handouts/notes/TODO.md

# Game ideas
 - Math dominos:
   - Each problem is a domino tile, by difficulty.
   - Score is sum if 1st try, max if 2nd try. Subtract min if no solution.
   - Each team can have 2-3 dominos at a time. No free swaps.
   - Pick up dominos without knowing problem.

 - что-где-когда:
  - All teams solve one problem at once.

 - Spacewar!:
   - Two teams, each starts in one root node.
   - Graph of problems, symmetric across middle
   - easy problems close, hard problems far.
   - Goal: capture as many nodes as possible
     - Solve a problem, capture a node
     - solve a problem on the other team's side, capture their node.
     - TODO: a fun way to resolve conflicts?


# Topics:
- Divisibility proofs & properties
- 1 exists ==> assume 2 exist
- <= , >= ==> =
- pidgeonhole

# Handout ideas:
- Notation toolbox
- Propositional logic
- Rubik's group
- Graph combinatorics
- Fourier transforms
- Probabilistic proofs
- Bayesian / Frequentist probability
- Data structures

# Handouts to clean up:
 - Euler's number
 - Lattices
 - Nim handout
 - Stocks

# Problems to record:
 - Nikita: weight of 100 cows
 - Seat swapping: everyone wants a seat that's not their own, no two people want the same seat. Each cycle, everyone swaps. Min # of cycles? Solution: 2, reflect. use even and odd cycles. Takeaway: composition of reflections is rotation.
 - Geometric optimization: ant on cube shortest path, ant on brick shortest path, ribbon on brick (over-under, h-shape) minimal length, Farthest point from corner of brick
 - 180: Sperner lemma and brouwer theorem
 - 25 horses. 5 at a time. find top 3? (7 races)