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Rolling Die (Posted on 2009-11-19) Difficulty: 2 of 5
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    
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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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