Students will learn the game of Nim, and how to always win!
Students will learn the fundamentals of basic optimization problems.
Students will study chapter 11, Conditional Probability, from the book Intermediate Counting and Probability by AoPS.
Students will study a tricky combinatorial problem that is important in computer science and has deep historical roots.
Students will learn the basic principles of counting and be able to apply combinatorial arguments to solve probability problems.
Students will learn about permutations and basic group theory. We will use this theory to solve the 15 Puzzle.
Students will continue to learn about the 15 Puzzle and will learn conditions under which it can be solved. We will also cover basic L1 geometry and solve interesting geometric problems.
Students will learn the mathematics behind games and optimal play over the course of the next two weeks. This will be a fun packet and accessible to everyone, but also contain several challenge problems in game theory.
Students will continue learning about more advanced concepts in game theory and build on what they learned last week.
Students will have a fun competition!