Hopping Induction to prove AM-GM Inequality:
Card Game: On each card there are 8 countries and if we choose any two cards there is a guaranteed match of exactly 1 country.
If there is one country on each card we need 2 cards and the number of countries are 1
If there are two countries on each card we need 3 cards and the number of countries are 3
If there are three countries on each card we need
Sumant's 1 page of Math 