[math-fun] Geometry puzzle

Let B = B_0 be a unit ball in 3-space that's tangent to the z-axis. Let K > 0 be an unknown but fixed constant. Now inductively, for all n > 0, place B_(n+1) so that it's tangent to both B_n and the z-axis, so that its center's z-coordinate exceeds that of B_n by K. QUESTION: --------- Find K_min := the least K such that all nonempty intersections between two B_n's are tangencies. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele