The main challenge here lies in devising a mathematically acceptable proof of this impossibility, which is where the foundations for what we today know as graph theory.

Solving sudoku puzzles may not require mathematics, but mathematicians have found plenty to say about the popular brainteasers.

It turns out that the Alcuin number of a graph is closely related to the size of a minimum vertex cover in the graph, and we unravel several surprising connections between these two graph parameters.

In theory, it cannot be ruled out that the algorithms might run for longer than the age of the universe. But in practice, many algorithms seem to work just fine.