Sudoku

Sudoku Solving Techniques

puzzle3x3x — Thu, 04 Mar 2021 21:07:02 +0000

Sudoku Solving Techniques

Sudoku became a very popular puzzle game primarily because it provides an engaging challenge to both, new beginner players as well as seasoned Sudoku puzzle solvers. The approach to solve the Sudoku puzzle might be different, but it all comprising of finding the one unique solution that will fit into the grid. Each Sudoku puzzle has only one unique solution.

You cannot solve a Sudoku puzzle through guesswork. Therefore, your first few times playing Sudoku can be somewhat intimidating and challenging.

Most of the time, newbies guess the easy allocation numbers, then keep perfecting their problem-solving skills as they understand how the game works.With the help of a few tips and some logic, you won’t need to struggle to solve a Sudoku puzzle. Here are some of the most straightforward Sudoku solving techniques you can use to solve many Sudoku puzzle.

One Direction Scanning and Missing Single numbers

One direction scanning’s primary strategy is to study the puzzle and identify the missing digits in each row. Simply chose a number and see where it fit within the row and column and if there is one possibility in the third row or column or within a 3 x 3 block. This strategy is not limited to rows alone; you can equally look through the columns, spot the missing numbers and fix them in the correct slots.

For Example

If we scan row 3 and row 2, we can see the 9 (marked in yellow) in cell R3C2 and R2C7, now if we scan row 1, there is only one possibility for the number 9 in R1C5 (marked in yellow)

Missing Singles

A missing single is an individual digit missing in a column or row. Finding an absent single is simple since you only have to look at the available numbers, figure out the missing one, and put it in its rightful spot.

Two-Direction Elimination

In every Sudoku puzzle, each row and column has to have all numbers between 1-9. Scanning in two directions (looking at both rows and columns) allows you to discover which number is missing in a row or/and a column.

This technique is similar to the one-direction scanning; only that in this case, you have to scan columns and rows simultaneously..

In this example we look at row 1 and row 2 with number 1. We see 2 possible cells to fill the number 1, R3C7 and R3C9, but since there is a 1 in R4C6, the only possibility for the digit one is in cell R3C9 (marked Green)

Eliminating a Digit from Columns, Rows, and Blocks

This strategy is similar to the single candidate search, only that in this scenario, you get rid of numbers that you have already used in the respective spaces. Once you determine which numbers are in the cells, you will discover those that are missing. From this point on, you have to use your pencil and some thinking to figure out which number goes where.

Unique Numbers

Another method to solve a Sudoku puzzle is to find unique numbers. These are digits that are missing in a 3 x 3 block. We know that each block should have one integer between 1 to 9. So, divide the puzzle into 3 x 3 blocks.( we have 9 3×3 blocks)) Check which common digits are available within each 3 x 3 block and see if this will lead to place this number in another 3 x 3 block that does not have it..

This will become clearer with the example below.

You will discover that particular digits are common to a majority of the blocks. For instance, you’ll see that most of the 3 x 3 blocks have the number 2 in them. However, 3 x 3 blocks 5 and block 8 (marked in blue) do not have the number 2 in them. Therefore, you will only have to find the blocks that do not have this number and find a befitting cell for them. Once you solve one box, it becomes easier to fill in other blanks in the other 3 x 3 boxes using this strategy.

In this case, you have to find a spot for this number (digit 2) in both boxes. Rows 6 and 7 do not have number 2, making them great places to look into. Now R6C6 (marked in yellow) and R7C4 (marked in green) make the best choices since there is no clashing number 2 in correspondent rows or columns. Now it is easy to figure that in 3 x 3 box 5 the best place to put a 2 is in cell R6C6 Because you cannot put a 2 in row 5 ( because of the 2 in R5C1) and in row 4 because of the 2 in R4C8 so the only choice is R5C5 or R5C6 out that the number 2 but column 5 has already a 2 in R3C5 therefore the ONLY place for the number 2 is in R6C6 ( marked in green) From there, it is easily figured that 2 will also go into 3×3 box 8 in cell R7C4 as it cannot be in any other cell in 3 x 3 box 8

Pencil Marking

Until this point, the Scanning and Elimination techniques above do not involve multiple candidates per cell. As you start to solve more challenging Sudoku puzzles, you will find that some cells can hold 2, 3 or more possible candidates. Pencil marking is the exercise of writing down little pencil marking of these number candidates in a cell in order to keep track of all the remaining possibilities. Most puzzle solvers prefer to scribble small numbers at the corner of a cell, making it easier to analyze where each probable number should go, thereby eliminating the odd ones. The idea is to help you recognize certain patterns and help to eliminate some candidates.

