This is a thread for helping each other solve and understand interesting/difficult problems in maths and physics. A good source of these is from the MAT, PAT, STEP and Olympiad exams. Here are some useful sites:
The idea is that by assisting others we'll all become more familiar with these types of questions which will help in university admissions tests and problem solving ability. Plus, they're fun to solve. Feel free to post questions you've already done and want to share.
Please put full solutions to questions people post in 'spoiler' tags by writing [SPOILER ] text [/SPOILER ] (without spaces).
This is a thread for helping each other solve and understand interesting/difficult problems in maths and physics. A good source of these is from the MAT, PAT, STEP and Olympiad exams. Here are some useful sites:
The idea is that by assisting others we'll all become more familiar with these types of questions which will help in university admissions tests and problem solving ability. Plus, they're fun to solve. Feel free to post questions you've already done and want to share.
you can also link the british maths olympiad website aswell. don leave us hanging π
A quick starter question that my physics teacher once gave me (don't google it - ruins the fun)
Show that ln(n!) = nln(n) - n + 1
There is a much more rigorous approach to this than what I used (but who knows just how smart some of you are) but it doesn't require anything beyond core modules.
A quick starter question that my physics teacher once gave me (don't google it - ruins the fun)
Show that ln(n!) = nln(n) - n + 1
There is a much more rigorous approach to this than what I used (but who knows just how smart some of you are) but it doesn't require anything beyond core modules.
Actually I like the idea of putting solutions in spoilers, so someone attempting a problem doesn't accidentally see the first step or two, which as you know are often the hardest parts of a problem.
Actually I like the idea of putting solutions in spoilers, so someone attempting a problem doesn't accidentally see the first step or two, which as you know are often the hardest parts of a problem.
A quick starter question that my physics teacher once gave me (don't google it - ruins the fun)
Show that ln(n!) = nln(n) - n + 1
There is a much more rigorous approach to this than what I used (but who knows just how smart some of you are) but it doesn't require anything beyond core modules.