Professor Layton and the Unwound Future/Chapter 3: The Enigmatic Future

Having narrowly escaped getting caught by the family, future Luke decides to take Layton to the restaurant at the arcade to meet an old friend.

Shipley's information
Move back from the casino entrance. Talk to the man to make him leave. Layton will note that the man left wet footprints, even though it had not rained recently. Back at the entrance of the arcade, talk to Belle for Puzzle 29, which will net you the Sweet Hunt course. Enter the arcade and go to the restaurant you visited before. Talk to Shipley the postman, who will tell you that evil Layton is keeping the missing scientists and the prime minister in the Towering Pagoda at a Family stronghold called Chinatown. Future Luke will leave to find a safe route to Chinatown. Shipley will tell you that Chinatown is located.

Move south and east, then talk to Minnie for Puzzle 30, which will net you a raincoat sticker. Talk to the Family Goon for Puzzle 31. Walk west and north twice to trigger another cutscene. Layton will see the woman from before and gives chase, but fails to catch up to her. She looks like Layton's former lover, Claire. You will get Mystery 9: Mystery Woman.

Approaching Chinatown
Once the cutscene ends, move right. Luke will spot a statue that bears a resemblance to him and Layton. Check the statue again for Puzzle 32, then talk to Raleigh for Puzzle 33, which will net you a coffee sticker. Move north and talk to Layman for Puzzle 34. Move north again and tap the white wooden structure repeatedly to break it. It leads to the casino's supply room, meaning that we can now secretly enter the casino. Check the leftmost locker repeatedly to find Puzzle 149. Go back outside and talk to Hardy to get Puzzle 35.

Move north and talk to Graham, who will clarify that he is not part of the Family, and that he is one of the most refined men in London. Move east and talk to Cuthbert to trigger Puzzle 36, which will net you a man sticker. Cuthbert will run off, but will also leave wet footprints. You will get Mystery 10: Suspicious Individuals. Repeatedly check the river flowing under the bridge for Puzzle 152.

Move east, then repeatedly check the red structure to the right for Puzzle 147. Talk to Segal, who will tell you that you're at a black market bazaar. After that, talk to Catanova the cat for Puzzle 37. Move north, then talk to the two guards standing up front. They won't let Layton and Luke pass. Layton notes that they resemble Inspector Chelmey and Constable Barton. and that Layton could find Chelmey to help him. Future Luke will overhear the conversation, and informs Layton he can arrange a meeting like that. He will tell us to move to the Shady Grove, so move south and west. At the Shady Grove, future Luke will say that we can go back to the past through the clock shop we arrived in, even though its door is bolted shut.