This is one of my favorite units. It's about problems which involve taking a fixed structure, and trying to figure out as much as you can about it --- the task the problem asks you to actually prove becomes unimportant, almost like an answer extraction at the end. Rigid problems often have so few degrees of freedom that a lot of what you'll be doing is writing down a lot of concrete examples, and then trying to figure out what they have in common. You will feel like you are discovering mathematics, rather than inventing it (in contrast to the Free unit).
Philosophy
Rigid is a lot about understanding certain structures, contrasting with Free which is about only understanding certain subsets of the structure. Rigid is a lot like Process, except the structures in Process are much harder to understand.
This unit lies on the easier-medium difficulty of a D "combo" (it's mostly about philosophy, so there are a couple of algebra/NT "styled" problems) unit.
Strategies
Trying simpler or base cases can be very useful for finding patterns. Often, these patterns are important to the structure and are lemmas to the solution. This means induction is an important strategy, as it's a lot about generalizing patterns you find. These problems are meant to be explored and soon the puzzle pieces will start to fit together.
Notable Problems
- TSTST 2012/9: a problem that demonstrates how small cases and observations can solve a problem with a seemingly difficult structure.
- USAMO 2015/3: a required problem that is also very instructive.