Puzzle Wizards and Mathematicians Invited to Solve Conway Soldiers Problem with Zvedelina Stankova
Professor of Mathematics, Zvezdelina Stankova invites mathematicians and clever puzzle solvers alike to join her in her Youtube video challenge solving number and combinatorial game theorist John Conway’s soldiers problem.
Soldiers is a variation of a peg jumping game familiar to many puzzle enthusiasts. Whereas the peg jumping puzzle is solved by a sequence of jumping moves that reduces a pattern of pegs to one, the Soldiers problem, also known as the checker-jumping problem, takes a standard checkerboard divided in half and considers how far across the dividing line a checker can advance using a sequence of limited jump moves.
Conway’s checkers, it was theorized back in 1961 when he introduced it can only advance four rows past the center dividing line.
In fact, Gareth Taylor and Simon Tatham demonstrated that the fifth row can only be reached through an approach that involves an infinite series of moves, a feat not practically implemented by humans with a finite life span.
The video opens with Stankova explaining the challenge and setting up the checkerboard. She works through a few moves to demonstrate the allowed sequences and increases the complexity to show that the center dividing line can be crossed.
With the help of her assistant, the patterns become increasingly complex, requiring a fair amount of advanced fore brain planning activity to get to the second and third rows.
Seemingly, to keep the video within 8 1/2 minutes, Stankova cuts to a pattern increasing from the initial four checkers to twenty showing that the fourth row across the line can be reached.
A major hurdle is discovered with developing an algorithm involving finite checker configurations that is capable of producing an arrangement pattern that can reach the fifth row, ever.
Stankova reveals that somehow “monovariance” creates an insurmountable obstacle that prevents us from gaining access to the fifth row. Being monovariant, she explains means that there is a feature that only increases in one direction, adding that somehow this is what keeps the seemingly simple puzzle from ever being solved to the fifth level.
For those who want the deeper mathematics and theory behind the monovariant aspects of the problem, Stankova offers her second 41 1/2 minute video delving into such mysterious aspects as the golden ratio.