What is the rectangle trick in Sudoku?

The following technique was described by Rod Hagglund. If two lines (e.g., a row and a column) cover all possible places for a given digit in some box, then that digit cannot occur on both lines outside that box, since that would not leave any place for the digit inside the box.

What is the Sudoku technique rectangle?

Unique Rectangle Type 1

This strategy applies when the player finds four cells with the same pair of candidates facing each other. They are grouped in parallel sets of two, sharing the same columns, rows, and blocks. This is a deadly pattern that results in a double solution for the puzzle.

What is the empty rectangle Sudoku?

An Empty Rectangle occurs within a box where four cells form a rectangle and do NOT contain a certain candidate. In Figure 1 we have some example spreads of candidate 8 within several boxes. For this work there must be more than two candidates in a box and four or more cells “empty” cells.

What is a Type 4 unique rectangle in Sudoku?

A Type 4 Unique Rectangle occurs when one of the digits belonging to the non-unique rectangle forms a conjugate pair in cells that have additional candidates. Thanks to this, we can remove the second digit of the non-unique rectangle from these two cells.

What is the uniqueness trick Sudoku?

As an application one has the Uniqueness Argument: Whenever one has a nonempty set of initially open cells, and two candidates at each of those cells, such that among these candidates each value occurs zero or two times in each row, column and block, then the actual solution differs in at least one cell from both ...

Lesson #10: X-Wings and the Rectangle Rule for Solving Medium to Hard Sudoku Puzzles

Is there a solution to every Sudoku puzzle?

Realistically, no! 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 best Sudoku algorithm?

Backtracking algorithm is the fastest algorithm to solve sudoku puzzles, It is by far the fastest compared to the other two methods. Also, let's note that each algorithm was faster with harder problems than with easier problems.

What is the unique rectangle rule?

UNIQUE RECTANGLE (TYPE 1) : If three corners of the rectangle are "Bi-Value" Cells with the same candidates and if one or both of these candidates are present in the Cell in the fourth corner, then none of these candidates can be the solution in the fourth corner; otherwise, this would lead to a Deadly Pattern.

How do you find hidden pairs in Sudoku?

If you're looking for hidden pairs, you're looking for two numbers which only exist in two cells within that area – even though there will be other candidates in the same cell “hiding” them. For triples, you'll be looking for three cells, and so on.

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 the least clues in Sudoku?

Sudoku fanatics have long claimed that the smallest number of starting clues a puzzle can contain is 17. Now a year-long calculation proves there are no 16-clue puzzles. 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.

What does a colon mean in Sudoku?

The challenge was to fill in the above snake with the digits 1 to 9, using each digit only once. The colon “:” means divide, and you must follow the standard order of operations, meaning that multiplication/division comes before addition/subtraction.

What is cross hatching in Sudoku?

Sudoku cross-hatching, or solving sections, is where you look at a single box with respect to two other boxes. You search for a specific number and see if that number will fit anywhere within the section you are looking at.

What is the ambiguity rule Sudoku?

During this process the designer must be careful not to remove two numbers that would cause an ambiguity (where those two numbers could be swapped and the puzzle could be completed two different ways, therefore having two solutions). This is what is called the sudoku ambiguity rule.

Can there be 2 solutions to a Sudoku puzzle?

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 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.

What is the rectangular formula?

Area of a rectangle = length × width .

What is the composite rectangle rule?

The composite rectangle rule is used to approximate the integral of a function f(x) over a closed and bounded interval [a, b] where a < b, by decomposing the interval [a, b] into n > 1 subintervals of equal length h = (b - a) / n and adding the results of applying the rectangle rule to each subinterval.

What is the 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.

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 should I look for first in Sudoku?

Look for the easy play first: When you first start to play a Sudoku puzzle, look for where you have the easiest opportunities to add a number. Usually this is where there is a crowded square or a row that is almost full of numbers.

What happens if I solve a Sudoku daily?

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.