[PDF] Barrel/Octagon 1 okt 2007 ... Octagonal Prism


Barrel/Octagon


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Solution: Use any solution method for the Rubik's Cube to solve it as far as possible If you need to flip one final edge thensimply flip that edge and one of the shaved (monochrome) edges If you need to swap two pieces then swap any two of the shaved columns



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    How to Solve the Rubik's Cube by Shelley Chang (appropriated by Lucas Garron) Notation A letter by itself (e.g. F) means turn that face 90 degrees clockwise with respect to the center of the cube. A letter with an apostrophe (F') denotes a 90 degree counter-clockwise turn.

What are the elements of Rubik's cube?

    Elements of Rubik’s cube. The cube contains: six center pieces which do not move relative to each other. twelve edge “cubies” each with two stickers on them. eight corner “cubies” each with three stickers on them.

How many permutations are there on a Rubik's cube?

    The number of possible permutations of the squares on a Rubik’s cube seemsdaunting. There are 8 corner pieces that can be arranged in 8! ways, eachof which can be arranged in 3 orientations, giving 38possibilities for eachpermutation of the corner pieces. There are 12 edge pieces which can bearranged in 12! ways.

How to solve a cube?

    It involves turning one face 45 degrees, prying outthe edge piecesticking out, and disassembling the cube using a screwdriver. Not much mathhere so we’ll move on. This is one of the most intuitive, but probably one of the slowest, ways tosolve the cube. It averages about 100 moves per solution. This ?rst layer must be done by inspection.

01/10/2007 05:07 PMBarrel/Octagon

Page 1 of 2http://www.geocities.com/jaapsch/puzzles/barrel.htm

Barrel/Octagon

This variation on the Rubik's cube is called the Magic Octagonal Prism, or just The Barrel or The Octagon. In Dutch it

is called 'Peperbus', which means pepperpot. It is exactly the same as the normal cube except that the four vertical

edges of the cube are truncated. The corner pieces of original cube now have only two colours and the four edge

pieces in the middle layer have only one colour.

The differences make this puzzle a little confusing. It is possible to get to a position where it seems that two pieces

need to be swapped or where one edge piece needs to be flipped, both of which are impossible on the original cube.

The number of positions:

There are 8 corner pieces with 3 orientations each, 12 edge pieces with 2 orientations each, giving a maximum of 8!

·12!·3

8 ·2 12 positions. This limit is not reached because:

The total twist of the cubes is fixed (3)

The middle layer edge pieces show no orientation (2 4 The colours of the vertical columns are equivalent (4!)

This leaves 8!·12!·3

7 ·2 8 /4! = 450,541,700,775,936,000 or 4.5·10 17 positions.

Solution:

Use any solution method for the Rubik's Cube to solve it as far as possible. If you need to flip one final edge, then

simply flip that edge and one of the shaved (monochrome) edges.

If you need to swap two pieces then swap any two of the shaved columns. For example if the shaved columns are

vertical, then RLD2R'L' will swap the DF and DB edges.

Some people prefer to hold the puzzle so that the last layer they solve is one with two shaved edges (e.g. the

01/10/2007 05:07 PMBarrel/Octagon

Page 2 of 2http://www.geocities.com/jaapsch/puzzles/barrel.htm

octagonal sides are at L and R). This way any final flips/swaps only involve pieces of the final layer.

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