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 Shuffle (Posted on 2009-01-09)
The graphic represents an unfolded cylinder that has a rotatable ring around its girth. Nine blocks, labeled 1 to 9 in order, occupy that band initially. There are three vertical grooves which intersect this band; the slots will always carry 2 blocks although the slot length is for three.

At any one time, if a block in one vertical is moved up or down, the blocks in the other slots move simultaneously in the same direction. Horizontal bands may be rotated left or right as many places as you wish (but one place per mouseover).

Position at initialisation:
 1 2 3 4 5 6 7 8 9 x x x

and then after several moves:
U
L
 6 7 1 2 3 x x x 4 9 8 5
R
D
Note: All of the links provide interaction.

1. Suggest how I can "backtrack" to the initial position in the shortest possible moves.
Consider R4, 4R or RRRR, all being equivalent, as 4 moves.

2. Then, is it possible to reverse the order of the digits? If so, how?

Note: mouseover on links is very sensitive.

 See The Solution Submitted by brianjn Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 any shuffling desired Comment 4 of 4 |

U 1R D 1R U 2R D 1R U 1R D 1R U 4R

will exchange the two numbers in positions 1 and 2.

U 1L D 1L U 1L D 2L U 1L D 1L U 4L

will exchange the two numbers in positions 6 and 7.

So with either of these moves, and an appropriate conjugation of any desired adjacent pair into the positions that get traded, used in combination, you can arrange the blocks in any order desired.

The 4R and 4L at the end were just to get the 1 and 2 into the first two positions with the 9 at the right. The major goal is accomplished just before either of these.

 Posted by Charlie on 2009-01-10 19:04:26

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