On the board below, someone has placed a die the same size as one square on the upper-left corner, with an X on its only marked face, on the top.

You proceed to roll the die, rotating it 90° about an edge that's on the board so as to get to the next square, with a new face of the cube now exposed. Continue doing this until the die is on the square marked 1, but with the X again on the top. What's the shortest way of doing this?

What's the shortest way if the goal is to get to the square marked 2, also with the X on top again? Likewise for the goals marked 3, 4, 5 and 6.

bonus:

What if, instead of an X, a Y was on the top face, in the correct orientation, and the goal was to get to the same numbered squares, in the correct orientation again? Is it possible? How?

X					1
					2
					3
					4
					5
					6

m_(n) = roll the die in the direction m, n times
D = down; U = up; R = right

N (number of rolls required)
1 : [7 rolls  ] D R₍₅₎ U
2 : [8 rolls  ] D R₍₃₎ D R U R 
3+: [4+N rolls] D R₍₃₎ D R D_(N-3) R

Posted by Dej Mar on 2009-11-19 17:45:58