Added notes

notes/TODO.md

@@ -0,0 +1,51 @@
+
+# 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)