introduction
It
is said that the average human being uses only a small part of the brain. The
rest remains unstimulated .In order to put the entire brain to use, we need to
engage in different kinds of activities, as different parts of the brain
control different aspects of our behaviour.It is the organ that controls our
emotions, creativity, logical thinking, communication, our dreams and how we
work towards achieving our goals and aspirations.Mental stimulation helps the
brain perceive and integrate new aspects.
Puzzles
are excellent brainteasers. They set the brain thinking and that in itself
helps with the development of the brain.While brain development is most
prominent in the early years of one’s life, it does not stop at any given
time.The brain can continually assimilate information even in old age.
It
is said that as long as one uses the brain,one will not fall victim to
senility,or a hoard of other mental diseases.So what one really needs is to
stay alert,think fast and develop good concentration.The focus is to do
something that will exercise the brain.Something that will jog it into action
and keep it ticking all the time a sort of mental aerobics.
Studies
show that solving puzzles involving maths,words,pictures,colours are all an
important part of leading a mentally stimulated lifestyle.Exercising the brain
improves memory,and increases concentration.It also teaches you to think,and
consequently increases creativity With the focus in the education department
slowly shifting towards cognitive learning,we take a look at the Rubiks
Cube,the decades-old puzzle that till today has people twirling and twisting it
in their fingers in a bid to solve it in
the minimum time possible.
The
cube is not just a puzzle that can keep you occupied for hours together till
you learn how to solve it that is it can also help you lead a mentally fit life
well into your old age.
As of January 2009, 350 millions of cubes have been
sold worldwide make it the world’s top selling puzzle game. It is widely
considered to be the world’s best selling toy.
Although the Rubik's Cube
reached its height of mainstream popularity in the 1980s, it is still widely
known and used. Many speedcubers continue to practice it and other twisty
puzzles and compete for the fastest times in various categories.
Since 2003, The World Cube
Association, the Rubik's Cube's international governing body, has organized
competitions and kept the official world recordsSo let us see the interesting things about this famous
Rubik’s cube in the following topics.
Invention
Rubik’s cube is a 3D-combination puzzle invented in
1974 by Hungarian sculptor and professor of architecture “Erno Rubik”. The
Rubik’s cube a 1974 invention of Erno Rubik of Hungary fascinated people around
the globe and become one of the most popular games in the early 1980’s have
been initially released as the “MAGIC CUBE” in Hungary in late 1977 and then
remanufactured and released in the western world as Rubik’s cube in 1980. The
puzzle was licensed by Rubik to be sold by ideal toy in 1980 via German businessman
Tibor Laczi and Seven Towns founder Tom Kremer and won the German game of the
year special award for best puzzle of that year.
It earned a place as a permanent exhibit in New
York’s museum of modern art and entered the Oxford English dictionary in 1982.
Liberty science centre and Google are currently
designing an interactive exhibit based on Rubik’s cube it will open at LSC in
Jessy city .NJ, In April 2014 in celebration of cube’s 40th anniversary before
travelling internationally for seven years. Exhibition element include thirty
five foot-tall roof top cube made of lights that people can manipulate with
their cell phones, a $ 2.5 million cube made of diamond, a giant walk- in the
cube displaying the inner working of the puzzle and cube solving robots.
Erno Rubik
In the mid of 1970 Erno Rubik worked department of
interior design at the academy of applied arts and crafts in Budapest. Although
it is widely reported that the cube was built as a teaching tool to help his
students to understand 3D objects, his actual purpose was solving the
structural problems of moving the parts independently without the entire
mechanism falling apart. He did not realize that he had created a puzzle until
the first time he scrambled his new cube and then tried to restore it.
construcion and stucture of rubik’s cube
In a classic Rubik's Cube, each of the
six faces is covered by nine stickers, each of one of six solid colours
(traditionally white, red, blue, orange, green, and yellow, where white is
opposite yellow, blue is opposite green, and orange is opposite red, and the
red, white and blue are arranged in that order in a clockwise arrangement).An
internal pivot mechanism enables each face to turn independently, thus mixing
up the colours. For the puzzle to be solved, each face must be returned to
consisting of one colour. Similar puzzles have now been produced with various
numbers of sides, dimensions, and stickers, not all of them by Rubik.
