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 Rolling Die (Posted on 2009-11-19)
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

 See The Solution Submitted by Charlie No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 dru my solutions | Comment 1 of 6
d=down, r=right, u=up.
The 1 is five squares from the start.  The direct path RRRRR does not work so the next shortest path might be 7 moves.  One does exist: RRRRDRU
The 2 cannot be done in 6 moves it can be done in 8: RDRRRDRU
The 3 cannot be done in 7 moves it can be done in 9: DDRRDRRRU
The 4 cannot be done in 8 moves it can be done in 10: RDDDRRRDRU
The 5 can be done in 9 moves: DRRRRRDDD
The 6 cannot be done in 10 moves it can be done in 11: RDDDDRRRDRU

I have not yet considered the bonus except that it seems you can rotate the Y by 180 but not by 90 degrees.

 Posted by Jer on 2009-11-19 15:17:32
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