Mastering Sudoku: Tips to Stop Guessing and Solve Puzzles with Strategy

Are you a Sudoku enthusiast looking to up your game?

Explore the reasons why people struggle with Sudoku, the importance of not guessing in the game, and strategies to avoid guessing altogether.

Delve into the common pitfalls and tips for using notes to improve your Sudoku skills, whether you are a beginner or a seasoned player.

These insights will help you master the art of Sudoku.

What is Sudoku?

Sudoku is a 9×9 grid that must be filled with digits from 1-9. The solution must have the constraint that in the columns, rows, and 3×3 boxes, each digit from 1-9 appears exactly once. The unique solution aspect refers to the fact that initial hints must be placed in the puzzle to ensure the solution is unique beyond a shadow of a doubt, and guessing is not necessary.

Conversations around sudoku will always center around one key theme. Everyone knows it and everyone loves it – the reduction of guessing. But no one really knows exactly what it is, not even in the world of academia. Perhaps the most authoritative academic definition of Sudoku was expressed in the Journal of the American College of Dentistry by Dr. Hugh Wagle, Professor Emeritus at the UCLA School of Dentistry. Dr. Wagle, working with Dr. Thomas von Hoff (a German software archaeologist who developed software generative algorithms), defined sudoku as a combinatorial matrix problem with an objective to complete the matrix using digits from 1 to 9 such that the digit of i-th row and j-th column are distinct.

Why Do People Struggle with Sudoku?

People struggle with Sudoku because a combination of psycho-logical issues such as laziness, panic, and guesswork often blinds them from recognizing certain patterns and strategies that can lead to a correct solution. Struggle originates when people try with little or no learning, but only guesswork and slog. The next three myths debunked on whether one should guess in sudoku illustrates common ways how people internalize these incorrect assumptions to their detriment.

Lack of Strategy

If one plays Sudoku with no prior knowledge and no strategy whatsoever, playing one round of a 9×9 grid teaches new players that they will solve the puzzle after spending a large amount of time for the organization stage because they have basic skills of filling cells with 3 missing cell blocks and finishing with only one possible block. Playing a round again, a player may note it is also possible to make guesses based on their deduction.

During 3 levels, people may not be able to finish the puzzle with the only organization or deduction strategy as it forces them to rely on guesses when filling empty cells for the organization stage proves extremely time-consuming or when organization offers no clues for deducing.

New players should play two more rounds to further their research on the best Sudoku skills, as they will learn that practicing organization and deduction helps them minimize guessing and get solutions faster.

Not Understanding the Rules

Difficulty in solving Sudoku puzzles comes when solvers do not fully understand the rules. Although the rules of Sudoku in terms of what you are allowed to do are simple enough, many newer players do not fully understand these. When people say that Sudoku is mostly made up of guessing and checking (which is inaccurate as the no repeated numbers rule should be followed), they might not understand the other rules before jumping to guesses.

Poor Number Placement

When you place the wrong number, this is considered guessing in Sudoku. Always prepare and choose your next step carefully, as undoing incorrect placements will confuse you and ruin the real Sudoku solving experience.

Explanations of what constitutes incorrect number placement in Sudoku include the following two cases according to the rules of Sudoku: 1. Illegal row or column placements. For instance, if the square contains the number 4 across but the rest of the row it lies in also contains additional 4’s, the placement of the new 4 is incorrect and would have to be changed. 2. Illegal sector placements. For instance, if the square contains a 3 and all the other squares in box 1 also have 3’s, then regardless of whether or not the number is legal in its row or column, it is not a very good number placement and could be illegal because the square lies within sector 1.

Getting an CPCV-inflicted puzzle may help prevent a situation where you have to swap out incorrect number placements.

What is the Importance of Not Guessing in Sudoku?

The importance of not guessing in Sudoku is that there are unique solutions to Sudokus that are reached without having to guess. If you reason your strategy produces no solution, then and only then should you guess.

