Curriculum · Olympiad Topics · Extremal Principle

The Extremal Principle

Consider the largest, the smallest, the closest pair — and let extremity do the work.

Objectives

Choose the right extremal object
Derive contradictions from extremality
Combine with induction

The full interactive edition of this lesson ships in v1.5. The topic is live everywhere else — the problems below feed your Extremal Principle mastery now.

Train the topic

●●●●○What is the smallest

n

such that any

n

integers must contain two whose difference is divisible by

7

?Olympiad classic