Why Is This 15-Puzzle Impossible? - Numberphile

Explore the mathematical intricacies behind the impossibility of solving the 15-Puzzle in this engaging video featuring Professor Steven Bradlow. Delve into the history of Sam Lloyd's challenge and uncover the mathematical concepts of permutations, invariants, and parity that explain why certain configurations of the puzzle are unsolvable. Learn about the significance of the blank space, the number of moves, and the role of even and odd permutations in determining puzzle solvability. Gain insights into predicting which puzzle configurations are possible and discover the good news hidden within this seemingly impossible challenge.

Introduction
The Mystery
Sam Lloyd
The Challenge
The Paper
Permutations
Possible
Sliding
Invariants
The blank space
The number of moves
Even number of moves
How to get 15
Can you
Odd
Good News
Prediction