Pencil marking may not be possible in all scenarios, especially if you play on your phone or tablet or online and these provisions are not available. In such cases, you can draw the Sudoku grid on paper, solve it, and then write down the grid’s answers.

Naked Subsets

Naked subsets occur when two or more number candidates for a cell in one row, or one column, or one 3×3 box containing few different numbers candidates, then those other cells with the same number candidate can be eliminated from the other cells in the row or column or 3×3 box.

Let’s look at an example to make it clear

.In this example, Cells R8C3 and R8C4 are both in the same row (row 8) and have both only candidates 3 and 9 left to occupy these cells.( highlighted in blue). Therefore if these 2 cells can have the number 3 or the number 9 It stands to reason that cell R8C2 CANNOT be 3 and therefore the number 3 can be eliminated leaving there number 7 (cell highlighted in yellow)\.

There are three types of subsets which are:

Naked pairs – When you are searching for only
two numbers
Naked triples – A scenario where you are
looking for three candidates
Naked quads – Happens when four digits are
missing from a block all with the same logic

Practice to Perfect Your Skills

What makes good Sudoku solvers? The answer is – Practice! The more one play, the more familiar one become with the different possibilities and the more proficient one become at solving the puzzle. Start

by solving the easy and simpler grids, then builds up to harder ones as your problem-solving skills improve. To learn more challenging Sudoku solving tips, try this article

Another important thing is that a Sudoku puzzle can be solved between 2 or more people as well. There will be one person responsible to put the suggestions in the grid, but this is a great game to play with your significant other or with friends.

Round-Up

Sudoku is a game that requires wit, skill and patience. You have to understand the metrics of each puzzle so that they can guide your decision-making process. If you’re playing a virtual game, you can use available tools to pencil-mark the prospective answers. However, if you’re solving one of those Sudoku puzzles in your daily newspaper, then the traditional pen and eraser will work just fine.

You can play free online Sudoku on our site by clicking here where you can play online or you can print the puzzle and solve it with pencil and eraser. It provide you with a chice between 3 difficulty levels – Easy, Meedium and Hard.

If you interested in our magnificent book with over 1100+ Sudoku puzzles from easy to Super hard,

Click Here

You can use each of the Sudoku’s solving tips above to solve a puzzle, yet by using a combination of all of these techniques makes the journey easier, and helping you finish up the puzzle faster. Remember, this game requires practice and patience so, do not sweat it if you cannot complete a puzzle in a short span of time or in one sitting. Remember – Practice make it perfect.

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Advanced Sudoku tips

puzzle3x3x — Thu, 18 Feb 2021 18:38:57 +0000

If you solved few Sudoku puzzles and got to the point where whatever you tried, you simply could not finish the puzzle, then it is a sign you need some advance Sudoku techniques to improve your solving skills,

The techniques below will help you in reducing the number of candidates that can go into a cell or in some cases, assist you to eliminate some candidates and find the specific number that will go into that cell. These techniques are more elaborate than the simple tips we provide in the beginners tips (see here) and they require focus, concentration and the ability to recognize these strategy patterns.

Here are few advance pattern recognition strategies

1. The X-Wing

This strategy helps us to eliminate some choices from penciled possibilities. This strategy consists of finding 2 rows and 2 columns where each pivot point contains a matching candidate number and forming a square or rectangular if connected. Now if any of the rows or columns that form the square or rectangular contains the same number candidate anywhere else on the row or column that form the square or rectangular, then it can be eliminated. This technique is named X-wing because the candidate matching numbers are diagonally across each other within the square or rectangle.

Let’s look at an example:

In this example, the penciled number 9 (marked in red) is positioned in row 5 in location R5C1 (Row 5, Column 1) and R5C7 and also in row 7 in positions R7C1 and R7C5. Therefore row 5 and 7 form a rectangle with column 1 and 7 with the optional candidate 9. These 4 cells are marked in blue.in the example above. You can notice they form a rectangular. This strategy is called X-Wing because the candidate matching numbers (in this case 9) are diagonally across each other within the rectangular and forming an X. Once we identify this form, and since the number 9 can appear only once in each row or column, then every other case of the candidate number 9 can be eliminated from other cells within the same row and column forming the rectangle. In the example below – we highlight in red all the candidate number 9 that now can be eliminated and highlight the box in yellow. As you can see, in box R7C3 once we eliminate the candidate number 9, we are left with the only option, which in this example is the number 2.

It takes a bit of practice to identify this form, and it is fairly common in the tougher puzzles. Once you identify this form, it will help you to eliminate number candidates in few cells and at times even finalize a candidate number (like the number 2 after eliminating the candidate number 9 in cell R7C3.in the above example)

This technique requires the player to pay attention to this format and adopt a bird’s eye view yet finding the x-wing format can be instrumental in advancing your skillset and help in resolving more complex Sudoku puzzles.

