An especially complicated logic game like Sudoku is more appealing to people who love technical things like computer geeks, mathematicians, computer engineers, etc. It is quite fascinating how Sudoku captured the hearts of millions.
The other very logical game that has gotten just as popular is Rubik’s Cube, which uses a three-dimensional grid that requires you to group the colors on each side. However, a Sudoku is a flat grid that usually contains a grid of nine rows by nine columns. It consists of 81 cells and nine smaller squares or sub-grids where the numbers are placed.
A set of numbers from 1 to 9 are places in each square with a digit appearing only once in each row and each column, which is actually the literal translation of its Japanese name meaning “single number”.
Each puzzle has a unique solution. Although you can see numbers, it doesn’t require you to use any form of math equations. This grid is known to be a special type of Latin squares credited to the 18th century mathematician Leonhard Euler, where an nxn matrix formula is filled with n symbols and each symbol appears only once in each row or column. A Sudoku puzzle is a combination of Latin squares with the additional requirement of treating the puzzle as a single grid, but the subgrids also contain the digits 1 through 9 which form an interaction and constraints with the other grids.
It seems that Sudoku is just a form of entertainment for most people, but for mathematicians it raises many questions that require investigation. One of the questions that arises in this regard is how many Sudoku grids can there be. To simplify this problem, mathematicians who focused solely on using logic were first able to arrive at an estimated value of 6,670,903,752,021,072,936,960 possible valid Sudoku grids. This is based on a study by Bertram Felgenhauer of the Technical University of Dresden in Germany and Frazer Jarvis of the University of Sheffield in England. This value has already been verified by other studies a couple of times.
However, if we only count those for grids that can be reduced to equivalent settings once, we arrive at a smaller value of 5,472,730,538. These numbers assure humanity that we won’t run out of puzzles to solve and that we can continue to enjoy solving Sudoku puzzles for the rest of our lives.
Another problem that currently baffles scientists is what is the fewest number of digits or symbols that a puzzle creator can put on an initial grid to arrive at a puzzle that produces only one solution. Gordon Royle of the University of Western Australia was able to collect a total of 38,000 examples that fit this criteria of having 17 as an answer to this question, but still cannot be translated to each other if elementary operations are performed.
It should be noted that the question of what is the maximum number of digits that can be placed in a starting grid and still get only one solution to the puzzle has not yet been reached. These are just some of the problems that still confuse and challenge Sudoku scientists.
