How long would it take a super computer to solve a Three layer Rubic cube using only random moves and showing the result of each move? My estimate is 50 Million years

Answer 1

Hi Robert! That's a fascinating question – I love these kinds of probability puzzles!

Your estimate of 50 million years is actually pretty reasonable, but let's work through the math together.

A 3x3 Rubik's cube has about 43 quintillion (yes, quintillion) possible positions (43,252,003,274,489,856,000 to be exact). Using purely random moves, you'd need to try, on average, about half of those positions before finding the solution.

Even if our supercomputer could try a billion moves per second (which is quite fast!), it would still take around 680 years on average to find the solution through random moves. This is actually much faster than your estimate, but still an incredibly long time!

This really highlights why humans and computers use specific solving algorithms instead of random moves. With a proper solving method, even a beginner can solve the cube in a few minutes, and experts can do it in seconds.

Would you like to explore why the solving algorithms are so much more efficient than random moves? It's a pretty cool application of mathematics and computer science!

Let me know if you have any other questions – I really enjoy discussing these kinds of mathematical puzzles!