How many possible combinations of 9x9 Sudoku?

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.

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.

What is the total number of rectangles in a Sudoku is 9x9 matrix?

How many sudoku puzzles can you possibly make with a regular 9*9 square? 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.

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 4 cell rule?

Rules of Quadruple Sudoku

The object of the puzzle is to fill in the whole 9x9 grid with numbers 1 through 9 (one number per cell) so that each row, each column, and each of the nine 3x3 boxes contains all the nine different numbers 1 through 9. The clues are in the form of sets of four special clue-numbers.

Is there a formula for Sudoku?

For example, in the first and fourth columns beginning from the left of the 9×9 grid, we can form the following equations: m+n=a, g+n+f=g+c. In the second and last rows beginning from the top of the 9×9 grid, the following equations can be formed: b+g+f=a+g, e+n+m=a+b+d.

Is a Sudoku a 9x9 grid?

A completed Sudoku is a 9 x 9 grid, where each row, column, and each 3 x 3 square must contain each of the numbers 1–9 (and once only). The grid below depicts a single row, column and square adhering to these constraints.

What is a 9 by 9 grid with numbers?

In its simplest and most common configuration, sudoku consists of a 9 × 9 grid with numbers appearing in some of the squares. The object of the puzzle is to fill the remaining squares, using all the numbers 1–9 exactly once in each row, column, and the nine 3 × 3 subgrids.

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 total squares are in a 10x10 grid?

How many squares are there in a 10 by 10 grid? As n varies from 1 to 10, so does 11-n, but in reverse order. So the answer is the sum of the squares from 1^2 to 10^2, which is 285 if I haven't made a mistake in my calculations.

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 rule of 2 Sudoku?

Rule 2 - Each column must contain the numbers from 1 to 9, without repetitions. The Sudoku rules for the columns on the grid are exactly the same as for the rows. The player must also fill these with the numbers from 1 to 9, making sure each digit occurs only once per column.

Are all Sudoku solvable?

The vast majority of puzzles don't require the trickier techniques, but there are some which just aren't solvable by simple logic alone, and require various forms of guessing to solve.

Can there be 2 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.

What is the best algorithm to solve Sudoku?

The simplex algorithm is able to solve proper Sudokus, indicating if the Sudoku is not valid (no solution). If there is more than one solution (non-proper Sudokus) the simplex algorithm will generally yield a solution with fractional amounts of more than one digit in some squares.

Can I solve Sudoku 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.

How long does it take the average person to solve a Sudoku puzzle?

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. While the game itself can be challenging and complex, several strategies can be used successfully to find the solution.

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).

What is the L rule in Sudoku?

The L pattern exists when there is a wall that has one populated cell adjacent to it. The wall and the adjacent cell must be in the same box.

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.

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.

What is a swordfish in Sudoku?

A Swordfish is a 3 by 3 nine-cell pattern where a candidate is found on three different rows (or three columns) and they line up in the opposite direction. Eventually we will fix three candidates somewhere in those cells which excludes all other candidates in those units.