Rubik obtained Hungarian patent
HU170062 for his "Magic Cube" in 1975. Rubik's Cube was first called
the Magic Cube (Bűvös kocka) in Hungary. The puzzle had not been patented
internationally within a year of the original patent. Patent law then prevented
the possibility of an international patent. Ideal wanted at least a
recognizable name to trademark; of course, that arrangement put Rubik in the
spotlight because the Magic Cube was renamed after its inventor in 1980.
The first test batches of the Magic
Cube were produced in late 1977 and released in Budapest toy shops. Magic Cube
was held together with interlocking plastic pieces that prevented the puzzle
being easily pulled apart, unlike the magnets in Nichols's design. In September
1979, a deal was signed with Ideal to release the Magic Cube worldwide, and the
puzzle made its international debut at the toy fairs of London, Paris,
Nuremberg and New York in January and February 1980.
After its international debut, the
progress of the Cube towards the toy shop shelves of the West was briefly
halted so that it could be manufactured to Western safety and packaging
specifications. A lighter Cube was produced, and Ideal decided to rename it.
"The Gordian Knot" and "Inca Gold" were considered, but the
company finally decided on "Rubik's Cube", and the first batch was
exported from Hungary in May 1980. Taking advantage of an initial shortage of
Cubes, many imitations and variations appeared.
A standard Rubik's Cube measures
5.7 cm (approximately 2¼ inches) on each side. The puzzle consists of
twenty-six unique miniature cubes, also called "cubies" or
"cubelets". Each of these includes a concealed inward extension that
interlocks with the other cubes, while permitting them to move to different
locations. However, the centre cube of each of the six faces is merely a single
square façade; all six are affixed to the core mechanism. These provide
structure for the other pieces to fit into and rotate around. So there are
twenty-one pieces: a single core piece consisting of three intersecting axes
holding the six centre squares in place but letting them rotate, and twenty
smaller plastic pieces which fit into it to form the assembled puzzle.
Each of the six centre pieces pivots
on a screw (fastener) held by the centre piece, a "3-D cross". A
spring between each screw head and its corresponding piece tensions the piece
inward, so that collectively, the whole assembly remains compact, but can still
be easily manipulated. The screw can be tightened or loosened to change the
"feel" of the Cube. Newer official Rubik's brand cubes have rivets
instead of screws and cannot be adjusted.
The Cube can be taken apart without
much difficulty, typically by rotating the top layer by 45° and then prying one
of its edge cubes away from the other two layers. Consequently it is a simple
process to "solve" a Cube by taking it apart and reassembling it in a
solved state.
There are six central pieces which
show one coloured face, twelve edge pieces which show two coloured faces, and
eight corner pieces which show three coloured faces. Each piece shows a unique
colour combination, but not all combinations are present (for example, if red
and orange are on opposite sides of the solved Cube, there is no edge piece
with both red and orange sides). The location of these cubes relative to one
another can be altered by twisting an outer third of the Cube 90°, 180° or
270°, but the location of the coloured sides relative to one another in the
completed state of the puzzle cannot be altered: it is fixed by the relative
positions of the centre squares. However, Cubes with alternative colour
arrangements also exist; for example, with the yellow face opposite the green,
the blue face opposite the white, and red and orange remaining opposite each
other.
TYPES OF CUBES
Initially Rubik invented the 3*3*3 cube (magic
cube) only but now several types of 3D puzzles have been invented like
pyramids, 4*4*4 , 5*5*5 , 6*6*6 , 7*7*7
,……., 17*17*17 cubes.
2*2*2- pocket cube
3*3*3- Rubik’s cube
4*4*4- Rubik’s revenge
5*5*5- professor’s cube
6*6*6- V-Cube
6
7*7*7- V-cube 7
There are different variations of Rubik's
Cubes with up to seventeen layers: the 2×2×2 ( pocket/mini Cube), the standard
3×3×3 cube, the 4×4×4 (Rubik's Revenge/Master Cube), and the 5×5×5 (Professor's
Cube), the 6×6×6 (V-Cube 6), and 7×7×7 (V-Cube 7). The 173
"Over The Top" cube (available late 2011) is currently the largest
(and most expensive, costing more than a thousand dollars) available. Due to
additional complexities inherent in manufacturing even-number-layered cubes,
all cubes 93 or larger (as of 2012) have an odd number of layers.
