Upon examining the surface of the lake more closely, Layton discovers some floating ice shelves thick enough to stand on. While the girl appeared to be walking on water, she was merely stepping across the ice.
Stepping on an ice shelf sets it in motion, and it keeps moving until it bumps into something or reaches the shore.
Using the floating ice shelves and the small islands in the lake to your advantage, help Layton catch up to the girl.
You're no doubt keen to get Layton tot he girl as quickly as possible, but this puzzle is a clear case of "more haste, less speed".
Trying to find the shortest and most direct route can actually lead to the professor taking lengthy detours!
If you start by moving Layton to the right, you'll soon find yourself unable to progress. You should instead start by moving him to the left.
From there, continue to have Layton ride the ice shelves as far as possible. So, from his starting position, the route should be: left, island, up, right.
Taking the steps given in Hint 2, you may have noticed Layton went straight past the girl, didn't he? While it's frustrating to get so close only to realise you're not quite there yet, there's no need to panic.
Move Layton onto the island, and then have him head for the top right of the lake. Next, move him down, then left, and you should find him by the island in the middle of the lake.
Following on from Hint 3, have Layton cross the island and take the ice shelf to the left shore.
Stick to the ice shelves now, and Layton will catch up to the girl in no time!
Solution
Correct
Ice cold!
What could the girl be looking for in the middle of this lake?