A river runs East to West and is 30 feet wide. In the river are six posts, three in an East-West line, 10 feet from the southern shore, and three in an East-West line, 10 feet from the northern shore. The posts are 10 feet apart. 10-foot planks can be attached between the posts, or between a post and the shore. With enough planks there are various ways to create a bridge from North to South.
The posts are only 1 foot above the river. A person in a raft wishing to travel from East to West will be blocked by any planks. If the planks create a complete bridge, there is no route for the raft.
Which is larger: the number of different routes for a walker from North to South, or the number of different routes for a raft from East to West? How many different routes for each are there?Source: Past puzzle experience.