View source for Square-1 (puzzle type)

{{Puzzle Infobox|
|NAME=Square-1
|IMAGE=Square-1 twists.jpg
|ALTERNATIVENAMES=[[Cube 21]], [[Back to Square One]], [[Cube for 21st century]]
|SHAPE=Cube
|MECHANISM=[[Square-1]], Bandaged [[Prism]]
|INVENTOR= Karel Hrsel
|INVENTOR2= Vojtech Kopsky
|YEAR= 1990
|COMPANIES=[[Moyu]], [[Calvin's Puzzle]], [[YJ]], [[QiYi]], [[FanXin]], [[ShengShou]], [[mf8]], [[YuXin]]
|TIME=From a few seconds to forever
|TPMUSEUM=494
|JAAPSCH=square1}}

The '''Square-1''' (short for '''Back to Square One''', also known as '''Cube 21''') is a cubic twisty [[puzzle]], with irregular [[cubie]]s. It's one of the most popular [[shape-shift]]ing [[Rubik's Cube variant]]s.

== Description ==

It has only 2 axes of rotation (the top/bottom faces and the entire right/left half of the puzzle).
The puzzle consists of two halves, each with [[corner]] and [[edge]] pieces indistinguishable to the [[core]]. That means that corners can be swapped with edges and otherwise.
The top and bottom [[layer]]s consist of triangular edge pieces and quadrilateral corner pieces. The middle layer consists of two trapezoidal pieces. When scrambled, it shifts to a random shape : it's a [[shape-shifting twisty puzzle]].
There are 552,738,816,000 positions (170 × 2 × 8! × 8!).

=== Goal ===
The goal is to return the cube to its cubic state with each side one solid color.
For the silver variation, the goal is only to return the cube to its cubic state.

== History == 
* Early 1990 : ''Invention'' by Dr. [[Karel Hrsel]] and Dr. [[Vojtech Kopsky]].
* Early 1990 : ''Original version'' is produced by Dr. [[Karel Hrsel]] and Dr. [[Vojtech Kopsky]].
* 8 November 1990 : ''Czechoslovak patent'' filed on 8 November 1990.
* 26 December 1990 : ''USA Design patent'' filed .
* 7 November 1991 : ''USA Puzzle patent'' filed .
* 26 October 1992 : ''Czechoslovak patent'' approved on 26 October 1992 with patent number [http://spisy.upv.cz/Patents/FullDocuments/277/277266.pdf 277266 B6].
* 16 March 1993 : ''USA Puzzle patent'' approved 16 March 1993 with patent number [http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=5,193,809.PN.&OS=PN/5,193,809&RS=PN/5,193,809 5,193,809].
* 5 October 1993 : ''USA Design patent'' approved with patent number [http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=D340,093.PN.&OS=PN/D340,093&RS=PN/D340,093 D340,093].
* 1999 : A version of square-1 with a ''Cube-21'' logo is produced.
* 2003/2004 : [[WCA]] is created. Square-1 became ''an official WCA event''.
* 2007 : ''[[MF8]]'' also produces the Square-1 since 2007.
* 2010 (or before): ''[[CubeTwist]]'' also sells a Square-1 produced by [[YJ]] since 2010 or before.

=== Patents ===
* Czechoslovak patent (filed on 8 November 1990 and approved on 26 October 1992 with patent number [http://spisy.upv.cz/Patents/FullDocuments/277/277266.pdf 277266 B6])
* USA patent :
** Puzzle patent (filed on 7 November 1991 and approved 16 March 1993 with patent number [http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=5,193,809.PN.&OS=PN/5,193,809&RS=PN/5,193,809 5,193,809]
** Design patent (filed on 26 December 1990 and approved on 5 October 1993 with patent number [http://patft.uspto.gov/netacgi/nph-Parser?Sect1=PTO1&Sect2=HITOFF&d=PALL&p=1&u=%2Fnetahtml%2FPTO%2Fsrchnum.htm&r=1&f=G&l=50&s1=D340,093.PN.&OS=PN/D340,093&RS=PN/D340,093 D340,093])

=== Product History ===

==== Original Square-1 (1990) ====
Original version is produced by Dr. [[Karel Hrsel]] and Dr. [[Vojtech Kopsky]] during early 1990.

==== Cube-21 Square-1 (1999) ====
This is the European version of the cube.  The logo was "Cube-21", which is a short for "Cube for 21st century", as it had been produced in 1999. It had also been produced the same year with a "silver edition". In this variation, there are only 2 colors and the goal is simply to shape it back to a cube.

==== MF8 Square-1 v1 (2007) ====
[[MF8]] also produces the Square-1 since 2007. It became a more popular cube.

==== CubeTwist Square-1 (2010 or before) ====
[[CubeTwist]] also sells a Square-1 produced by [[YJ]] since 2010 or before.

==== MF8 Square-1 v2 (2011 or before) ====
[[MF8]] came out with a new version with a ball core that could corner cut.

==== Calvin's Square-1 (2012 or before) ====
[[Calvin's Puzzle]] produced a puzzle that was considered the best before the QiYi version.

==== QiYi Square-1 (2015) ====
[[QiYi]]'s version is considered the first "good" Square-1, being much better quality than others at the time, and was highly influential in popularizing the event. [https://www.youtube.com/watch?v=SSurFBEcJL8 BrodyTheCuber history]

== Square-1 Notation ==
{{Main Article|Article=Square-1 notation}}
Square-1 Notation refers to the description of what symbols indicate what [[move]]s to apply on a square-1.

The original Square-1 notation, created by [[Jaap Scherphuis]], uses moves of the form (x,y) and moves of the form /. In an (x,y) twist, ''x'' indicates the number of 30-degree increments that the top layer should be twisted clockwise (an edge is 30 degrees and a corner is 60 degrees), and ''y'' indicates the number of 30-degree increments that the bottom should be twisted clockwise. A / twist simply refers to turning the entire right half of the puzzle by 180 degrees.