2. The Swordfish

If the X-wing technique consists of finding 2 rows and 2 columns where each pivot point contains a matching candidate number, the Swordfish technique is like the X-Wing technique on steroids and consists of finding 3 rows and 3 columns where each cross point between a row and column contains a matching candidate number.

Like the x-wing, this technique helps to eliminate some number candidates. Let’s look at an example to make this technique clearer

In the example shown above, a Sudoku Swordfish pattern happens in rows 1, 8, and 9.( highlight in light blue) The three columns are 1, 6, and 9. (A blue line cross it) Each row has the number 1 in only two cells in this case. In row 1 the cells are R1C1, and R1C6, In row 8, the cells are R8C1, and R8C9. In row 9, the cells are R9C6 and R9C9. These cells are highlighted in yellow. The number 1 can only reside in three of the six highlighted cells

We do know that it must reside in three of the six positions highlighted. (They are locked pairs.) Therefore it is safe to eliminate the 1s from all three columns (or rows) except for the six highlighted positions. In the example above, the two cells in red (highlight in Green) may have the number 1 removed from them safely. Once you removed the 1s, you now expose a naked single 3 in R3C9.

This is not an easy formation to find, and it takes practice and focus to recognize the pattern and find it, however, it is an effective method to eliminate some candidate numbers (in our example it is the number 1) and it is another effective strategy in your advance strategy toolbox to make the process of completion and solving the puzzle easier.

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Adults who regularly take part in word and number puzzles like Sudoku have sharper brains, according to the largest online study to date

puzzle3x3x — Fri, 12 Feb 2021 22:37:21 +0000

Crosswords and Number Puzzles like Sudoku are Linked to Sharper Brain

“Regular crosswords and number puzzles linked to sharper brain in later life.” ScienceDaily. www.sciencedaily.com/releases/2019/05/190516082349.htm

The more regularly adults aged 50 and over played puzzles such as crosswords and Sudoku, the better their brain function, according to research in more than 19,000 participants, led by the University of Exeter and King’s College London.

The findings emerge from two linked papers published today (May 16th) in the International Journal of Geriatric Psychiatry. The researchers have previously presented their findings on word puzzles at the Alzheimer’s Association International Conference in 2018. The new research builds on these findings and also reports the same effect in people who regularly complete number puzzles.

Researchers asked participants in the PROTECT study, the largest online cohort in older adults, to report how frequently they engage In word and number puzzles and undertake a series of cognitive tests sensitive to measuring changes in brain function. They found that the more regularly participants engaged with the puzzles, the better they performed on tasks assessing attention, reasoning and memory.

From their results, researchers calculate that people who engage in word puzzles have brain function equivalent to ten years younger than their age, on tests assessing grammatical reasoning and eight years younger than their age on tests measuring short term memory.

Dr Anne Corbett, of the University of Exeter Medical School, who led the research, said: “We’ve found that the more regularly people engage with puzzles such as crosswords and Sudoku, the sharper their performance is across a range of tasks assessing memory, attention and reasoning. The improvements are particularly clear in the speed and accuracy of their performance. In some areas the improvement was quite dramatic — on measures of problem-solving, people who regularly do these puzzles performed equivalent to an average of eight years younger compared to those who don’t. We can’t say that playing these puzzles necessarily reduces the risk of dementia in later life but this research supports previous findings that indicate regular use of word and number puzzles helps keep our brains working better for longer.”

The study used participants in the PROTECT online platform, run by the University of Exeter and Kings College London. Currently, more than 22,000 healthy people aged between 50 and 96 are registered in the study, and the study is expanding into other countries including Hong Kong and the US. The online platform enables researchers to conduct and manage large-scale studies without the need for laboratory visits. PROTECT is a 25 year study with participants being followed up annually to explore how the brain ages and what might influence the risk of dementia later in life. PROTECT is funded by the National Institute for Health Research (NIHR) Bioresource, including through its NIHR Clinical Research Network (CRN). In addition to taking part in vital research, participants in the PROTECT study have access to a brain training programme that has already been shown to benefit brain function, as well as having the opportunity to take part in exciting new research studies into brain health and dementia prevention.

Clive Ballard, Professor of Age-Related Diseases at the University of Exeter Medical School, said: “PROTECT is proving to be one of the most exciting research initiatives of this decade, allowing us to understand more about how the brain ages and to conduct cutting-edge new studies into how we can reduce the risk of dementia in people across the UK. If you’re aged 50 or over, you could sign up to take part in research that will help us all maintain healthy brains as we age.”

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