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CZECH Puzzles ( in English) / Square ONE, Square 1, Cube 21

Square One (puzzle)

From Wikipedia, the free encyclopedia

The Square One, also known as Back to Square One and Cube 21, is a puzzle similar to the  Rubik's Cube. Its distinguishing feature among the numerous Rubik's Cube variants is that it can change shape as it is twisted, due to the way it is cut, thus adding an extra level of challenge and difficulty. A Super Square One puzzle was recently introduced, which has two additional layers that can be scrambled and solved independently of the rest of the puzzle.

The Square One puzzle in one of its unsolved states.
The same puzzle in its original (solved) state.

Contents

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[edit]History

The Square One, with the full name "Back to Square One", and alternative name "Cube 21", was invented by Karel Hršel and Vojtěch Kopský around 1990. Application for Czechoslovak patent was filed on 8 November 1990, the patent was approved on 26 October 1992 with patent number CS 277266 B6. On March 16, 1993, it was patented in the USA with patent number US5,193,809.[1] Its design was also patented on October 5, 1993, with patent number D340,093.

[edit]Description

The Square One consists of three layers. The upper and lower layers contain  and  For the puzzle to be in cube shape, the upper and lower layers must have alternating kite and triangular pieces, with 4 kite and 4 triangular pieces on each layer, and the middle layer must have a square shape. However, since only two shapes are possible for the middle layer, there is a quick sequence of twists which changes the shape of the middle layer from one to the other without touching the rest of the puzzle.edit]

The middle layer contains two 

Once the puzzle has a cube shape, the upper and lower layers are cut in an Rubik's Cube, the pieces are coloured. For the puzzle to be solved, not only does it need to be in cube shape, but each face of the cube must also have a uniform colour. In its solved (or original) state, viewing the cube from the face with the word "Square-1" printed on it, the colours are: white on top, green on the bottom, yellow in front, red on the left, orange on the right, and blue behind. Alternative versions of the Square One may have different colour schemes A good number of solutions for this puzzle exist on the internet. Some solutions employ the classical layer-by-layer method, while other approaches include putting the corner pieces in place first, then the edge pieces, or vice versa. Some solutions are a combination of these approaches. Although these solutions use different approaches, most of them try to restore the cube shape of the puzzle first, regardless of the placement of the pieces and the parity of the middle layer, and then proceed to put the pieces in their correct places while preserving the cube shape., the solutions of Square One depend on the use of algorithms discovered either by trial and error, or by using computer searches. However, while solutions of rely on these algorithms more towards the end, they are heavily used throughout the course of solving the Square One. This is because the uniform shape of the pieces in the Rubik's cube allows one to focus on positioning a small subset of pieces while disregarding the rest, at least at the beginning of a solution. However, with the Square One, the free intermixing of corner and edge pieces can sometimes cause a certain desired operation to be physically blocked; so one must take all pieces into account right from the beginning. Some solutions of the Square One rely solely on the use of algorithms.Number of positions

If different rotations of a given permutation are counted only once while reflections are counted individually, there are 170 × 2 × 8! × 8! = 552,738,816,000 positions.The current world record for the Square-1 is held by Piotr Michal Padlewski with the time of 10.96 seconds set at the World Rubik's Cube Championship 2009. The current world record of an average of 3 attempts is held by Jianwei Zhu with the time of 14.61 seconds set at the Beijing Summer Open


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