That’s fair, though I’m not sure what else to put in the title in this case. It’s necessarily going to be a compressed version of what I’m actually asking for.
A good mathematician who hasn’t seen the problem before should take anywhere from 30 minutes to 2 hours to solve it.
The solution should only involve undergraduate level maths. Difficult Putnam problems are a good benchmark for what kind of maths background should be required to solve the problems. The background required can be much less than this, but it shouldn’t be more.
For whatever reason you think the problem should be more widely known. The reason is completely up to you: the solution might include some insight which you find useful, it might be particularly elegant, it might involve some surprising elements that you wouldn’t expect to appear in the context of the problem, et cetera.
It’s fine if the problem is well known, your examples don’t have to be original or obscure.
‘Good 0.5-2 hour undergraduate problems you think should be more widely known.’
Overall, the tricky thing about it is finding a problem that meets all those requirements.
This has a good problem, that might take awhile if you’re not familiar with linear algebra. It might or might not be useful to spreading basic understanding of linear algebra, or what (some of) that is about.
Is this good mathematician an undergrad?
The background required can be much less than this, but it shouldn’t be more.
I didn’t read this the first time through, and I think it suggests me posting the above link here, even if it doesn’t take long enough.
This has a good problem, that might take awhile if you’re not familiar with linear algebra
The problem is very simple without linear algebra—just notice that relative parities are preserved (i.e. if there are an even number of reds and an odd number of blacks, then after any sequence of moves they will always have opposite parities).
The given solution is to highlight a strategy, not the easiest way to solve the problem.
I wouldn’t have necessarily characterized that as
That’s fair, though I’m not sure what else to put in the title in this case. It’s necessarily going to be a compressed version of what I’m actually asking for.
‘Good 0.5-2 hour undergraduate problems you think should be more widely known.’
Overall, the tricky thing about it is finding a problem that meets all those requirements.
https://www.lesswrong.com/posts/R82zuc4MZXvG2dJXY/if-your-solution-doesn-t-work-make-it-work
This has a good problem, that might take awhile if you’re not familiar with linear algebra. It might or might not be useful to spreading basic understanding of linear algebra, or what (some of) that is about.
Is this good mathematician an undergrad?
I didn’t read this the first time through, and I think it suggests me posting the above link here, even if it doesn’t take long enough.
The problem is very simple without linear algebra—just notice that relative parities are preserved (i.e. if there are an even number of reds and an odd number of blacks, then after any sequence of moves they will always have opposite parities).
The given solution is to highlight a strategy, not the easiest way to solve the problem.