Professor Layton and the Diabolical Box/Chapter 3: A Diverging Path

This is a relatively short chapter. There isn't any optional puzzles you need to seek out, but there are a series of puzzles you will be forced to solve to progress the story.

Layton's Room
Start off by talking to everyone in the train on the way to Observation Deck. Apparently, the train is about to enter a pitch-black tunnel and all passengers are requested to stay in their cabins. Even the dining car is closed temporarily.

Observation Deck
Talk with Hank and then walk back.

Car 06
On the way you will meet Conrad. After talking to the artist Conrad, make your way back to the door of the deluxe cabin.

Car 04 - Room
On the way to the deluxe cabin talk with Marjorie to learn something about a vampire town.

Car 03
You'll now need to solve Puzzle 056 to gain access into the deluxe Car 02. You also receive a Block Hamster Toy for solving it.

Car 02
There are two hint coins in this car, one in the farthest lamp and one at the bottom strip of the left door. Note that once you've solved the puzzle in the cabin with the open door, you can no longer return to the Molentary Express, so check that you've not missed any hint coins.

Deluxe Room
When you're ready, enter the cabin. Sammy will ask you to decorate the cabin with some roses, which automatically triggers Puzzle 057. After solving the puzzle, be sure to collect two hint coins, one on the table below the window and another in the right sofa cover. Once you try to leave the room, you won't return.

After a cutscene where Professor Layton, Luke and Flora doze off, Luke will wake up in the middle of what appears to be a dream. You will automatically trigger Puzzle 058. It seems that train car number 2 has been swapped on to another engine. You also receive a Light Bulb Hamster Toy for solving it.

You will then have to solve Puzzle 059. Having solved Puzzle 59, you will also have solved the A Ticket With No Destination mystery! You now have enough Hamster Toy to get your hamster down to Level 2. Leave the cabin to trigger another cutscene. It seems that we've arrived in the phantom town of Folsense!