As you progress through Crow Country and through Fairytale Town, you'll come across a strange swan ride with some broken parts. Fixing up this swan ride is key to finishing the puzzle and getting a key item. Here's how to solve the Swan Ride puzzle in Crow Country.
How To Solve The Swan Boat Ride Puzzle
The Swan Ride is found in the Fairytale Town area of Crow Country, and will likely be one of the first places you visit as you explore the amusement park. Inside, you'll find a broken down swan ride in need of repairs. A staff note tells you that, to fix the ride, you can put an egg (or an egg-shaped item) inside of the swan's mouth.
Getting The Egg-Shaped Item
You don't have that egg-like item quite yet, so you're going to have to find it. Another staff note will tip you off that there's an "egg-shaped" item inside the Haunted Mansion in the Haunted Hilltop area.
If you haven't already completed the Fairy room puzzle to get the Bronze Key, you'll need to do that before opening up the gates to the Haunted Hills area. You'll also need to grab the Crank from the save room behind the Crypt. It's inside the safe.
Once you've got the Crank, head inside the Haunted Mansion by ringing the bell five times and then letting go. The doors will open up, and you'll be in a large room with a piano and several paintings, as well as two big clocks. Ignore the paintings and the piano for now, and head over to the clocks with the big demon painting in the middle.
By inspecting the demon painting, you'll find out that this demon is known for being "responsible for many deaths between 10:00 and 11:15." So, set the clock to the left of the demon to 10:00 using the crank, and set the one on the right to 11:15. Once the clocks are set to the right time, a large egg-shaped red gem will emerge from the demon's mouth. Grab it, and you're good to go on to the final step of the puzzle.
Fixing The Swan Ride
Finally, you can return to the swan ride and place the egg in the swan's mouth, right next to the wheel. This will activate the ride.
Use the 'Accelerate' button to move the swan to the edge of the water, and then approach it. You can then remove the Chain from its neck, allowing you to complete the puzzle!
Now that you have the Chain, you can bring it over to the Dig Site right across from the Swan Boats and use it to solve that puzzle, with the help of some Gasoline and the Crank you found earlier.