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
• Probabalistic proofs
• Bayesian / Frequentist probability
• Data structures

Handouts to clean up:

• Euler's number
• Lattices
• Nim handout
• Stocks
• Continued fractions

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)