# A Combination Of Numbers And Operations Is Called A Formula The Science Behind the Sudoku Puzzles

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## The Science Behind the Sudoku Puzzles

A logic game, especially one as complex as Sudoku puzzles, is more often liked by people who love technical things, such as computer geeks, mathematicians, computer engineers, etc. It is quite fascinating how Sudoku captured the hearts of millions.

Another highly logical game that gained the same popularity is the Rubik’s Cube, which uses a three-dimensional grid that requires groups of colors on each side. However, a Sudoku puzzle is a flat grid that usually contains a nine-row, nine-column grid. It consists of 81 cells and nine smaller squares or sub-squares where numbers are placed.

The set of numbers from 1 to 9 are the places in each square that appear only once in each row and each column, which is actually a literal translation of its Japanese name, which means “married”.

Each puzzle has one unique solution. While you may see numbers, it doesn’t require you to come up with any mathematical equation. This grid is known to be a special type of Latin squares by the 18th century mathematician Leonhard Euler, where the nxn matrix formula is filled with n symbols, with each symbol appearing only once in each row or column. A Sudoku puzzle consists of a combination of Latin squares, plus the requirement to treat the puzzle as a single grid, but the sub-grids also contain the numbers 1 to 9, which creates interactions and constraints with other grids.

Sudoku seems to be just entertainment for most people, but for mathematicians, it raises many questions that require investigation. One of the questions raised about this is how many Sudoku grids can exist. To simplify this problem, mathematicians who first focused only on using logic were able to arrive at an estimate of 6,670,903,752,021,072,936,960 possible valid Sudoku grids. It is based on Bertram Felgenhauer from the Technical University of Dresden in Germany and Frazer Jarvis from the University of Sheffield in England. This value has already been verified a few times by other studies.

However, if we consider only those grids that can be reduced to equivalent configurations once, we get a smaller value of 5,472,730,538. These numbers assure humanity that we will not run out of puzzles to solve and that we can enjoy solving Sudoku puzzles for the rest of our lives.

Another problem currently puzzling researchers is what is the smallest number of numbers or symbols that a puzzle maker can place on the starting grid to arrive at a puzzle that has only one solution. Gordon Royle of the University of Western Australia was able to collect a total of 38,000 examples that fit the criterion of 17 as the answer to this question, but still cannot be translated into one another under elementary operations.

It should be noted that the question of what is the maximum number of numbers that can be placed on the starting grid and still get only one puzzle solution has not yet been reached. These are just a few of the issues that still confuse and challenge researchers when it comes to Sudoku.

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