World four hundred and two is with two inert boxes that hide two slots, three normal boxes and three ice boxes.
Step by step solution
Go DOWN, LEFT and push DOWN. Go UP, RIGHT, UP, RIGHT, RIGHT, DOWN, DOWN, push DOWN, DOWN and DOWN. Go UP, UP, LEFT and push DOWN. Go LEFT and push DOWN. Push LEFT, go RIGHT, RIGHT, RIGHT, UP, UP, UP, UP, UP, LEFT, push DOWN, DOWN, DOWN, go RIGHT, DOWN, DOWN, LEFT, LEFT, UP and push RIGHT.
Go LEFT, DOWN, LEFT, DOWN, LEFT, LEFT, UP, UP, RIGHT and push RIGHT. Go RIGHT, DOWN, RIGHT, RIGHT, UP, UP, LEFT, UP, UP, LEFT, LEFT, DOWN and push RIGHT. Go UP, RIGHT, RIGHT and push DOWN. Go UP, LEFT, LEFT, LEFT, DOWN, LEFT, LEFT, UP, UP, RIGHT and push DOWN.
Go RIGHT, RIGHT, RIGHT, RIGHT, DOWN and push LEFT. Go LEFT, UP, LEFT, LEFT, LEFT, DOWN, DOWN, DOWN, RIGHT, RIGHT, UP and push UP. Go DOWN, DOWN, RIGHT, DOWN, RIGHT, RIGHT, UP, push UP and UP. Go LEFT, LEFT, LEFT, DOWN, DOWN, LEFT, LEFT, UP, UP, UP, RIGHT and push RIGHT.
Go DOWN, DOWN, DOWN, DOWN, DOWN, LEFT and push UP. Go RIGHT, RIGHT, RIGHT, RIGHT, UP and push LEFT. Go LEFT, DOWN, LEFT and push UP. Go UP, UP, push LEFT, go RIGHT, DOWN, DOWN, DOWN, LEFT, LEFT, UP, UP and push UP. Go RIGHT, RIGHT, RIGHT, UP and push LEFT.
Congratulations. You have completed world four hundred and two. Get ready for world four hundred and three.