There are six villages along the coast of the only perfectly round island in the known universe. The villages are evenly distributed along the coastline so that the distance between any two neighboring coastal villages is always the same. There is an absolutely straight path through the jungle connecting every pair of villages. These paths create thirteen crossings in the interior of the island, one of which is in the middle of the island where paths from every village meet.
The island has a strange courtship custom. Before a father will give permission for his daughter to marry, her suitor must bring the father a fish each day until he has traveled by every route from his village to the father's village. The young man only travels along routes where he is always getting closer to his destination. The young man may visit other villages along the way.
On April 1, father's three sons come to tell him of their intent to woo a bride, each from a different village. The brides' villages are the first three villages encountered when traveling clockwise around the island.
If the sons begin their courtship today and the couples are married on the day following each son's last trip, what are the three wedding dates?
Bonus Question: If the coastline of the island is ten miles long, how long is the longest route that any of the sons takes to reach their betrothed's village?
Let's start with the nearest bride and see if people can agree on that.
I see 5 routes to the nearest bride, so the wedding occurs on April 6.
Label the three brides as 1 (nearest), 2 (middle) and 3 (furthest).
The routes to bride 1 are:
a) Go straight to 1.
b & c) Head out towards 2. At the first intersection you can either turn left and head to 1, or continue straight to the next intersection and then turn left to 1.
d & e) Head out towards 3. At the first intersection, you must turn left towards 1, because any other route leads further from the destination. At the next intersection, you can either continue on to 1, or you can turn right towards 2 and then turn left towards 1 at the next intersection.
Here is some notation, where the first number is the initial heading and each number after that is the direction you travel from the next intersection. Using this notation, the routes are:
a) 1
b) 2-1
c) 2-2-1
d) 3-1-1
e) 3-1-2-1
The nearest bride (partial spoiler)
