How to solve Sudoku puzzles quickly and reliably


People that are new to Sudoku puzzles are going to have great difficulty in solving one. On one side there are so many numbers, and it seems so mathematical. Moreover, on the other side, if you do not have any appropriate solution techniques, it is going to take a lot of guessing and checking as well. In reality, these puzzles are well structured and pretty predictable like general mathematics. There are a few aspects of Sudoku puzzles. Before learning more about them, let’s take a look at some of the basics of Sudoku including the rules, in the game, and terminology.

What is Sudoku?

For anyone who is still not aware of it, we should know that Sudoku is s a logic-based and number-placement puzzle. It is in the format of a box divided into 9*9 rows and columns including 3*3 sub-grid which results in a total of 81 cells which are also called Latin square.

The aim here is to fill a grid with numbers in a way that each of the columns, each row, and all the grids must contain numbers with digits from 1 to 9. Every Sudoku puzzle starts with some of the cells already filled in. The players use these hints as a starting point so that they are able to find a unique solution. The main point to note here is that you cannot repeat the numbers from 1 to 9 in any of the rows or columns. Although you can repeat these along the diagonals. You have to cross all the constraints of the box.

Sudoku Variants:

There are many variations in Sudoku-like Mini Sudoku, Killer Sudoku, Wordku, and Cross sums Sudoku to name a few.

Rules of the game:

While you might think solving Sudoku can be a difficult challenge, the rules of the game are very simple and straightforward. They are following below:

Every row, column, and square can have each number from 1 to 9 exactly one time.

You can see a small number printed in the corner of row and column. The sum of all the numbers in any row, the column should match with that small number. When we talk about the traditional Sudoku Puzzles that feature numbers 1 to 9 the sum is equal to 45.

When you actually want to solve such a puzzle, you should maintain discipline and patience. Also, you should be much focused.

How to solve hard Sudoku:

There are some puzzles that you might not still be able to solve. These are difficult Sudoku puzzles. There are few possibilities explained below that why you are not able to solve a Sudoku puzzle even after using the techniques:

It is, in fact, a puzzle that you can solve but it needs some extra rules to solve.

It is not a valid Sudoku puzzle as it either has more than one of the possible solutions that need you to make guesses or it does not have a solution at all. If the puzzle does not head to a solution it returns false.

So how can a person solve hard Sudoku? Well, it is a technique called the Forced choice or also sometimes known as the Forced chain. This is the situation where we assume that you have filled all the cells that you could find out with certainty. After which you have penciled in suitable and possible candidates. Now you have to use the Forced Choice technique. In this, you select one cell that has only two choices, and you have to go to with one of them as your choice. Always remember that these choices are not for sure correct. Actually, you are only following a hypothesis towards its conclusion. This is going to lead to two conclusions.

Either you are going to come to a point where your choice is going to contradict another one, or you will have your puzzle solved.

There can be a third possible outcome as well. Here neither your choice will contradict, nor you will be able to solve the puzzle. In such situations, you will need an even higher and advanced level of Sudoku solving techniques.

How to solve Sudoku mathematically

Many Sudoku problems you can solve using mathematics and by applying various algorithms. Generally, a Sudoku puzzle solving involves n*n* blocks and its name is NP-complete. When the value of n is equal to three, the results do not have much importance. You can solve in fractions of seconds using simple algorithms like Dancing Links.

Sudoku solver algorithm:

There are many Sudoku solving algorithms that are easy and going to solve a 9*9 puzzle only in a fraction of seconds. One of these techniques is here:

Back Tracking:

Some people have been able to develop a computer program. It is able to solve a Sudoku puzzle using the backtracking algorithm. It is an in-depth first search. And it is going to completely investigate one branch to a possible answer before moving to a new branch. It is a type of ‘Brute Force’ search.

There are many advantages to using such an algorithm such as:

  • You can find out a solution definitely as it always returns the true value.
  • The time to solve the puzzle is not related to the level of difficulty.
  • It is a simple to use algorithm compared to any of the other algorithms.

Sudoku puzzle-solving strategy in 7 ways:

Here are seven Sudoku solving techniques that will help you in understanding puzzles.

1. Only Choice Rule:

In this technique, there can only be one choice for a particular square. You will have a group that has eight allocated squares, and you have only one choice left. So it will be very easy to fill the remaining number in that only square. You can use this technique by scanning for the 8 allocating squares in rows of columns or regions.

2. Single Possibility technique:

When you look with care at the individual squares, you will be able to find out that there is only one possibility left for the square. This will be the outcome as the groups intersect in such a way that there is more than one unallocated square. And yet only one option exists for the square.