The largest order magic cube is 17*17*17 cubes large and consists of 1,539
parts. It was created by Oskar van devente (Netherland) and presented at the
New York puzzle party symposium in New York in Feb 2011.
Non-licensed physical cubes as large
as 11×11×11 based on the V-Cube are commercially available to the mass-market
circa 2011 in China; these represent about the limit of practicality for the
purpose of "speed-solving" competitively (as the cubes become
increasingly ungainly and solve-times increase exponentially). These cubes are
illegal (even in China) due to the fact that they violate Panagiotis Verdes'
patents; however some countries do not enforce patent law strictly, leading to
their general availability. In addition, Chinese companies have produced 3×3×3
cubes with variations on the original mechanism that, while legally
controversial, are generally considered to be superior for competitive
speedcubing.
MATHEMATICS
INVOLVED
PERMUTATION
The original (3×3×3) Rubik's Cube has
eight corners and twelve edges. There are 8! (40,320) ways to arrange the
corner cubes. Seven can be oriented independently, and the orientation of the
eighth depends on the preceding seven, giving 37 (2,187) possibilities.
There are 12! /2 (239,500,800) ways to arrange the edges, since an even
permutation of the corners implies an even permutation of the edges as well.
(When arrangements of centres are also permitted, as described below, the rule
is that the combined arrangement of corners, edges, and centres must be an even
permutation.) Eleven edges can be flipped independently, with the flip of the
twelfth depending on the preceding ones, giving 211 (2,048)
possibilities.
This is approximately 43 quintillion
.
The puzzle is often advertised as
having only "billions" of positions, as the larger numbers are
unfamiliar to many. To put this into perspective, if one had as many standard sized
Rubik's Cubes as there are permutations, one could cover the Earth's surface 275
times.
The preceding figure is limited to
permutations that can be reached solely by turning the sides of the cube. If
one considers permutations reached through disassembly of the cube, the number
becomes twelve times as large:
Which are approximately 519
quintillion possible arrangements of the pieces that make up the Cube, but only
one in twelve of these are actually solvable. This is because there is no
sequence of moves that will swap a single pair of pieces or rotate a single
corner or edge cube. Thus there are twelve possible sets of reachable
configurations, sometimes called "universes" or "orbits",
into which the Cube can be placed by dismantling and reassembling it.
SOLVING TECHNIQUES AND ALGORITHM
Algorithms
In Rubik's cubers' parlance, a
memorised sequence of moves that has a desired effect on the cube, is called an
algorithm. This terminology is derived from the mathematical use of algorithm,
meaning a list of well-defined instructions for performing a task from a given
initial state, through well-defined successive states, to a desired end-state.
Each method of solving the Rubik's Cube employs its own set of algorithms,
together with descriptions of what effect the algorithm has, and when it can be
used to bring the cube closer to being solved.
Many algorithms are designed to
transform only a small part of the cube without interfering with other parts
that have already been solved, so that they can be applied repeatedly to
different parts of the cube until the whole is solved. For example, there are
well-known algorithms for cycling three corners without changing the rest of
the puzzle, or flipping the orientation of a pair of edges while leaving the
others intact.
Some algorithms do have a certain desired effect
on the cube (for example, swapping two corners) but may also have the
side-effect of changing other parts of the cube (such as permuting some edges).
Such algorithms are often simpler than the ones without side-effects, and are
employed early on in the solution when most of the puzzle has not yet been
solved and the side-effects are not important. Most are long and difficult to
memorize. Towards the end of the solution, the more specific (and usually more
complicated) algorithms are used instead.
- Fridrich Method
- Petrus
- ZB
- ZZ
- Corners First
- Beginner CF
- Beginner CFOP
Faster methods
While the above method may be good for
a beginner, it is too slow to be used in speedcubing. The most popular method
for speedcubers is very similar to the method above, except steps 2 and 3 are
combined, and the last layer is solved in two steps instead of three. The
inventor of this common method is Jessica Fridrich. With this method,
speedcubers with good dexterity and memory can average under 20 seconds after a
few months of hard practice. However, to learn the method you must learn 78
algorithms. There are methods just as fast that requires far fewer algorithms
to be memorized. Here is a brief synopsis of several popular speedcubing
methods
Layer by Layer methods
Fridrich Method A very fast First 2 Layers (or F2L) method, start by solving a
cross on one face, then proceeding to solve the First 2 Layers pairing up edge
and corner combinations and putting them into their slot. This is
followed by solving the Last Layer in two steps, first orienting all pieces
(one color on the last layer), then permuting them (solving the ring around the
last layer). The basic method has 78 algorithms (without the inverse of them),
and is recognized as one of the fastest methods currently in use.
