The use of symmetry in solving problems

When I learned mathematics at school and at college, various concepts and techniques were taught. The most powerful, and perhaps the most useful, was calculus. We learned a little about symmetry, but it was not regarded as powerful or useful; discussions of symmetry were more like "look at the pretty flower". I only realised much later that symmetry could be used to solve problems. Here are some problems that can be solved using symmetry.

This is one of several miscellaneous pages.