This is the famous windmill problem from the 2011 International Math Olympiad in Amsterdam. You need no theory to solve this problem though a couple of meta-heuristics do help here such as:
- Exploring and Playing around with the problem
- Looking for changes and things that stay the same as a transformation is happpening
Timestamps:
00:00 - 00:38 Problem statement and call to action
00:38 - 00:50 Strategy 1
00:50 - 01:25 Enacting strategy 1
01:25 - 01:50 Call to action and a question
01:50 - 02:30 Playing with an example
02:20 - 03:05 An example with a problem and call to action
03:05 - 04:10 Problem solving philosophy
04:10 - 06:10 A failed idea and things we noticed there
06:10 - 06:40 Why we moved to another idea
06:40 - 07:50 A general heuristic we explore
07:50 - 08:40 A question and idea
08:40 - 09:50 Call to action
09:50 - 10:30 Windmill examples!
10:30 - 11:30 Idea #1 from the examples
11:30 - 12:05 Call to action and question
12:05 - 12:50 Important Problem Solving Philosophy!
12:50 - 13:25 Call to action and question
13:25 - 13:40 The question behind the idea
13:40 - 14:50 The idea #2
14:50 - 15:10 Call to action
15:10 - 16:00 Exploring the validity of the idea
16:00 - 16:35 Further exploration
16:35 - 17:00 A question
17:00 - 17:10 Call to action
17:10 - 18:00 Answer to the question
18:00 - 18:10 Question
18:10 - 18:40 Answer to the question
18:40 - 19:33 Implications of findings
19:33 - 19:42 Call to action
19:42 - 20:50 Seeing why this was useful
20:50 - 21:30 Faulty reasoning
21:30 - 21:40 Catching our faulty reasoning
21:40 - 22:40 Idea #3
22:40 - 22:50 Call to action
22:50 - 23:45 Intuition behind idea
23:45 - 24:20 Idea #4
24:20 - 24:40 Call to action
24:40 - 25:45 Proof of idea
25:45 - 25:55 WRITE A SOLUTION!
25:55 - 26:30 #1 The invariant
26:30 - 28:36 #2 (n-1)/2 points
28:36 - 30:05 #3 Rotation and uniqueness
30:05 - 30:24 Bringing it together
30:24 - 30:31 Thanks for problem solving