F2L
Alternatives Methods that follow the same principle
as Fridrich's method, but using different algorithms. Many of the algorithms
are shared but there are a few differences, so there should be one to suit your
fingers.
ZB
method This
method was developed independently by Ron van Bruchem and Zbigniew Zborowski in
2003. After solving the cross and three c/e pairs, the final F2L pair is solved
while orienting LL edges. This is known as ZBF2L. The last layer can then be
solved in one algorithm, known as ZBLL. The ultimate method requires several
hundred algorithms. Lars Vandenbergh's site has ZBF2L algorithms, used in his
VH system. ZBLL algorithms can be found on Doug Li's webpage.
ZZ
method This method was created in 2006 by
Zbigniew Zborowski, the co-creator of the ZB method. It has three basic steps:
EOLine, F2L, and LL. EOLine stands for Edge Orientation Line. The orientation
of edges is defined as either good or bad. Good meaning the edge can be placed
into the correct position with a combination of R, L, U, D, F2, or B2, moves.
Bad meaning it would require an F, F′, B, or B′ move to be moved into its
correct position. Any F, F′, B, or B′ move will cause the four edges on that
slice to change from its current state, good or bad, to the opposite state. The
Line portion of EOLine is forming a line on the bottom of the cube that
consists of the DB edge and the DF edge in their correct positions. The next
step is F2L, First 2 Layers. It uses block building techniques to solve the two
remaining 1x2x3 blocks of the F2L using only R, U, and L moves. This allows for
very quick solving of F2L as it does not require cube rotation. The final step
of the ZZ method is LL, Last Layer, and it can be broken into multiple steps or
maintained as one depending on the algorithms used. There are two main
approaches to this method OLL and PLL , Orientation of LL and Permutation of
LL, and COLL and EPLL, Corner OLL and Edge PLL. The first, OLL and PLL, is to
use one of 7 algorithms to solve the top layer (OLL) and then permute the edge
and corners into their correct positions (PLL), this requires 21 algorithms.
The total algorithms required for the first approach of solving LL is 28. The
second approach to solving LL is to solve the top and the corners in one algorithm
(COLL) and then solve the edges (EPLL). COLL requires 40 algorithms and EPLL
requires 4, making the total 44 algorithms. The second approach is faster due
the ease of recognition and speed of execution of EPLL.
VH method Created
by Lars Vandenbergh and Dan Harris, as a stepping stone from Fridrich to ZB.
First, F2L without one c/e-pair is solved with Fridrich or some other method.
Then the last pair is paired up, but not inserted. Then it's inserted to F2L
and LL edges are oriented in one go. Then, using COLL, corners of LL are solved
while preserving edge orientation. Then edges are permuted.
Block methods
Petrus System Created by Lars Petrus. One of the shortest methods in terms of
face turns per solve, the Petrus method is often used in fewest moves contests.
Petrus reasoned that as you construct layers, further organization of the
cube's remaining pieces is restricted by what you have already done. For a
layer-based solution to continue after constructing the first layer, the solved
portion of the cube would have to be temporarily disassembled while the desired
moves were made, then reassembled afterwards. Petrus sought to get around this
quagmire by solving the cube outwards from one corner, leaving him with
unrestricted movement on several sides of the cube as he progressed. There are
not as many algorithms to learn compared to the other F2L methods, but it takes
a lot of dedication to master. The basis of the method is to create a 2 × 2 × 3
block on the cube, then proceed to solve a 3 × 3 × 2 block, but also flipping
the edges on the Last Layer. Then the Last Layer is solved in two steps, first
corners and then edges.
Heise method Created by Ryan Heise. First, one
inner square and three outer squares are built intuitively. Then they are
placed correctly while orienting remaining edges. After that you create two
c/e-pairs, and solve the remaining edges. The last 3 corners are solved using a
commutator.
Gilles Roux Method
Another unique method, but works in blocks like
the Petrus method. You start by solving a 1 × 2 × 3 block and then solve
another 1 × 2 × 3 block on the other side of the cube. Next you solve the last corners
and finally the edges and centers, has only 24 algorithms to learn.
