# Bogglers Solutions

Sunday, February 06, 2005

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The Cubies

1 There are 6 cubies colored on one side, one in the middle of each face of the cube. There are 12 cubies colored on two sides, one in the middle of each edge of the cube. And there are 8 cubies colored on three sides, one at each corner of the cube. There is 1 uncolored cubie in the center of our imaginary cube. There are no cubies colored on four, five, or six sides.

2 The three pairs of colors on opposite sides of the cube that never appear together on a single cubie are blue and green, yellow and white, and red and orange.

3 The cube has six faces, and each face can be twisted 90 degrees clockwise or counterclockwise, for a total of 12 possible face twists.

4 When you twist a face, 19 cubies stay in position: the center cubie of the twisted face, and the 18 cubies in the rest of the cube. (This answer applies only to our imaginary cube. An actual Rubik’s Cube has no center cubie.)

5 Since the center cubie of each face never changes position, it always signals which color that face should be in the solved cube.

The Colors

For each cube, the pair of diagrams on top shows the answer, and the pair of diagrams on the bottom shows where the grayed-out cubies would be in the cube’s starting position.

The Variations

1 Pyraminx needs 36 stickers: nine triangles in four different colors. The Skewb Cube needs 30 stickers: four triangles and a square in each of the six different colors.

2 Pyraminx has eight twists: two each along four different axes perpendicular to the four faces. The two basic twists are at right.

The Skewb Cube has four twists: one along each of the four different axes that connect opposite corners of the cube. The basic twist is shown below. If we remove the rotating half, we see that the plane of the cut is a hexagon, as seen below.

3 Pyraminx is made of 14 smaller units of three different colorations: 4 corner tetrahedrons colored on three sides (red), 6 edge tetrahedrons colored on two sides (orange), and 4 center octahedrons colored on three nonadjacent sides (yellow).

The Skewb Cube is made of 14 smaller units of two different types: 8 corner tetrahedrons colored on three sides and 6 center squares colored on just one side.