Thanks and please do continue! There's quite a bit to digest and read there. Most of it seems to be what I've learned at school/university (and since mostly forgotten about), but it's nice to have it presented in this way i.e. important fundamental ideas in a particular area. I am definitely interested in more but it'll take me some time to get through this post and I'm just about to start work. I'll come back once I've finished work.
The first 3 that I haven't solved yet are 93, 94 and 100. 94 is a triangle problem! I think part of the problem is that I'm not used to reasoning about maths very much these days, so I can take a step or two and then hit a brick wall. But seriously don't put time into this that could be used preparing for your exam. I can wait.
So I solved 94! Thanks for the tip. In order to solve it I took your approach, and failed. I assume because not every n, n, n ± 1 forms a valid triangle and my filtering was obviously wrong. Using brute force feels wrong, but of course I do use that. It just seems like there must be a better approach and the large numbers in the questions are obviously there to discourage brute-force. My winning approach was to generate pythagorean triples (as I already had code to do just that) and use those which apply to the question. Although relatively slow (still < 1 minute) it got me into the forum which shows a couple of much faster, very direct approaches to the solution. Since lots of Euler questions involve solving for integers - often with 2 variables - I'd like to request an introduction to diophantine equations - and I keep coming across Pell's equation in the forums which looks like it's related. Once you've solved it you get a link to a forum topic for that question. There are usually lots of good advice in those. Ad. 93 ... I would love to get explanations and tips myself actually.