Friday Puzzle #3

15 09 2011

There is a horizontal plane which has two vertical axles that are 1 unit apart. Both axles have a rotor with two blades, each 1 unit long (hence the assembly of two blades has a diameter of two units). Both rotors can rotate freely without touching each other – but just barely, because the length of a rotor blade equals the distance between the axles. When the rotors are spun, the friction gradually slows them down until eventually they each stop at a random angle.

An attempt to visualize follows:

When both rotors have stopped, what is the probability that their blades overlap?

Again, post your answer and reasoning as a comment to this article. Lengthy and tedious integrals are fine ;-) but let me hint that the puzzle has a very neat intuitive solution.

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