3. Slice'n'Dice technique:

It is also known as the cross-hatching technique as well. It is the rule of necessity and the method of completion. In simple terms, completion means, if you leave one place in a row, column or square, you do know what digit belongs to that particular place. Only because there can be perchance only one digit that is left to be used. The rule of necessity tells you that you should be able to find a place to put each digit in each row, column, or square.

4. Penciling in:

In the basic form, penciling in is the process of writing down all the possible answers in the empty cells. After which by using the cross-hatching technique we cross off all the answers that do not qualify. This has more advantages as it helps us to get an insight into more number of cells.

5. X wing:

This is a technique to remove the candidates. For this, you need to consider the two parallel rows or the two parallel columns. You cannot involve blocks here. If you are able to find a row that has the same pencil marks in exactly two places. Also, another parallel row mirrors it. You will be able to use this information to remove the similar pencil marks in the columns that have passed through those marks.

6. Swordfish technique:

In the swordfish technique, three columns or three rows are inbuilt. These places can be difficult to find. When all the three columns have coinciding end squares the rule applies like the X wing technique. If you are able to use this technique and solve the puzzle, For sure, you are going to feel a sense of achievement.

7. Naked Pair:

This is more of an advanced technique. In general, it is also called a Naked Subset" or "Disjoint Subset." In this technique, you will have to find candidates that you can remove by placing other digits. Naked pair means there are only two candidates to look for. You can apply the same technique to the larger group as well as triplets and quads.

Benefits of Sudoku for students:

Here we are giving you some of the important reason and benefits of Sudoku for students:

Sudoku brings a feeling of order and keeps you calm:

Regardless of how hectic your life is, Sudoku offers an unwinding approach to take a break from your stressful surroundings. Many students make Sudoku a part of their everyday plan since it helps them to refresh. It enables them to complete other tasks in life with full energy and enthusiasm. Playing Sudoku additionally enables students to feel a sense of mastery. This is one motivation behind why the game is so popular. This also helps the students to do well in other subjects as well.

Sudoku may enable your brain to stay healthy:

The American Alzheimer's Association has supported Sudoku as a "mind diversion". That may help lessen the danger of Alzheimer's illness. A few scientists trust that playing such logical games like Sudoku may also help to diminish our danger of dementia as we get older. So the earlier we start the better, and this will also help the students to focus better on their studies.

Sudoku gives an escape:

Sudoku is a fun game that you can play whenever, anyplace – making it simple to use these games, can be the best fun activity to do when you feel boredom. Many students feel that Sudoku and alike games are "addictive". But yet it is more beneficial than other bad habits like smoking.

Sudoku is a good time for all ages:

Kids can play Sudoku, grown-ups, and seniors alike. There are unique Sudoku games made for kids (for instance, Sudoku confuses with the numbers 1-4 rather than the standard 1-9). The tenets of the diversion, the different online Sudoku recreations, and Sudoku versatile applications that are straightforward for anybody to get up to speed on the game, regardless of whether they see themselves as "educated" or "great at math."

Sudoku can even be a fun amusement for parents to play with their kids. You can both sit together and enable your way to figure out how to fill in the spaces on the framework. This will develop intelligent critical thinking aptitudes. It will also help your kid feel a feeling of achievement with each completed puzzle.

Sudoku can help dispose of "earworms":

Have you at any point had an "earworm?" Not a parasitic worm in your ear – It is a tune that gets stuck in your mind and won't quit replaying. Researchers at Western Washington University found that playing Sudoku helped individuals get the tunes out of their heads faster. Isn’t this a cool trick to try out next time a song gets in your head?

Sudoku develops leadership:

Sudoku is a session of logic and critical thinking. And settling on fast choices in view of pieces of evidence that are available. Children love Sudoku since it gives them more control and freedom. With Sudoku, kids take in the prompt association between their actions and the outcome. If they are able to analyze the puzzle in the correct way, they will have a favorable result.

Sudoku is more "dynamic" than other stationary exercises:

Many parents stress that their children invest excessive energy in playing computer games, sitting in front of the TV, or gazing at screens by hiding. Sudoku is an all the more rational dynamic, participatory kind of entertainment. On the grounds that when kids play Sudoku, their brains are actually working the whole time.

Sudoku focuses on the details:

Sudoku is a game that prizes players who have a decent focus on details. Seeing themes, spotting openings, and finding the correct minute to make a move. It promotes a child’s focus on the details. It helps the students to become more logical and methodical thinkers. Regardless of what games your child wants to play in the future, it is going to help them have a clearer mind. It is going to be actually well organized which in turn is going to help your child in their work environment.

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