![]() ![]() If the problem can be solved relatively quickly, then so can every problem that satisfies property (1).Įven though checking a solution of an NP-complete problem can be done relatively quickly and easily, there is no known algorithm for finding a solution to begin with, because the time needed for computation increases so fast compared to the size of the problem.Any solution to the problem can be checked relatively quickly, i.e. ![]() The more cells are pre-filled the easier the puzzle. As you gradually gain more experience with this puzzle, you’ll be able to develop your concentration, patience, and thinking skills. You start a Sudoku puzzle with some cells already filled in with numbers. The puzzle game Sudoku is a game that works on improving logical thinking but doesn’t require you to solve complex mathematical operations. So each row, column or region contains nine cells. An NP-complete problem satisfies the following two properties: In each Sudoku puzzle you have a 9x9 grid, divided into nine 3x3 square regions (you can just look above to get an impression). This places the game of solving rank-n Sudoku puzzles in a class of problems that computer scientists have named NP-complete. As the rank of a Sudoku increases from n to n+1, the extra computational time needed to find a solution increases quite fast. Find two different solutions.įor 4×4 Sudoku, a case-by-case analysis utilizing the two essentially different grids proves that a well-formed puzzle must have a minimum of four distinct digits in the givens.įinally, it is intriguing to note that even though there are computer programs that can quickly and easily solve rank-3 Sudokus by employing a backtracking method, solving a Sudoku of arbitrary rank n is a much more difficult problem. The next exercise illustrates this with a specific example.Įxercise: The following rank-2 Sudoku has 2 2-1=3 distinct digits among the givens. Recall that the converse of a true statement is not necessarily true. It is important to note that this is not the same as stating that if a Sudoku of rank n has n 2-1 distinct digits in the givens, then it is well-formed. The fact discussed above can be restated as follows: If a Sudoku of rank n is well-formed, then it must have n 2-1 distinct digits among the givens. In particular, for the usual rank-3 Sudoku, at least 3 2-1=8 distinct digits must be used in the givens for the puzzle to be well-formed otherwise, the puzzle will have more than one solution. This is because if we had a rank-n puzzle where only n 2-2 symbols were used and we found a solution, then interchanging the places of the two symbols missing from the givens would result in another, different solution. However, the minimum number of givens for which a rank-3 Sudoku can be well-formed is not known.Įxercise: Can you come up with a Sudoku puzzle that is not well-formed?Īnother interesting question (that you may have considered when solving the above exercise) is how many distinct symbols need to be used among the givens for a puzzle to be well-formed? It turns out that for a Sudoku of rank n, at least n 2-1 distinct symbols must be used for the puzzle to have a unique solution. There are examples of rank-3 Sudoku puzzles with 17 givens that are well-formed. A Sudoku puzzle can have more than one solution, but in this case the kind of logical reasoning we described while discussing solving strategies may fall short. Playing sudoku daily can boost your concentration, ease depression and even prevent Alzheimer's disease.The Math Behind Sudoku Some More Interesting FactsĪ well-formed Sudoku puzzle is one that has a unique solution. Can you imagine that there are 5,472,730,538 possible sudoku puzzles? Enter numbers into the blank spaces so that each row, column and 3x3 box contains the numbers 1 to 9 without repeats. The Times in London helped spread Sudoku to Western culture by publishing its first daily sudoku in 2004. Every Sudoku has a unique solution that can be reached logically. In this puzzle you will see there are four 3x3 shaded areas. Therefore, in the sudoku game, we have to fill in numbers without repetition. A Hyper Sudoku puzzle is very similar to a normal Sudoku puzzle, but there are four extra regions. What is Sudoku? 'Su' in Japanese means numbers while 'Doku' means single. The best part of the game: This free online sudoku game delivers a new puzzle each and every day! Interesting Facts about Sudoku The goal of the game is to fill every square on the grid with a number from 1-9, where the numbers can only appear once in every row, column and 3x3 box. You can place notes, find sudoku tips, manage the timer and save the sudoku game by clicking the menu bar in the top-right corner. Worried about damaging your sudoku puzzle with eraser marks? When you play our free online sudoku game, there's no need! You can choose easy sudoku, medium sudoku, or even sudoku for experts if you are confident. ![]()
0 Comments
Leave a Reply. |