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# Rolling blocks gather much interest

## Question

Eight cubes are placed on a 3x3 grid with the center location vacant.

The top of each cube is distinguished by a certain color, say, as is the bottom, but by a different color.

The side faces do not matter.

Any adjacent cube may be "rolled" into the vacant location by giving it a 1/4 turn about a bottom edge.

By a series of such rotations, a configuration may be reached where the eight cubes are inverted,

and the center location is again vacant.

What is the minimum number of moves that accomplishes this?

All moves are by rotation.

A cube may not be slid into the vacant spot.

You can simulate this puzzle using eight dice.

Initially a "1" shows on the top faces; finally a "6" shows on the top faces.

To record a solution, U, D, L and R can be used for up, down, left and right.

The first three moves will alternate vertically and horizontally.

Therefore, you may begin your solution with URD.

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I found a 36 long solution:

URDL ULDR DLUR DRUU LDLU RDRU LDLU RRDL LDRU
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I've seen one in a Escape the Room Game. Since we are just playing for the least rolls it might be helpful if we use the mini program

http://www.jaapsch.net/puzzles/javascript/eightcubj.htm .Enjoy ..Don't press SOLVE.

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I've seen one in a Escape the Room Game. Since we are just playing for the least rolls it might be helpful if we use the mini program

http://www.jaapsch.net/puzzles/javascript/eightcubj.htm .Enjoy ..Don't press SOLVE.

Great.

Start out all white, end up all yellow. Fewest moves.

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I found a 36 long solution:URDL ULDR DLUR DRUU LDLU RDRU LDLU RRDL LDRU

Good solve.

As far as I know this is the minimum number of moves (proven by simulation.)

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I solved it with by exhaustion over all possible paths of moves less than 38.

I saw that Martin Gardner's column of 1975 had a 38-move solution, so I started there.

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