Rubik’s Cubes

[This is a back-issue of one of this site’s newsletters]

As Google may have already told you, this week marks the 40th anniversary of invention of Erno Rubik’s famous cube.

Many people find the cube horribly difficult to solve. If you’re one of those people, take heart in this or this.

Some mathematical thoughts on the cube, summarised from a Rubik’s Cube website I made a long time ago:

When the cube first came out, it was marketed with the slogan “more than 3 billion combinations!” Since the cube actually has over 43 billion billion combinations, that’s like MacDonalds boasting “Over a hundred burgers sold!”

The number of combinations is mindbogglingly big. Perhaps this will help you wrap your head around it.

  • Suppose you got a cube, and messed it up, completely randomly scrambling it. Then you sent this scrambled cube to someone.
  • Suppose you kept doing this, sending scrambled cubes to different people.
  • Suppose you kept this up, until you’d sent a cube to ever man, woman and child on earth.
  • Suppose you persuaded everyone else on earth to do the same, so that everyone on the whole planet was sending and receiving billions and billions of cubes through the mail.

After all that, there’d be a bit less than an even chance that one of those cubes would arrive at its destination solved, purely by chance.

To dispose of these cubes, we could send them into space, where they’d form a Rubik’s cube moon, about 250km (150 miles) across.

Ok, that’s enough about Rubik’s cubes. The next video in my series of ruler-and-compass constructions is this construction of a hexagon. The hexagon is easy to construct with a compass and straightedge, and therefore makes a nice introduction tot he topic. It’s also much easier than solving a Rubik’s cube!