How do get to the Deluxe carriage on the Professor Layton puzzle?

Answer 1

Whilst on the train you should continue walking up and down the train solving all the puzzles that you come across, eventually, one of the puzzles you solve will allow you access to the deluxe carriages.

Answer 2

Continue going up and down the train, eventually Sammy will challenge you to a puzzle, when you have solved his puzzle you will gain entry into the Deluxe Carriages.