26 Sep
2003
26 Sep
'03
9:40 a.m.
If n >= k I think that we can require each ball to kiss k-1 others in addition to the central one.
I can't see any way to prove that any ball after the second can be chosen to touch any more than ONE previous ball, and I'm confident that you can't, either.
I think I can prove that the *last* ball can be chosen to touch more than one other... --Michael Kleber kleber@brandeis.edu