Why is the Rubik's cube so hard? (episode 1)

Have you ever wondered why a Rubik's cube is so hard to solve? The reason the Rubik's cube is so hard to solve is because a Rubik's cube can be twisted into many different positions, yet there is only one position that is solved.

So, how many positions can one twist a 3x3x3 Rubik's cube? It turns out the answer is more than 43·1018. That sounds big, but just how big is it?

Well, here's one way we can think about it. Let's imagine I wanted to see every position of a Rubik's cube. So what I did was I drew each position on a separate piece of paper. Then I stacked all 43·1018 papers. Let's see how high the stack would be.

So I started on the kitchen table. It didn't take long before I needed a ladder. Soon, the house wasn't big enough. I had to take it outside. The ladder wouldn't take me high enough so I found a crane. Pretty soon, even that wasn't high enough. With the help of a hot-air balloon I continued to stack. Now my stack was higher than the tallest building in the world.

I really began to enjoy this project. Soon it took me where no one else had ever been. Now I was further than the Moon. I really got to know our solar system. There's the Sun, Mercury, Venus, Earth, Mars, the asteroid belt, Jupiter, Saturn, Uranus, Neptune and Pluto. Pluto's no longer a planet, but let's just assume I didn't get the memo.

I continued the stack and took myself on a grand tour of our solar system. I went straight toward Pluto. Once at Pluto, I realized I was low on fuel and food, and should probably start heading back. So I started a stack on Pluto back toward Earth. The trip back seemed to go by quickly, and eventually I returned to Earth.

It was depressing to know I wasn't even half way done. After fuelling up the tank, it was time for another trip. Resolved to finish this epic quest, I set out on multiple trips. I finally finished all 43·1018 positions. It only took 728 stacks.

Hidden out in the mass of papers is one paper that is special. Each paper has a unique picture of a Rubik's cube, but only one paper has the picture of a solved Rubik's cube. It's your job to find that paper. Good luck!

Taken and edited from Kenneth Brandon's video.

Used math:
paper thickness: 0.01 cm
total stack size: 4.3·1015 m = 4 300 000 000 000 km
1 AU: 149 598 000 km
distance to Pluto: 5 906 376 272 km = 39 500 AU
length of stack in AU: 28 743.7
number of stacks: 727.69

The distance from Pluto to Sun was used, because over the course of a couple years, that would be the average distance from the Earth to Pluto as well.

It's 728 stacks where the last stack isn't a full stack.