The importance of guessing is ultimately to reinforce a rock-solid logical-only approach as that is the strategy that leads consistently and quickly to solutions. Some complex, high-difficulty puzzles may require advanced techniques when they no longer lend themselves to traditional solving methods. At Jazz Media, we do not recommend guessing as your go-to strategy.

Dr. Arto Inkala, an internationally renowned software engineer known for his PhD dissertation on detailed complexity analysis of the puzzle, says Sudoku has a unique solution and that it defeats the fundamental purpose of the puzzle if guessing is needed.

Maintains the Logic of the Puzzle

The primary benefit of not guessing in Sudoku is that the solution is not only correct but reached in the most efficient way (Peter Norvig). When you guess, you change a puzzle that you were designed to be logically filled in. By guessing, you get answers to certain spots and make the rest of the board easier to work with, which can make the puzzle take less time, but is not logically sound.

Prevents Mistakes

Guessing in sudoku is widely detested by most players because it often prevents the downward validation of correct solutions. Error Checking in Sudoku encourages only definitely valid moves. Players who implement the process will typically not be more than one to three moves away from checking at a point where the error is easily recognized, and therefore there is little need to guess. If there is a rare situation where there is more than one definitive move to make, this is also an indication that not enough of the puzzle is validated and players should return to checking previous moves or to the last definite checkmark to ensure the progression of valid moves. When there is only one correct move, players will not have made a mistake when transitioning from the easy part of the puzzle to the more complex part of the medium or hard ranges. Error Checking in Sudoku encourages only definitely valid moves so guessing is limited.

Improves Problem-Solving Skills

• It improves critical thinking and pattern recognition transitioning into engineering, computer science, and investing.
• Sudoku is a productive and enjoyable way to pass the time.
• One can earn a living by becoming a Sudoku game developer or YouTuber.
• Finally, the simple answer can never be understated that Sudoku helps kill time while an individual is waiting around.

Complex cognitive behavior, involving decision-making, problem-solving, planning and execution, working memory, delay of gratification, conservation, mental flexibility, and insights are all defined as cognitive skills. Cognitive skills account for the individual’s ability to understand the world, interact with others, and function properly.

The brain builds a ‘cognitive reservoir’ with repeated use of these skills, improving the functioning of the brain as a whole. Sudoku is a numerical puzzle that improves an individual’s cognitive skills if one chooses it to be such. Problem-solving is the basic skill developed while playing Sudoku, which includes critical thinking, pattern recognition, and hypothesis testing which is also an essential aspect of cognitive skills.

Plus this, Aurora Wolf in a research paper published in the Journal of Higher Education Theory & Practice did find that crossword puzzles similar to Sudoku did help older adults with their cognitive skills.

Research led by the University of T bingen experimentally determined that inexperienced Sudoku learners not only enhanced their abilities rapidly, but also altered brain structure and function significantly. Such cognitive pattern puzzles minted as miniature exercises for the brain help prepare key learning centers in the hippocampus and let a person implement problem-solving abilities in everyday living.

But merely doing Sudoku or any other problem-solving puzzle won’t necessarily make an individual smarter. It’s a good thing to get better cognition, and it teaches you certain problem-solving skills that are beneficial throughout life, but it doesn’t make you more intelligent beyond the specific task.

What Strategies Can Be Used to Avoid Guessing in Sudoku?

The following strategies can be used to avoid guessing in Sudoku:

1. Candidate Tables: Write down where all possible numbers can go before each move in order to visualize for each cell how the different possible numbers restrict the placement of other numbers in the same row, column, and boxes. This will make logical deductions easier than guessing.
2. Scanning: Involves scanning rows, columns, and boxes for clues with which to place numbers (candidates). By doing it repeatedly, the grid is gradually reduced to the solution by the process of elimination.
3. Clues Look Strategy: After each step, look for the next clue before proceeding ahead. Make sure to anchor your logic to the initial numbers rather than the numbers you just inserted.
4. Candidate Line: A chain of candidates that immediately determines one or more numbers. Similarly, Killer Cages and Remote Pair? strategies help create a line that leads toward solving the puzzle.

