13. A cube is placed with one face on square 1 in the maze shown, so that it completely covers the square with no overlap. The upper face of the cube is covered in wet paint. The cube is 'rolled' around the maze, rotating about an edge each time, until it reaches square 25. It leaves paint on all of the squares on which the painted face lands, but on no others. The cube is removed on reaching the square 25 . What is the sum of the numbers on the squares which are now marked with paint?

A 78
B 80
C 82
D $\quad 169$
E 625
Solution: B
We track the position of the side of the cube which is covered in wet paint. We imagine that the maze is horizontal, and that we are looking at it from the side with the squares which are marked with the numbers $1,16,15,14$ and 13 . We use T, B, F, S, L and R for the Top, Bottom, Front, Stern (back), Left and Right sides of the cube, as we look at it, respectively.
Initially, the wet paint is on Top. We see from the diagram that the wet paint is on the bottom of the cube when the cube is on the squares labelled $3,7,11,15,20$ and 24 . The sum of these numbers is $3+7+11+15+20+24=80$.