Friday

Today the first group learned the pigeon hole principle, which states that if x number of objects are distributed among y pigeonholes, and x > y, then at least one pigeonhole will have more than one object.

With relevant application as always, here is an example: Li is the largest surname in the world. More than 80 million people in the world have the last name Li. Is it possible to find at least two Mr. Li's with the same number on their heads? Note: Each head has a maximum of 2 million hairs. So, if we filled each "pigeonhole", or number of hairs, with one person, there would be 78 million people left to distribute...thus it is possible to find at least two Mr. Li's with the same number of hairs.

They also learned how to solve proof by contradiction.

The second group worked on inequalities and coin problems. They learned how to make a table as an efficient way to problem solve.