Princess in a Box 1 (Maiden's Escape in the UK version) is a puzzle in Professor Layton and the Curious Village. The puzzle must be solved in order to progress the story.
You might think you'll get stuck within moments of starting this puzzle, but as long as you aren't repeating the same moves over and over, you'll get that block out eventually.
This trick should give you some wiggle room.
Try to move the blue blocks so that both of them are directly above or below the red block.
As a matter of fact, hold off on thinking about how to move the red block to the exit until you finish this step.
Here's one more trick that should help you move those blocks around.
While sliding blocks around, see if you can't move two green blocks to the immediate right of the red block. Then move the purple block to the right of those.
Solution
Correct
Wonderful!
This is a classic example of a sliding puzzle.
Initial Position
Move the higher central green block right
Move the lower central green block right
Move the purple block right
Move the lowest left green block up
Move the middle green block at the bottom left and up