It is important to note that in this notation the puzzle must be held so that the layers containing the corners and edges are on the top and bottom, and the middle layer should be in a position so that, on the front side, the shorter middle-layer [[sticker]] should be on the left. Thus, from a solved state, the turn (1,-1)/ is possible, but (-1,1)/ is not.

In the newer official notation, adopted by the WCA, there is no /. The WCA regulations (version 2008 v1) say: "(x,y) means: turn upper layer x stickers clockwise, turn bottom layer y stickers clockwise, turn right half of the puzzle 180 degrees. Stickers are counted on the outside of the upper slice." Thus, every (x,y) move is considered to be followed by a / move.

[[Mike Masonjones]] proved in 2005 God's Number for the Square-1 to be equal 13 (in the twist metric). That means the puzzle can be solved in 13 twists or less. (12 if the middle layer is ignored).

== Methods ==
{{Main Article|Article=Square-1 methods}}
The puzzle is much easier to work with when it is in the shape of a cube so generally the first step is to somehow (there are several methods) get the pieces arranged so that the puzzle is cubic. Then, the pieces are separated into their correct layers, and permuted. Note that there is no possible incorrect orientation for pieces, since the middle layer can only rotate through 180 degrees at a time (many talks about separation as "orientation").

== Variations ==
=== Super Square-1 ===
{{Main Article|Article=Super Square-1 (puzzle type)}}
Invented at the same time by [[James Lee]] and an unidentified person in 2007, the [[Super Square-1]] is a Square-1 with 4 layers. It's mass-produced since 2008 by [[MF8]].

=== Square-2 ===
{{Main Article|Article=Square-2 (puzzle type)}}
Firstly built by [[David Litwin]] in 1995, the [[Square-2]] is an un[[bandaged]] version of Square-1 : corners are cut in half. Then, it has been independently built by [[Jake]] and [[Noda]] in 2003, and by many people in 2008. The name ''Square-2'' has been choosen by [[Noda]]. It's mass-produced since 2012 by [[hknowstore]].

=== 2-Layers Square-1 ===
{{Main Article|Article=2-Layers Square-1 (puzzle type)}}
Firstly built by [[Li Chung Man]] in 2008, the [[2-Layers Square-1]] is a version of Square-1 with 2 layers. It can be easily built out of a [[Super Square-1]]. It's mass-produced by [[QJ]].

=== Square-1-II ===
{{Main Article|Article=Square-1-II (puzzle type)}}
Firstly built by [[Anthony Greenhill]] in 2002, the [[Square-1-II]] is a version of Square-1 with 2 layers : the middle layer has been removed.

=== Ghost Square-1 ===
{{Main Article|Article=Ghost Square-1 (puzzle type)}}
[[Ghost Square-1]] is a shape-transfomation of Square-1. There are different versions : [[Rex Rossano Perez]] in 2016, [[Aj Lu]] in 2013, ...

=== 5-Layers Super Square-1 ===
{{Main Article|Article=5-Layers Super Square-1 (puzzle type)}}
[[Claus Wenicker]] built a version of Super Square-1 with 5 layers in 2010.

=== Greenhill's 5-Layers Square-1 ===
{{Main Article|Article=Greenhill's 5-Layers Square-1 (puzzle type)}}
[[Anthony Greenhill]] built a version of Square-1 with 5 layers in 2003.

=== 6-Layers Super Square-1 ===
{{Main Article|Article=6-Layers Super Square-1 (puzzle type)}}
[[Claus Wenicker]] built the [[5-Layers Super Square-1]] with a [[6-Layers Super Square-1]], that has been invented in 2010.

=== Time Machine ===
{{Main Article|Article=Time Machine (puzzle type)}}
Firstly built by [[Li Chung Man]] in 2009, the [[Time Machine]] is a mix between a [[2x2x2]] and 3 [[Square-2]]. Its first name was ''Pipe Connector''.

=== Time Machine II ===
{{Main Article|Article=Time Machine II (puzzle type)}}
[[A J Lu]] made a Time Machine II in 2010. It is a mix between a [[1x2x2]] and 3 [[Square-2]].

=== Wheel of Wisdom ===
{{Main Article|Article=Wheel of Wisdom (puzzle type)}}
Mass-produced by [[Dayan]] and invented by [[Daqing Bao]] in 2013

=== Time Machine : back to Square-1 / 3 Square in 1  ===
{{Main Article|Article=Time Machine : back to Square-1 (puzzle type)}}
{{Main Article|Article=3 Square in 1  (puzzle type)}}
Invented by [[Li Chung Man]] in 2011 and [[Olivier Polspoel]] in 2008, this is a mix between a [[2x2x2]] and 3 [[Square-1]]. It's a bandaged version of [[Time Machine]]. The difference between these 2 puzzles is only the shape.

== Square-1 Software ==
* [http://ruwix.com/online-puzzle-simulators/square-1-simulator.php Ruwix Square-1 online simulator]
* [http://www.jaapsch.net/puzzles/extra/square1.zip PC Square-1 Solver]

== See also ==
* [[:Category:Square-1 solvers]]
* [[List of World Records/Square-1]]
* [[Square-1 methods]]
* [[Square-1 notation]]

== External links ==
* [http://en.wikipedia.org/wiki/Square_One_(puzzle) Article on Wikipedia]
* [http://www.jaapsch.net/puzzles/square1.htm Jaap's Square-1 page]

{{Cubics}}

[[Category:Twisty puzzles]]
[[Category:Twisty puzzles used in WCA-official events]]
[[Category:Square-1]]