@TheMaskedAvenger You cannot empty three bins if you start from {3,2,1}.

Zsban, yes. Can you characterize all such positions, or find a similar block for 4 bins using such moves N?

@TheMaskedAvenger I did a quick random simulation. There's even a small chance that I got the code right. With the sticks used as the six edges of the tetrahedron in a pre-determined order, the probability that they give a tetrahedron is likely between 0.011 and 0.013 .

Does anybody know what happened to the online archive of K-Theory, the Springer journal? I tried to access a few papers of this (which were not available on the arxiv), and all links turned up dead, and the Springer page does not seem to give any information on the journal at all. I know the journal became defunct in 2006-7, but the disappearance of all articles is worrisome...

@TheMaskedAvenger Probability (again with fixed order of the six edges) is likely about 0.125 from more numerical experiments, if my code is correct.

@JanJitseVenselaar, K-Theory is currently unavailable because of an ongoing lawsuit between Anthony Bak (the former chief editor) and Springer. It's a complete travesty. If you're interested in more details just ask.