TheSquare-1 (previously called as Cube 21 & Back khổng lồ Square One) is a shape-shifting three-layered twisty puzzle. Its solution is very unique because the kite-shaped corners & the triangularedges are indistinguishable to lớn the puzzle"s inner mechanism, meaning that corners can be swapped with edges & therefore it"s possible khổng lồ have 10 pieces in the upper layer while only 6 in the bottom.

The puzzle was invented in 1990 by Karel Hršel và Vojtech Kopský. It"s an official WCA competition event, the fastest solution being held by Martin Vædele Egdal (4.59 seconds).

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Variations: Super Square-1, Square-2, Two Layered & Four Layered versions

How to lớn solve the Square-1

The main idea of the solution is the same as the Rubik"s Cube method: We divide the puzzle into layers & solve them one by one, not messing up the pieces already fixed. This puzzle has a completely different mechanism, so we have to lớn introduce new notations and algorithms.


The top và bottom layers of a Square-1 are made of thin triangle edgesand thick kite-shaped cornerpieces. An edge piece is 30o(1 step), while a thick piece is 60o (2 steps) wide.

In the algorithms we specify how many steps to turn the top và bottom layers between theslice moves.

/ - a slice is lượt thích a 180o R rotation on the Rubik"s Cube (image). Square-1 scramblers usually neglect the slice move.(1, 0) / - rotate the top layer 30o clockwise và slice(0, 3) / - rotate the bottom layer 90o and slice. Equivalent to the D move on the Rubik"s Cube./ (0, -1) / - start with a slice, rotate bottom layer 30o counterclockwise then slice again (2, -1) / - rotate the đứng đầu layer 2 steps, the bottom anticlockwise 1 stepand bởi a slice

1. Bring the puzzle khổng lồ a square shape

The puzzle is much easier to lớn work with when it is in the shape of a cube. Try to lớn bring the Square-1 khổng lồ a cube shape in the first step. This is not a complicated stage because there are no solved pieces you can mess up. Use this step to lớn familiarize with its operation.

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Try lớn group the small pieces together to size a cube with the method below

The two examples below describe how to lớn make a cube from two easy-to-reach positions, when the thick pieces are collected in the bottom và the narrow pieces are grouped together on the top, as much as possible.

Case 1: If every small piece is grouped in the đứng top layer


Case 2: If there"s a lonely small piece in the vị trí cao nhất layer


To bring the cube to lớn a square shape first you need khổng lồ collect the tiny pieces next lớn each other or leave maximum one lonely piece between two thick corners. This is not that hard to lớn accomplish, it can be done intuitively. When this is done follow the steps on the pictures above. The black vertical line marks where to lớn make the slice

Wrong middle layer


If the middle layer is not square, do the following: (0, -1) / (6, 0) / (6, 0) / (0, 1)

2. đứng top (yellow) corners

First bring all corner pieces khổng lồ the corresponding layer: Hold the cube with the red side facing you và the green on the right. The yellow has to come to lớn the top & the white lớn the bottom.This step is not so complicated, it can be done intuitively, if not, here"s a little help lớn swith two pieces in the top and bottom layers:

(0, -4) / (0, 3) / (0, 1)

When every corner is in the correct layer, bring the yellow corners khổng lồ their final position, swithching two pieces in the đứng top right side:


(1, 0) / (0, -3) / (0, 3) / (0, -3) / (0, -3) / (0, 6) / (-1, 0)

3. Edges khổng lồ their layers

Yellow edges lớn the top, trắng edges khổng lồ the bottom layer. To lớn swap two pieces move them khổng lồ the đứng top right & bottom right of the cube then bởi the algorithm.


(1, 0) /(0, -3) /(0, -3) /(-1, -1) /(1, 4) /(0, 3) /(-1, 0)

Repeat this until every edge gets lớn its layer. It doesn"t matter if they"re not on the exact final spot. At the over of this step you should see the white and yellow faces solved.

4. Swap corners

In the second step we sent every top-layer corners to their final position. Now vày the bottom corners. Use the trick below to swap the two front-facing corners in the bottom layer.

/ (3, -3)/ (0, 3)/ (-3, 0)/ (3, 0)/ (-3, 0)/

5. Permute the edges

At this point every edge should be at its correct layer, we just have lớn put them lớn their final position.

Switch two pieces on the top và two in the bottom layer at the same time. The algorithm below switches the right-top with the back-top edge and the right-bottom with the back-bottom edge.

(0, 2) /(0, -3) /(1, 1) /(-1, 2) / (0, -2)

In most cases your Square One puzzle should be solved at the end of this step. If there are two edges that need lớn be fixed then you have a parity.

6. Parity

If there are only two edges left tofinish the cube then you"ve got parity. Use this long algorithm to switch two edges on the vị trí cao nhất then go back khổng lồ point 5.

/ (3,3) / (1,0) / (-2,-2) / (2,0) / (2,2) / (-1,0) / (-3,-3) / (-2,0) / (3,3) / (3,0) / (-1,-1) / (-3,0) / (1,1) / (-4,-3)