{"id":92837,"date":"2016-05-22T08:00:43","date_gmt":"2016-05-22T06:00:43","guid":{"rendered":"http:\/\/mygaming.co.za\/news\/?p=92837"},"modified":"2016-05-21T23:55:08","modified_gmt":"2016-05-21T21:55:08","slug":"how-to-solve-a-rubiks-cube-in-under-five-seconds","status":"publish","type":"post","link":"https:\/\/mygaming.co.za\/news\/features\/92837-how-to-solve-a-rubiks-cube-in-under-five-seconds","title":{"rendered":"How to solve a Rubik’s cube in under five seconds"},"content":{"rendered":"

This week, 14-year-old Lucas Etter set a new world record for solving the classic Rubik\u2019s cube in Clarksville, Maryland, in the US, solving the scrambled cube in an astonishing 4.904 seconds<\/a><\/strong>.<\/p>\n

The maximum number of face turns needed to solve the classic Rubik\u2019s cube, one that is segmented into squares laid out 3×3 on each face, is 20, and the maximum number of quarter turns is 26.<\/p>\n

It took 30 years to discover these numbers, which were finally proved<\/a><\/strong> by Tomas Rokicki and Morley Davidson using a mixture of mathematics and computer calculation. The puzzle does have 43,252,003,274,489,856,000 (43 times 1018<\/sup>, or 43 quintillion) possible configurations after all.<\/p>\n

So how do the likes of Lucas Etter work out how to solve Rubik\u2019s cube so quickly? They could read instructions, but that rather spoils the fun. If you want to work out how to do it yourself, you need to develop cube-solving tools.<\/p>\n

In this sense, a tool is a short sequence of turns which results in only a few of the individual squares on the cube\u2019s faces changing position.<\/p>\n

When you have discovered and memorised enough tools, you can execute them one after the other in order as required to return the cube to its pristine, solved condition.<\/p>\n

These tools require experimentation to discover.<\/p>\n

Here\u2019s how I did it myself: go on holiday with a Rubik\u2019s cube and a screwdriver. Do experiments to find tools.<\/p>\n

The trouble is that most experiments just scramble the cube horribly and you forget what you did so you cannot undo your moves.<\/p>\n

Now you have a choice, either buy another Rubik\u2019s cube, or take out your trusty screwdriver.<\/p>\n

Turn one face through 45 degrees, and place the screwdriver under a central piece of the rotated face. Using the screwdriver as a lever to gently prise it out, it\u2019s then easy to take the cube apart completely and reassemble it in pristine form.<\/p>\n

The final move of reassembly will be the reverse of the screwdriver trick: rotate one face 45 degrees and apply gentle pressure to put the final piece back in place.<\/p>\n

\"Rubiks<\/a><\/p>\n

Sequences of moves of a cube form something that mathematicians call a group. If A<\/em> is a sequence of moves, then let A-1<\/sup><\/em> (that\u2019s \u201cA inverse\u201d) be the same sequence of moves performed in reverse. So if you perform A<\/em> and then A-1<\/sup><\/em>, the cube will be in the same state as was it when you began. The same is true if you first perform A-1<\/sup><\/em> followed by A<\/em>.<\/p>\n

Now suppose that B<\/em> is another sequence of moves. Many tools have the form of what mathematicians call a commutator: do A<\/em>, then B<\/em>, then A-1<\/sup><\/em> and finally B-1<\/sup><\/em>.<\/p>\n

If A<\/em> and B<\/em> commute, so that performing A<\/em> then B<\/em> is the same as doing B<\/em> then A<\/em>, then the commutator does nothing. From a mathematical point of view, a commutator measures failure to commute, and is a key notion in group theory.<\/p>\n

When I had a Rubik\u2019s cube in one hand, and a screwdriver in the other, it was natural to look at how commutators behave.<\/p>\n

Think of the overall structure of the different configurations of a Rubik\u2019s cube as a labyrinth, which has that many chambers, each of which contains a Rubik\u2019s cube in the state which corresponds to that chamber.<\/p>\n

From each chamber there are 12 doors leading to other chambers, each door corresponding to a quarter turn of one of the six faces of a cube. The type of turn needed to pass through each door is written above it, so you know which door is which.<\/p>\n

Your job is to navigate your way from a particular chamber to the one where the cube on the table is in perfect condition.<\/p>\n

The tools that you have discovered are ways of getting nearer to the goal.<\/p>\n

So you don\u2019t need to plan your route in advance, you just execute the rotations of each tool so that you get steadily closer to and finally reach the winning chamber.<\/p>\n

The mathematical result in Rokicki and Davidson\u2019s paper shows that, no matter where you are in the labyrinth, it\u2019s possible to reach the winning chamber by passing through at most 26 doors \u2013 although the route you find using your tools is not likely to be that efficient.<\/p>\n

How to put this to use to solve the cube in five seconds? Someone like young Lucas Etta who is interested in speed solutions will not only have memorised a large number of tools, they\u2019ll also have practised them until they can perform it very quickly.
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