This article is a summary of a YouTube video "The trick that solves Rubik’s Cubes and breaks ciphers" by polylog

Solving the Rubik's Cube in the Fastest Possible Way

TLDRLearn how to solve the Rubik's Cube using the meet-in-the-middle algorithm, which finds the shortest solution in less time than previous methods. This algorithm explores configurations exponentially, making it efficient for solving complex problems.

Key insights

🧩The number of moves to solve a Rubik's Cube can be measured, and the current world record is 4.73 seconds.

📈A new approach to solving the Rubik's Cube is to measure the number of moves instead of time, leading to more efficient algorithms.

🔢Every Rubik's Cube can be solved in at most 20 moves, which was proven in 2010.

🌐The configurations of a Rubik's Cube can be represented as a graph, and finding the shortest solution is equivalent to finding the shortest path in the graph.

💡The meet-in-the-middle algorithm allows for searching from both ends of the graph simultaneously, reducing the time and memory complexity of finding the shortest solution.

Q&A

What is the current world record for solving the Rubik's Cube?

The current world record for solving the Rubik's Cube is 4.73 seconds.

How many moves does it take to solve a Rubik's Cube?

Every Rubik's Cube can be solved in at most 20 moves.

How was it proven that a Rubik's Cube can be solved in at most 20 moves?

The proof was done using a computer program and was completed in 2010.

What is the meet-in-the-middle algorithm?

The meet-in-the-middle algorithm is an efficient method for finding the shortest solution to a problem by searching from both ends simultaneously.

How does the meet-in-the-middle algorithm reduce the time and memory complexity?

The meet-in-the-middle algorithm reduces the time and memory complexity by exploring configurations exponentially and finding the intersection point where the two searches meet.

Timestamped Summary

00:04Felix Zemdegs holds the world record for solving the Rubik's Cube in just 4.73 seconds.

00:22By measuring the number of moves instead of time, we can develop more efficient algorithms for solving the Rubik's Cube.

01:17Every Rubik's Cube can be solved in at most 20 moves, which was proven in 2010 using a computer program.

02:23Using graph theory, we can represent the configurations of a Rubik's Cube as a graph and find the shortest solution by finding the shortest path in the graph.

07:59The meet-in-the-middle algorithm allows for searching from both ends of the graph simultaneously, reducing the time and memory complexity of finding the shortest solution.