Entry Combo
A beginner combinatorics unit, meant to help get people oriented with typical proof styles for olympiad problems. Induction, recursion, invariants, and algorithms.
Unit Overview
This unit features a variety of problems. Problems involve induction, proving something is (im)possible, finding the smallest or largest value that works, invariants, describing algorithms, and also counting the number of ways.
An important concept is recognizing two-part problems. For "find the max/min" problems:
- Prove the bound
- Prove the bound is achievable
This also applies to "find all" problems:
- Prove the solution set works
- Prove those solutions are the only ones that work.
Note: Entry combo was originally one massive unit with 50 problems, and is now split into two separate units.
Notable Problems
- USAMO 2011/2: Instructive problem involving an invariant.
- Canada 2018/1: Good example of a two-part problem.
- Shortlist 2009 C1: Required problem where the goal is to show something is possible or impossible.
- JMO 2021/4: A "find the minimum problem".
Advice
This unit is good if you need some combo practice. You should also take a look at Rigid. This unit has a minimum amount of required clubs 45, if you have time 60, and maximum 95.