How many Sudoku possibilities are there?

There are exactly 6, 670, 903, 752, 021, 072, 936, 960 possible solutions to Sudoku (about 10^21) . That's far more than can be checked in a reasonable period of time. But as luck would have it, it's not necessary to check them all. Various symmetry arguments prove that many of these grids are equivalent.

How many possible Sudokus exist?

There are 6,670,903,752,021,072,936,960 possible solvable Sudoku grids that yield a unique result (that's 6 sextillion, 670 quintillion, 903 quadrillion, 752 trillion, 21 billion, 72 million, 936 thousand, 960 in case you were wondering). That's way more than the number of stars in the universe.

How many 9x9 Sudoku combinations are there?

They discovered that the number of possible 9 by 9 Sudoku grids is N=6670903752021072936960 which is approximately 6.671×10²¹.

Can there be multiple solutions to Sudoku?

A well-formed Sudoku puzzle is one that has a unique solution. 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. There are examples of rank-3 Sudoku puzzles with 17 givens that are well-formed.

What is the 45 rule in Sudoku?

The 45 rule is a basic solving-technique in Killer Sudoku. Each house (row, column, nonet) must add to 45 (the sum of the digits 1 through 9).

Sudoku Tutorial #40 A must know technique.

What is the hidden triple rule in Sudoku?

"Hidden triples" applies when three cells in a row, column, or 3x3 block contain the same three Notes. These three cells also contain other candidates, which may be removed from them.

What is Sudoku rule of 1?

Rule 1 - Each row must contain the numbers from 1 to 9, without repetitions. The player must focus on filling each row of the grid while ensuring there are no duplicated numbers. The placement order of the digits is irrelevant. Every puzzle, regardless of the difficulty level, begins with allocated numbers on the grid.

Can all Sudoku puzzles be solved without guessing?

Can all Sudoku puzzles be solved without guessing? According to Sudoku Of The Day, “Sudoku is a puzzle involving logic—no arithmetic or guessing is required!” While you can, guess, of course, if your guess is wrong, it will throw off the rest of the puzzle and you'll need to start over.

Is there a pattern in Sudoku?

Patterns are essentially a series of completed numbers (either givens or numbers that have been filled in) in a specific order in one of the boxes on the sudoku grid. Patterns help you organize the remaining numbers and eliminate possibilities in a box, and in related boxes, rows and columns.

Is Sudoku good for the brain?

Sudoku keeps your brain active and reduces the risk of Alzheimer's, a most common cause of dementia that affects a person's thinking and behavioural skills. Stimulates your mind: The game works on your logical thinking process as you are absorbed in solving a puzzle and eventually improve your number skills.

What is the last possible number rule in Sudoku?

Last possible number is a simple strategy that is suitable for beginners. It is based on finding the missing number. To find the missing number you should take a look at the numbers that are already exist in the 3x3 block you are interested in, and in the rows and columns connected with it.

Is there 16 * 16 Sudoku?

16 x 16 sudoku puzzles work just the same as regular 9 x 9 sudoku puzzles, but they are, well, a lot bigger! Infact whereas a normal sudoku has 81 squares in it, a 16x16 sudoku has 256 squares in it, so you get a lot more puzzle for your money.

Is Sudoku always 3x3?

The game of Sudoku consists of a grid of nine rows and nine columns subdivided into nine 3x3 subgrids. It has two basic rules: Each column, each row, and each box (3x3 subgrid) must have the numbers 1 to 9. No column, row or box can have two squares with the same number.

What is the minimum Sudoku problem?

The fewest clues required for a proper Sudoku is 17, but not all completed grids can be reduced to a proper 17 clue Sudoku. About 49,000 unique (non-equivalent) Sudokus with 17 clues have been found. (A proper Sudoku has only one solution).

Are you smart if you can solve Sudoku?

From this case study it can be concluded that an individual who is skilled at solving Sudoku puzzles likely has a high general IQ. The results of the weak correlation between Sudoku scores and the WAIT test indicates that in some cases a high Sudoku doesn't necessarily mean a high general IQ.

Is there a logic to Sudoku puzzles?

To solve a Sudoku puzzle, one needs to use a combination of logic and trial-and-error. More math is involved behind the scenes: combinatorics used in counting valid Sudoku grids, group theory used to describe ideas of when two grids are equivalent, and computational complexity with regards to solving Sudokus.

Does Sudoku only have one right answer?

Sudoku is a number puzzle consisting of a 9 x 9 grid in which some cells contain clues in the form of digits from 1 to 9. The solver's jobs is to fill in the remaining cells so that each row, column and 3×3 box in the grid contains all nine digits. There's another unwritten rule: the puzzle must have only one solution.

What is the fastest Sudoku time ever?

A Sudoku Master from China Wang Shiyao solved 9x9 sudoku grid in 54.44 seconds at the World Sudoku & Puzzle Championship held in Prague. However...

What is the most clues in Sudoku?

An ordinary puzzle with a unique solution must have at least 17 clues, but this is not mathematically proven. There is a solvable puzzle with at most 21 clues for every solved grid, with the largest minimal puzzle found so far has 40 clues in the 81 cells.

What is diabolical Sudoku?

Classic sudoku: fit the numbers in the grid so that each row, column and square contains the numbers one to nine once only. If you think it sounds simple then try our diabolical sudoku to see how hard it can be. All Sudoku Diabolical Puzzles.

What is the 159 rule in Sudoku?

Normal sudoku rules apply: Each row, column, and region indicated by thick borders in the grid must contain the digits 1 to 9 once each. 159: Digits in column 1 indicate the column in which the digit 1 appears in that row (e.g. if r4c1 is a 6, r4c6 is a 1).

What is the average time to solve a Sudoku?

It can be incredibly challenging to solve a Sudoku puzzle. That's what makes it fun. It is believed that the average Sudoku player spends approximately 20 minutes solving a typical Sudoku puzzle. For very hard puzzles, that number can be much higher.

What is the magic number in Sudoku?

Now Gary McGuire, a mathematician at University College Dublin, has come up with what he says is a proof that finds the minimum number of clues, or starting digits, needed to complete the game is 17.