A plane is tiled with regular hexagons of side 1. A is a fixed hexagon vertex.
Find the number of paths P such that:
(1) one endpoint of P is A,
(2) the other endpoint of P is a hexagon vertex,
(3) P lies along hexagon edges,
(4) P has length 60, and
(5) there is no shorter path along hexagon edges from A to the other endpoint of P. Tilingcombinatoricscombinatorial geometryhexagon