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

the firstone can be obtained by rolling the dice 4 times to the right. soits in position X1

Then roll the dice one place down then one place right and then one place up. Itwillbe in correct position. moves taken = 7

For reaching 3 roll right twice, down once, right thrice, down once. moves taken = 7

for reching 5 roll right 4 times, down once, right once, down thrice. moves taken = 9

For 2, 3 right, one down, 1 right, 1up, 1 right, 1 down. 8 moves

Posted by Vishal Gupta on 2009-11-19 15:29:38