Corners first methods
Waterman
Method Created by Mark Waterman. Advanced corners first
method, with about 90 algorithms to learn. Solve a face on L, do the corners on
R and then solve the edges, an extremely fast
Jelinek Method: Created
by Josef Jelinek. This method is very similar to Waterman's.
books on rubik’s cube
The following books are considered to
be best books for solving the Rubik’s cube..
·
Algorithms ESA 2011
By Erik D.Demance , Martin
L.Demaine,Sarah Eisenstal,Anna Lubilal,Andrew window.
·
Simple solutions for Rubik’s cube.
By James G Nursal.
·
Funskool Rubik’s cube
By Funskool
·
Rubik’s cube
Phillip Morales
More than 959 e-books have been created for
solving the Rubik’s cube.competitions and records
Speedcubing (or speedsolving) is the
practice of trying to solve a Rubik's Cube in the shortest time possible. There
are a number of speedcubing competitions that take place around the world.
The first world championship organised
by the Guinness Book of World Records was held in Munich on March 13, 1981. All
Cubes were moved 40 times and lubricated with petroleum jelly. The official
winner, with a record of 38 seconds, was Jury Froeschl, born in Munich. The
first international world championship was held in Budapest on June 5, 1982,
and was won by Minh Thai, a Vietnamese student from Los Angeles, with a time of
22.95 seconds.
Since 2003 the world cube association
the Rubik’s cube international body, has organised competitions and kept the
official world records.
Since 2003, the winner of a
competition is determined by taking the average time of the middle three of
five attempts. However, the single best time of all tries is also recorded. The
World Cube Association maintains a history of world records.] In
2004, the WCA made it mandatory to use a special timing device called a
Stackmat timer.
In addition to official competitions,
informal alternative competitions have been held which invite participants to
solve the Cube in unusual situations. Some such situations include:
- Blindfolded solving
- Solving the Cube with one person
blindfolded and the other person saying what moves to make, known as
"Team Blindfold"
- Multiple blindfolded solving, or
"multi-blind", in which the contestant solves any number of
cubes blindfolded in a row
- Solving the Cube underwater in a
single breath
- Solving the Cube using a single
hand
- Solving the Cube with one's feet
- Solving the Cube in the fewest
possible moves
Of these informal competitions, the
World Cube Association sanctions only blindfolded, multiple blind folded,
fewest moves, one-handed, and feet solving as official competition events.
In blindfolded solving, the contestant
first studies the scrambled cube (i.e., looking at it normally with no
blindfold), and is then blindfolded before beginning to turn the cube's faces.
Their recorded time for this event includes both the time spent examining the
cube and the time spent manipulating it.
In multiple blindfolded, all of the
cubes are memorized, and then all of the cubes are solved once blindfolded;
thus, the main challenge is memorizing many - often ten or more - separate cube
positions. The event is scored not by time but by the number of solved cubes
minus the number of unsolved cubes after one hour has elapsed.
In fewest moves solving, the
contestant is given one hour to find his or her solution, and must write it
down as an algorithm.
Records
This list contains only records achieved in official
competitions.
3*3*3:
The best time for restoring the cube in an official championship.
The following table gives the world record history.
