Layton's challenges are the hardest puzzles in the game. They are found under the bonuses section. Each one has a different way of being unlocked.

Challenge	How to unlock
The Puzzle Keeper's House	Complete 165 puzzles.
The Hotelier's House	Beat all ten toy car courses.
The Messenger's House	Complete all 12 parrot delivery errands.
The Storyteller's House	Complete all three picture books.
The Time Traveler's House	Beat the game.