Networks & Sudoku
As I’ve been learning the concepts covered in Networks, I’ve been noticing a significant amount in common with the strategies used in sudoku, making me realize that the game of sudoku is largely just a game of networks. Specifically, matching markets relate closely to the behavior of how sudoku is played. Each tile has a certain set of numbers it can house, while each number needs to be in every nine-box of the board. This fact is combined with the negative and positive relationships every number has with surrounding numbers on the board in order to derive a viable solution. Each number 1-9 has a positive relationship with every other number and a negative with its own, and in order to balance the board no negative relationships can occur. This is one of the core rules that enables sudoku puzzles and constitutes one of the most basic strategies applied in the game, filling a set of nine with the only missing number. By applying this rule you get a limited set of possibilities for each tile and for each number, creating something of a bipartite graph with generally only one solution, the perfect match. These possibilities generally follow a pattern of having a few potential setups that have unique strategies towards solving them, strategies that at this point have been well documented.
One such strategy incorporated into the game is known as a continuous network. As the title implies, it bears a particularly strong resemblance to the concepts gone over in this course. It follows a similar technique to one we had used in lecture when trying to pair off bipartite sets. The idea is that by knowing two of the nine numbers in a particular nine-box can only go in two of the nine available spaces, it implies that no other number can go into either of those boxes, as it would result in one of the original pair having nowhere to go. This is the same as the idea of avoiding a constricted set in order to achieve a perfect match, as a constricted set here means no possible solution, while a perfect match would be the solution. This idea is applicable to more than two of the nine boxes, as long as a set of numbers can only fit into a section of the nine-box of equal size to the set. Going into this course I expected to find commonalities with social media or a habitat’s ecosystem. Sudoku was far from my list of expectations, but its dependence as a game on the rules and strategies we have learned even in this short time since the semester has begun has helped me to realize the versatility of the concepts of networks.
Sources:
https://sudoku.com.au/Finding-Continuous-Networks-Study-01.aspx