RECORD HOLDER
|
EVENT
|
SECONDS
|
|
Ronald Brinkmann (Germany)
|
West German Championship 1982
|
19
|
|
Robert Pergl (Czechoslovakia)
|
Czechoslovakian Championship 1982
|
17.02
|
|
Dan Knights (USA)
|
World Championship 2003
|
16.71
|
|
Jess Bonde (Denmark)
|
World Championship 2003
|
16.53
|
|
Shotaro Makisumi (Japan)
|
Caltech Winter competition 2004
|
15.07
|
|
Shotaro Makisumi (Japan)
|
Caltech Winter competition 2004
|
14.76
|
|
Shotaro Makisumi (Japan)
|
Caltech Spring competition 2004
|
13.93
|
|
Shotaro Makisumi (Japan)
|
Caltech Spring competition 2004
|
13.89
|
|
Shotaro Makisumi (Japan)
|
Caltech Spring competition 2004
|
12.11
|
|
Jean Pons (France)
|
Dutch Open 2005
|
11.75
|
|
Leyan Lo (USA)
|
Caltech Winter competition 2006
|
11.13
|
|
Toby Mao (USA)
|
US Championship 2006
|
10.48
|
|
Edouard Chambon (France)
|
Belgian Open 2007
|
10.36
|
|
Thibaut Jacquinot (France)
|
Spanish Open 2007
|
9.86
|
|
Erik Akkersdijk (Netherlands)
|
Dutch Open 2007
|
9.77
|
|
Ron van Bruchem (Netherlands)
|
Dutch Championships 2007
|
9.55
|
|
Edouard Chambon (France)
|
Murcia Open 2008
|
9.18
|
|
Yu Nakajima (Japan)
|
Kashiwa Open 2008
|
8.72
|
|
Erik Akkersdijk (Netherlands)
|
Czech Open 2008
|
7.08
|
|
Feliks Zemdegs (Australia)
|
Melbourne Cube Day 2010
|
7.03
|
|
Feliks Zemdegs (Australia)
|
Melbourne Cube Day 2010
|
6.77
|
|
Feliks Zemdegs (Australia)
|
Melbourne Summer Open 2011
|
6.65
|
|
Feliks Zemdegs (Australia)
|
Kubaroo Open 2011
|
6.24
|
|
Feliks Zemdegs (Australia)
|
Melbourne Winter Open 2011
|
6.18
|
|
Feliks Zemdegs (Australia)
|
Melbourne Winter Open 2011
|
5.66
|
|
Mats Valk (Netherlands)
|
Zonhoven Open 2013
|
5.55
|
Matt
Valk from the Netherlands holds the current world record for completing a
formal Rubik’s cube in 5.55 seconds.
- 5
attempts, average of all but fastest and slowest attempt: 7.53 sec by Feliks Zemdegs (Australia)
at the Australian Nationals 2012. The times for solving the cube were
7.56, 6.78, 7.16, 11.44 and 7.86 seconds.
- blindfold,
fastest time (including memorising): 23.80 seconds, Marcin Zalewski (Poland) at the Polish Nationals
2013
- blindfold,
most cubes: 24, Tim Habermaas (Germany) at
the German Open 2008 in Gütersloh
- one
handed: 9.43 seconds. Giovanni Contardi
(Italiy) at the Italian Championships 2012 in Rome
- with
feet only: 27.93 sec, Fakhri Raihaan
(Indonesia) at Celebes Cube Competition 2012
- 24 hours: 4786 cubes solved, Milán Baticz (Hungary) on 16/17 November 2008.
The
largest mosaic made from scrambled Rubik's Cubes measured 67 m [220 ft] x 4 m [13 ft]. The mosaic, showing the
Macau skyline, was created in December 2012 by Cube Works Studio from
85,794 cubes. It took 90 days from design to completion
|
||
The individual
record was a Christmas tree composed by
Bernett Orlando (India) from 2025 cubes in Cologne (Germany) in December 2009
(see photo, more photos can be found. The fastest robot to solve a Rubik's Cube is CubeStormer II, developed by Mike Dobson and David Gilday. It solved a Rubik's Cube in 5.27 seconds. PREVIOUS RECORD HOLDER Ruby, developed by Swinburne University students (Australia), 10.18 seconds Rubot II, developed by Peter Redmond (Ireland), solved a scrambled Rubik's Cube within 64 seconds (including the time to scan the initial position) on 8 January 2009 at the Young Scientist show in the Royal Dublin Society . The largest Rubik's Cube was built by Daniel Urlings (Luxemburg). It could contain 64 normal sized Rubik's Cubes. The most working layers has a 17x17x17 cube constructed by Oskar van Deventer (Netherlands). The smallest working Rubik's Cube is 8 mm wide. It was created using a 3D-printer by Evgeniy Grigeriev (Russia). The most expensive Rubik's Cube was the Masterpiece Cube, produced by Diamond Cutters International in 1995. The actual-size, fully functional cube features 22.5 karats of amethyst, 34 karats of rubies, and 34 karats of emeralds, all set in 18-karat gold. It has been valued at about US-$ 1.5 mio.
The youngest person who solved a Rubik's Cube in a competition was Ruxin Liu (China),
who was 3 years 118 days old when she solved the cube in 1:39.33
at the Weifang Open on 14 April 2013.
|
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