

First set is live!
https://www.physicsforums.com/threads/basic-math-challenge-may-2018.946356/

 

[mfb]

Can we talk about the classification "basic"? Most of them are certainly not high school level.

 

[fresh_42]

Can we talk about the classification "basic"? Most of them are certainly not high school level.

But many can be found by a little internet research. E.g. the solution to the differential form exists on Wikipedia as well as on PF; and the only difficulty with the metrics is to look up how they are defined. Today's students have much more tools and possibilities to figure out things, and they have to learn how to use them. However, you're right and we are in a learning process here. It appears that we can rely much more on ordinary textbook questions for the "B" level thread. Let's wait and see, and hopefully improve over time.

Another basic difficulty for us is, that we have a rather widespread membership, so "Basic" isn't easy to define. The fifteen days advisor ban was therefore meant to separate two main groups a bit. Most of the questions need an understanding of the concepts, rather than a tricky method for solution. But concepts can be looked up, although some of them addresses undergraduates more than high schoolers. The hope is also to make them a little curious and maybe ask questions in one of our other forums. We will improve on next month's problems, because we're learning, too, hopefully.

 

[lekh2003]

But many can be found by a little internet research. E.g. the solution to the differential form exists on Wikipedia as well as on PF; and the only difficulty with the metrics is to look up how they are defined. Today's students have much more tools and possibilities to figure out things, and they have to learn how to use them.

It is important to not that literally everything can be found online, but little can be understood fully. If we continue by that logic, we can simply combine "I" and "B" sections since the students who don't understand "I" level questions can simply "search it up".

Basic math challenge problems might refer to some of the harder questions from the IMO or the such, not Putnam questions designed for undergraduates.

 

[fresh_42]

... who don't understand "I" level questions can simply "search it up".

I implemented some obstacles, e.g. the example wasn't on the English Wiki, and I recognized some minor typos in the version on PF. Point is, you cannot guarantee that something isn't anywhere on the net. However, this usually isn't a problem, as a search for "differential form" will very likely produce a million links before the one in question. This way it will contribute to the understanding in general, because one has to learn a bit about the terms to search for.

The distinction between "B" and "I" indeed isn't settled, yet. Some "I" questions are easy as soon as one understood the language, but this is also true for many theorems: once you know what to do, a calculus II proof might well be taught in high school. Esp. algebra questions are often difficult just because of the fact, that school kids don't know what a field extension is. To prove e.g. $\mathbb{C} \cong \mathbb{R}[x]/(x^2+1)$ is easy. Nevertheless will many consider the RHS as difficult. And if I had chosen $z$ as variable name, confusion might be complete.

You cannot totally eliminate overlapping, since a classification in "B" and "I" is by its nature subjective to a certain degree.

 

[lekh2003]

You cannot totally eliminate overlapping, since a classification in "B" and "I" is by its nature subjective to a certain degree.

If such overlapping is even possible, then the B level is much too advanced. B level seems to be easy questions for undergraduates and graduates as yourselves, but unimaginably difficult question for high schoolers (which seem to comprise the majority of PF members).

Furthermore the May problems have all been answered by students either way ahead of the curriculum in Year 12 or the undergrad and graduate members of PF. Where do us measly high schoolers stand?

I propose that the current difficult level considered "B" be merged with "I" and a new level tailored for high school students be created. Nothing which requires complex calculus work, but instead something which can be solved using the skills high schoolers might have learned and a little thought.

 

[fresh_42]

I propose that the current difficult level considered "B" be merged with "I" and a new level tailored for high school students be created.

I agree. Just that I'd lower the degree of difficulty in "B" instead of a new one. I'll discuss this with the others. At least it would make life easier to find good questions.

 

[lekh2003]

I agree. Just that I'd lower the degree of difficulty in "B" instead of a new one. I'll discuss this with the others. At least it would make life easier to find good questions.

Thank you very much, I look forward to it.