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Paul Adams - Rubiks Cube: How to Solve the Shepherd Cube and Tartan Cube

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Rubiks Cube: How to Solve the Shepherd Cube and Tartan Cube
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Paul Adams
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Paul Adams
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2009
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RUBIK'S CUBE: HOW TO SOLVE THE SHEPHERD CUBEAND THE TARTAN CUBE

Paul N. Adams

Smashwords Edition

- o0o -

INTRODUCTION

In May 2002 I purchased a Shepherd Cube anda Tartan Cube. I noticed that there was no solution online, so Iworked out a simple one for each and put them on a web site. I havenow combined the two into a simple eBook.

Paul N. Adams

Los Angeles

May 11, 2002.

SHEPHERD CUBE

1 A generalized Shepherds cube is based ona regular 3x3x3 Rubiks cube - photo 1

1. A generalized Shepherd's cube is based ona regular 3x3x3 Rubik's cube, except each of the fifty-four cubiefaces differs only in orientation. When solved, each of the sixcube faces has all nine of its cubie faces with the sameorientation. The clearest design is a black arrow on a white field,with the arrow pointing up, down, left or right. A solved cubecould be oriented so that just looking straight at it (without theviewpoint shifts associated with standard Singmaster notation) thetop face points left, the left face towards you, the front face up,the right face away, the far face down and the bottom face right.Opposite faces point in opposite directions.

2. There are only four different types ofedge piece, three of each type. Similar-looking edge pieces can beconsidered interchangeable, with the one exception described below.Read an edge piece as if it were in the top front position, lookingat the top face and then the front face, for example, "left-up."This is equivalent to "down-right," which is how it would appear ifyou flipped the cube over either physically or mentally. There isno need to list out the different types of edge piece.

3. There are only four different types ofcorner piece. Similar-looking corner pieces can be consideredinterchangeable, with no exceptions. The four types are:

A. One corner piece, when viewed in the topleft front position, that has the top face left, the left facetowards, the front face up. Any one of the three arrows will pointto another face on the same cubie. If you twist this cubie eitherclockwise or counterclockwise, it will still look the same, solet's call it a "samie."

B. One corner piece, found diametricallyopposite on a solved cube, that when viewed in the top left frontposition has the top face towards, the left face up, the front faceleft. Any one of the three arrows will point to the same cubie.This is the other "samie."

C. Three " matchable" corner pieces, each ofwhich has or could have the up face aligned (either left/right orup/down) with the up center and edge pieces. It might sound complexbut visually it's obvious: either the arrow blends in or it's atright angles and stands out as wrong. No further description ofthis kind of corner cubie is necessary.

D. Three "unmatchable" corner pieces, eachof which does not have or could not have the up face aligned(either left/right or up/down) with the up center and edgepieces.

4. I am basing this description on theelementary Singmaster 2 solution, i.e., make a cross on the upface; solve three corners correctly on the same up face; flip thecube over and solve three of the edge positions in the middlelayer; solve three edge positions on the up layer; solve the tworemaining edge positions; put the five remaining corner pieces intothe correct positions; solve the orientations of those five cornerpieces. But use this solution with the modifications as shownbelow. You can adapt these modifications to your own favorite wayof solving a regular cube.

5. Start with the top face center cubiepointing left; rotate the left face so the center cubie pointstowards you; the front one up; the right one away; the back onedown; the bottom one doesn't matter for now. The reason for alwaysstarting with the same orientation is so that if you put the cubedown, or look away too long, it is easier to figure out where youare up to in the procedure.

6. Make a cross on the up face, startingwith the "left-up" edge position, then "down-right," then"right-down," then "up-right." Then put in three corners correctly,starting with the first "samie." For each of the next two, firstselect a "matchable" corner cubie, and then make sure to align itcorrectly as you put it into position. Again, if you always solvethe same positions in the same order it is easier to figure outwhere you are if you get lost.

7. Flip the cube over and solve the threeedge positions in the middle layer, reading them the same way asbefore even though you are solving each in the front right positionand not the front top position.

8. Orient the center cubie of the up facecorrectly, i.e., the opposite way to the down face.

9. Now for the remaining edge pieces. Solvethe top front edge position, then the top left edge position, thenthe top back edge position, in that order. At this point comes thatexception mentioned above, where similar-looking edge pieces arenot necessarily interchangeable. There are two possibilities atthis point: situation one, the two remaining edge pieces arealready correct or just need to be flipped in place with theregular BU'B'UR'URU'; or situation two, they aren't. With situationtwo, you need to interchange one of the remaining edge pieces withone or the other of its similar-looking fellows. One swap willwork, i.e., transform into situation one, the other won't. So ifthe first swap doesn't work, the second swap will.

10. Now all the edge pieces are in place andthere are at most five corners left to do, with the down right backposition being (usually) unsolved. Locate the (usually) unsolved"samie" cubie and put it in the correct position, taking care notto move it afterwards. Rotate the up face so a mismatched cubie isin the up left front position, and put it into a position where itmatches. Repeat until all five corner cubies are in correctpositions.

11. Do the usualclockwise/counterclockwise twists to solve the corners. There isonly one difference you will frequently run into: everythingappears solved except for one corner, which needs to be twistedclockwise or counterclockwise. Use a "samie " as the other cubie of the pair andtwist as normal.

TARTAN CUBE

1 A Tartan cube asinvented by Dan Hoey is a regular 3x3x3 Rubik s cube - photo 2

1. A Tartan cube, asinvented by Dan Hoey, is a regular 3x3x3 Rubik ' s cube, except that each of thefifty-four cubie faces is divided into quarters, with one of thecolors red, green, yellow, blue in each corner. Each of the sixfaces has these four colors in different positions, with each cubieface on one cube face looking the same. When solved, the cube couldbe oriented so that each cubie in the top face reads green, yellow,red, blue when reading top left, top right, bottom left, bottomright respectively. The other faces are oriented as in step7.

2. Always begin and continue the same way sothat when taking breaks or getting lost it is easy to orient thecube correctly to see where you are up to.

3. ALWAYS read colors in the same sequence,i.e., top left, top right, bottom left, bottom right. ALWAYS readan edge piece ending with the common edge, like GYRB or GYBR (samepiece). ALWAYS read a corner piece ending up with the commoncorner, like GYRB or YRGB or RGYB (same piece). It doesn't matterwhich way you are looking at it. For example, if you put a solvedcube on the table and look at the up face without moving your headand the center cubie is, say, GYRB, the back up left corner cubieis BRYG; the back up right corner cubie is RGBY, the left up edgecubie is YBGR and so on. This takes a little bit of getting usedto, but it is THE key point in solving this cube rapidly.

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