Slithering the Sea
Answer: DAVY JONES
Liam Thomas and Olga Vinogradova (Shanty chorus by Kevin Zhou and Eric Wei)

This is a broken up version of an all values given slitherlink logic puzzle as clued by the title and the name of the ship in the sea shanty, the "Slithering Link". The shanty tells us we must reassemble the map and gives some additional pointers, i.e. the map fragments may not be rotated and the path must be a loop as per normal slitherlink rules.

After reconstructing the map and solving the slitherlink grid, the second verse of the shanty tells us we need to take 2's inside the resulting loop. Using the extraction grid at bottom of the puzzle and taking letters at the 2's results in a partial answer MONKEEBRITSINGER, the answer to which is the final solution to the puzzle. There are several logic paths to reassembling the grid. A sample path follows:

Step 1: Pieces will be referred to by the numbers in the top row of each 3x3. Pieces 132, 232, and 331 may first be resolved completely. Pieces 113 and 223 are nearly completely resolved except for corner 3's.

Step 2: A few observations may be drawn from this point from knowing that the final grid is 9x9. For example: Piece 132 must be in the center column in either of the top two spots, Piece 331 is in the middle row in one of the two left spots, Piece 113 cannot be in the left column. The only piece that can go to the left of Piece 132 is Piece 222. The others may be discarded mostly due to conflicting positions of the 3's. Therefore Piece 222 is on the left edge. No remaining piece fits above Piece 132 without contradictions, therefore 132 is on the top edge.

Step 3: After resolving the top left, Piece 331 can only go in the leftmost spot of the middle row. Piece 121 is the only one to not contradict the current path in the very center.

Step 4: The rest of the pieces are placed more simply. Piece 223 can only go in the very left spot of the bottom row. The piece which fits in the center column bottom spot must have a 1 in the top left, which is only on Piece 113 of the remaining ones.

Step 5: Finally, based on existing paths drawn in the left two columns, the remaining three pieces are placed.

For reference, sea shanty lyrics are below. The shanty is sung to the tune of the recently popularized Wellerman song.

There once was a ship that made us think
And the name of the ship was the Slithering Link
The winds blew hard, the map got torn
But still we carried on, hey!

Soon may the logic boat come
To slither the seas in a loop we run
One day when the linking is done
We'll take our ans'r and go

To fix the map this is what I say:
Map rotation it will lead astray
But when you chart the course today
Take twos inside your loop, hey!

Soon may the logic boat come
To slither the seas in a loop we run
One day when the linking is done
We'll take our ans'r and go