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.

How many combinations of Sudoku are possible?

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.

What is the time complexity of 9 by 9 Sudoku?

Time Complexity : O( n ^ m ) where n is the number of possibilities for each square (i.e., 9 in classic Sudoku) and m is the number of spaces that are blank. where T(N) is the running time of the solution for a problem size of N. Solving this recurrence will yield, O(9^M).

How many rectangles does a 9x9 grid have?

First looking at the squares:

So there are 204 squares. Then looking at rectangles: There are 9 vertical lines and 9 horizontal lines on the chess board. To form a rectangle you must choose 2 of the 9 vertical lines and 2 of the 9 horizontal lines.

How many 6x6 Sudoku puzzles are possible?

The number of reduced Rodoku grids, s(6), is 816.

Sudoku Tutorial #40 A must know technique.

Can a 9 * 9 Sudoku have multiple solutions?

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 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).

How many 4x4 Sudoku puzzles are possible?

Your students could now be asked to find all the sixteen possible arrangements with the digits 1, 2, 3, 4 in that order across the top row. Then they should show that the top row can be rearranged in 4! = 24 different ways. Hence the total possible 4x4 Sudoku Latin squares is 16 x 24 = 384.

How many squares do you see on a 9x9?

Wiki says: The number of classic 9×9 Sudoku solution grids is 6,670,903,752,021,072,936,960, or around 6.67×1021. This is roughly 1.2×10−6 times the number of 9×9 Latin squares.

How many squares in a 9x9 board?

For our chessboard there are 81 (9 x 9).

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 6 minutes good for Sudoku?

5 minutes is more than enough time to jump start your brain, re-evaluate your Sudoku strategy, and develop a new perspective on how to view the Sudoku grid. So “take 5” and give yourself a new chance at solving Sudoku puzzles!

Can Sudoku be bigger than 9x9?

Large Sudoku Puzzles - 16 by 16 Grid [Page 12 of 14])

Sudoku Dragon also supports other larger sizes than the standard 9x9: 10x10; 12x12; 14x14; 15x15 and 20x20 as well as 16x16.

Can 1 Sudoku have multiple solutions?

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.

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.

Can you solve Sudoku mathematically?

In fact, mathematical thinking in the form of logical deduction is very useful in solving Sudokus. The most basic strategy to solve a Sudoku puzzle is to first write down, in each empty cell, all possible entries that will not contradict the One Rule with respect to the given cells.

Is a sudoku 9x9 Matrix?

A Sudoku puzzle consists of a 9x9 grid of squares, broken up into a 3x3 grid of blocks made up of nine squares each. The goal of a puzzle is to fit the numbers 1 through 9 into each of the 81 squares of the grid so that each row, column, and block has exactly one of each number.

What is the magic square of 9x9?

9x9 magic square of order 9 and the astrological Moon with magic constant 369. The sum of numbers in any row, column, or diagonal is always three hundred sixty-nine.

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 puzzle is harder than Sudoku?

A Calcudoku is similar to a Killer Sudoku, except that (1) any operation can be used to compute the result of a "cage" (not only addition), (2) the puzzle can be any square size, and (3) the Sudoku rule of requiring the numbers 1.. 9 in each 3×3 set of cells does not apply.

How many Sudoku puzzles should I do a day?

Make an effort to complete at least one sudoku puzzle a day and you might see your improved reasoning skills transfer to your job and other problems you come across with in your everyday life.

Can we use 0 in Sudoku?

Sudoku Rule № 1: Use Numbers 1-9

Each row, column and square (9 spaces each) needs to be filled out with the numbers 1-9, without repeating any numbers within the row, column or square.

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.

Is 7 minutes good for Sudoku?

The good sudoku time is one where one is able to solve a complex sudoku game which is in itself a combination of 5 or more sudokus. From the competition point of view, the lesser time one takes the better it is. For very hard say 5 to 7 minutes should be great.