* Challenging: This implies the puzzles are complex and require thought and effort.
* Intricate: This emphasizes the puzzles' complexity and the need for careful analysis.
* Complex: This focuses on the puzzles' many parts and elements.
* Tough: This suggests the puzzles are hard to solve but not impossible.
* Tricky: This implies the puzzles involve cleverness and the need to think outside the box.
The best word depends on the specific type of puzzles Harry solves and the desired emphasis.