Necklace (Dan Dima)

Discuss about this problem

http://domino.research.ibm.com/Comm/wwwr_ponder.nsf/challenges/January2005.html The general case: A necklace is made up of K(a,b) beads forming a closed loop, each bead being of one of 'a' distinct colors. Determine the smallest possible length K(a,b) in order to have an arrangement for the beads such that every one of the 'bCa' combinations of the 'a' colors taken 'b' at some time (i.e. b-tuple of different colors) occurs at least once as a set of 'b' consecutive beads. Please send us a simpler description.