@ryandong
Profile
Registered: 3 years, 5 months ago
The mathematical and playful aspects of sudoku
Over the last few years, mathematicians have shown an increasingly consistent interest in Sudoku. One of the first questions that the experts asked themselves concerns the total number of different grids that can be built: finding an answer was not an easy task, to the point that it was necessary to use the computer to arrive at the exact calculation of the solutions that could be considered valid. Well, these are several trillions of billions of options, which is a much higher figure than the number of molecules that make up a mass of substance or the number of stars in the universe.
The mathematical questions
Mathematicians then found themselves faced with another question, namely the smallest amount of numbers that must be entered by a free online Sudoku creator in the initial scheme to ensure a single solution: well, the answer is seventeen. In fact, if sixteen digits were entered in the diagram, there would be two solutions available; after which the quantity of solutions would grow exponentially as the figure in question decreased. It must be said, however, that in most cases between twenty and thirty digits are inserted in the schemes: as you can guess, reaching a solution is all the more complicated the lower the number of digits that are present in the initial scheme. .
The opposite question
Obviously the mathematicians also questioned themselves in the opposite direction: in other words, they wanted to understand which was the highest number of digits that does not guarantee a single solution. Well, it has been discovered that with eighty digits the solution is only one, and so also with seventy-nine or seventy-eight; therefore the answer to this question is seventy-seven.
How computers work
Computer scientists and mathematicians are very interested in understanding what a computer can do for programming a web Sudoku scheme and its solution. A calculator, in fact, is able to elaborate with a certain ease the programs that allow to solve the various starting grids. The systematic approach based on trial and error simulations is the most popular program for this purpose, and is characterized by the modification of partial solutions, which are changed as soon as their incorrectness is registered. If the program is accurate, it is possible to identify all the various hypotheses and then arrive at the solution you are looking for, provided there is one. Obviously, this solution technique cannot be put into practice by humans due to the time limits that characterize it.
The variants of the game
There are certainly not a few variations of the game: for example, in some of them additional constraints are used, while in others different structures are used to replace the square sub-grids. There are also variants that provide for the overlapping of various schemes. It is not certain that the classic 9 x 9 scheme is always the starting one, given the departure of higher schemes. In fact, computer scientists are dedicated to the design of programs capable of inventing and solving sudoku puzzles characterized by an ever higher level of complexity. As it is easy to imagine, with the increase in the amount of starting cells, the time that the computer needs to reach a solution increases significantly.
A worldwide success
When online Sudoku first appeared, not many years ago, the game was greeted with a certain skepticism: it was believed, in fact, that it would capture the attention of a small number of people, that is to say above all computer and mathematical experts. The predictions, however, have been disproved by the facts, and the game in a short time has achieved such popularity as to become a competitor of crosswords and many other pastimes. The reasons for success are few and easy to identify, starting with the simplicity of the rules: to try your hand at sudoku, in fact, you need a form of essential logic that we all have, including children.
The characteristics of sudoku
Even if the Sudoku puzzle is based on numbers, in reality mathematics has little to do with it: to be able to complete the schemes, no arithmetic operation is required. The fact that it is not necessary to know mathematics to solve a Sudoku puzzle is easy to prove: it is enough to replace the numbers with letters and the game would not change, but in reality it could also be replicated with images, symbols, and so on. . A peculiarity of sudoku is that for each scheme there is only one solution. In short, few rules but clear and really intriguing, almost synonymous with mystery.
Related Resources :
Effective exercises to stimulate the brain and develop thinking
The use of Sudoku in the development of logical thinking in preschoolers
Forums
Topics Started: 0
Replies Created: 0
Forum Role: Participant