Recursion

Combinatorics Progress

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Recursion

Recursion and its applications in combinatorics.

Authors: Jaden Park, Gabriel Liang

Introduction

Refer to the recursion lesson in algebra to get a decent understanding of what recursion is.

In combinatorics, problems which require recursion are solved similarly to those the ones in algebra.

Here are some practice problems.

Practice Problem

Fred wants to climb a $10$ step staircase. He can climb either $1$ or $2$ steps at a time. In how many ways can he climb the staircase?

Practice Problem

(2013 British Mathematical Olympiad Round 1 Q4)

Isaac is planning a nine-day holiday. Every day he will go surfing, or water skiing, or he will rest. On any given day he does just one of these three things. He never does different water-sports on consecutive days. How many schedules are possible for the holiday?

Final Notes and Tips

Avoid miscomputing a value, from personal experience, the idea behind the solutions themselves are not too hard to think of.

Pigeon Hole Principle

Conditional Probability

Combinatorics Progress

Counting

Principles

Miscellaneous

Introduction

Practice Problem

Practice Problem

Final Notes and Tips

Introduction

Practice Problem

Practice Problem

Final Notes and Tips