Ellipses (Christian Wolinski) | Discuss about this problem |
Construction : Place : 1. Connectors 2. Chambers To satisfy following : There are any number of connectors. Connectors are vertical and connect every chamber they intersect. Connectors pose no restrictions inside chambers. There are exactly K chambers on levels 0 thru M. Every pair of chambers does not intersect. Every chamber is a horizontal ellipse of any orientation, eccentricity, size. Every chamber has at least 1 and at most 3 connectors. Traversal : Traversal path consists of exactly N directed straight line segments. A path begins in chamber 1, connector 1, at point A=[1,0,0] and ends in chamber 2, connector 2, at point B=[-1,0,0] Every segment of a path is contained in one chamber. Every endpoint of a segment lies either on a connector or on a chamber's boundary. If a segment ends on a connector then the next segment must originate with this connector. If a segment ends on a chamber boundary the next segment must follow a reflection. Score equals the log of the number of distinct traversal paths. Please send us a simpler description. |