Story Puzzle 3: The Black Crow's Identity

After you access the Black Market, you go into an auction stage, where you encounter the Black Crow. You ask it about the Specter's Flute, but the Black Crow isn't about to give up information so easily.
Layton then reveals he knows the Black Crow's identity, but he promises to keep it a secret, hinting that he expects the Black Crow to help out in their investigation in gratitude. Remi and Luke are surprised by this, but Layton then asks them several multiple choice questions which lead up to the identity of the Black Crow.
The first question is aimed at Remi, he asks what the chase felt like --
Maybe the Black Crow is a champion runner, or was using ESP, or was pulling a trick on them.
Once you get this right, Layton then asks how the chase could have been pulled off -- by using mirrors, puppets/stand-ins, or by having more than one person.
Once you get this right, Layton reveals that during the chase, he noticed under the Black Crow's coat that there were some candies. Earlier you encountered a candy seller, who refuses to sell candy to adults. From this, Layton asks what you can assume of the Black Crow -- perhaps the Black Crow is a thief and stole the candy, or is actually a child and could buy the candy outright, or is a bully and forced the candy seller to sell some candy.
Once you solve all three questions, the story puzzle is solved, the identity of the Black Crow is revealed, and you learn more about the Specter's Flute!

Story Puzzle 2: Door Puzzle

You first meet Luke in his room. However, he has locked himself away, and won't open the door for you. He tells you that surely the great Professor Layton will have no trouble figuring out this puzzle. There are a number of items around the door you can click on and learn more about. However, something around the door is odd. When you are ready, you tell Luke, who gives you 15 seconds to figure out (and tap) the item that is odd. Once you are successful, Luke will open the door and talk to you.
This is both a visual puzzle (which of the items around the door are important?) and logic (what makes the item important? What is Luke really asking you to do?) The 15-second time limit is an interesting twist to keep you on your toes.

Story Puzzle 1: Bridge Puzzle

The first story puzzle takes place as Layton and Remi are trying to cross a bridge. The bridge is blocked off by a set of ropes tied in a lattice. Layton looks at the ropes and says that you only have to cut one of them to open up the route again. You are given about 6 options of which rope to cut.