It's a bit like the math on Rubik's cubes, where there were two different proofs: there exists a configuration of the cube that takes n moves to solve, and for all configurations it takes at most m moves to solve the cube. Those numbers finally reached the same value at 20. Hopefully I won't have to go through that much to figure out the right number of bikes with my partner. After I get my frame fixed I'm still probably getting another, and that's how it starts.
