Windmill Invariant — IMO 2011 Problem 2

A rotating line pivots through every point equally — the invariant that proves it

Speed: 15°/s
Invariant
Color Count (must never change)
Blue count: 2
Brown count: 2
Pivot: P2
Progress
Angle θ: 0.0°
Half-turns: 0
Total pivots: 0
Visited this half-turn
Blue (left)
Brown (right)
Current pivot
Key insight: When the line hits a new point and pivots, one side's count stays constant. Starting with ⌊(n-1)/2⌋ blue = 2 (for n=5), every point becomes pivot exactly once per 180°. Try the "Wrong Start" button — one point is forever skipped!