Find the total number of distinct ways to join the six islands below by bridges such that
- each island can be reached from any other island via the bridges,
- 1 of the islands has 1 bridge leading from it,
- 2 of the islands each have 2 bridges leading from them, and
- 3 of the islands each have 3 bridges leading from them.
Details and Assumptions:
- Neither of the 2 islands on the far left can be joined directly to either of the 2 islands on the far right.
- There can be more than 1 bridge between 2 islands.
- Mirror images and 180-degree rotations are not counted as distinct.
- No two bridges can intersect with each other.
Adapted from a Puzzle book.