Formulas
Based on Yang Liu's class "Write Down Formulas" at MOP 2018. This unit consists of problems which involve manipulations of fairly involved formulas, such as combinatorial recursions or number theoretic power sums. Despite officially being algebra, there are just as many (maybe more) problems that would be classified as C or N.
Philosophy
This is a unit where you deal with larger algebraic expressions and you usually have to write things out. You often have to manipulate certain sums that are tricky to deal with, and many of the problems here would also fit in the Sums unit. This unit is good for getting a sense of when just doing calculations will work, which is more often than people expect.
This unit can be compared with the Grinding unit; however, while Grinding feels more wide and shallow in terms of cases and computations, Formulas is more narrow and deep.
Strategies
- Recursion and strong induction usually work well with these problems
- Write things out!
- Contrary to the sums unit, you will not have to swap the order of the summation often.
Difficulty
This is a shorter unit which is on the average side of difficulty for a D leveled unit.
Notable Problems
- USAMO 2017/2: A lengthy but instructive walkthrough.
- USAMO 2010/5: A beginning problem that's pretty nice and instructive.
- Shortlist 2014 N6: A not too difficult required problem that's rather nice.