Scanning

Scanning is a visual technique you can use to reduce the possibilities for a specific box, column, or row. Rather than guessing, you’re scanning the board for patterns that eliminate impossible answers.

For example, in row 6 if you have seven cells filled but none of them is a 9 or 3, then you know the 9 and 3 must be in the final two blanks. If column 1 has 1, 3, and 7 filled in three boxes but not in boxes 4 and 9, you can eliminate 2 and 5 from the blanks, since columns 4 and 9 already have those filled in.

Another scenario in which scanning helps is with the naked pair technique. If 2 out of 3 cells in a row share exactly 2 candidates, you know for certain that those 2 candidates must be placed in those two cells, regardless of your remaining candidates.

During the course of playing typically challenging sudoku puzzles, you are always scanning. Try to be methodical in your scanning. Scanning. Sudoku is a strategic game that requires an eye for discerning patterns or lacks thereof. If squares can include many possibilities, you can expand the possibility to a column or box to make the scanning simpler.

Crosshatching

This is the second rule of constraint propagation in Sudoku (the first is box-avoidance), and it is the technique that prevents backtracking. Crosshatching is the next most powerful technique right behind box avoidance, since it can eliminate as then can eliminate as many or more candidates per move. Those are the ultimate basics of Sudoku; without these the grid is impossible to work out. Constraint propagation applies assignment of a candidate right across the board.

How to switch candidates quickly? If you choose to play with the less capable grid and candidates do not get removed, the game gets harder when the player has to backtrack, which is often. That’s why backtracking is the worst way to solve a Sudoku grid, and thereby violates the rules of constraint propagation. Via crosshatching, you should make sure there are aline replacements available to all candidates to eliminate as many as possible after every move. Playing with advanced candidates such as the X Wing technique afterward can simplify the patterns.

Penciling In

Penciling in refers to filling in small digits into multiple cells as potential values for a particular cell. This is advantageous because it cuts down unused possibility for the cell being filled with another number than guessed in the first step. See cells B3 and D4. Pencils-in can be helpful in easy and medium puzzles for determining potential candidates for a square or when identifying familiar patterns, with a larger window for error. A key advantage is that there are time-saving techniques from further guesses are likely to be needed.

What Are Some Other Tips to Improve Sudoku Skills?

Additional tips to improve Sudoku skills are to pay closer attention to relevant statistics, playing with minimum tools or freehand to amp up the challenge. Dr. Arto Inkala, an expert on the difficulty levels of Sudoku, provides strategies to solve puzzles that have reached a standstill. That solution is at most two steps away and is always done by systematically checking the twos (n=2) or threes (n=3) as group shots against the elimination rules set forth by the peers in the same band. The 2006 article by Dr. Inkala for the University of Warwick’s Mathematics Department can provide guidance for other more advanced strategies as well.

Practice Regularly

Practicing regularly helps build the skills and thought processes required to logically solve sudoku puzzles without using guesses. The more you play, the quicker you become at quickly scanning through potential candidate lists of lone singles and naked doubles. Regular play accelerates the development of numbers-based processes for identifying singles, doubles, hidden pairs, naked triples, etc. as fast as possible, ultimately leading you to a solution without needing any guesswork.

Start with Easy Puzzles

There are differing opinions on whether starting with easy puzzles is the best blocking for guessing in sudoku strategies. Some sudoku experts believe cutting their sudoku-playing teeth with only easy puzzles is the best way for beginners to learn basic scanning, locking, and pointing techniques, making guessing in subsequent harder puzzles unnecessary.

M-Xelon, the self-proclaimed sudoku addict who has solved millions of sudoku puzzles in a couple of decades, is an advocate of this approach. Others, however, insist that beginning with easy puzzles provides no clear knowledge of advanced techniques or an understanding of different sudoku strategies which might be needed in more challenging puzzles.

An estimated 5 high-rated expert sudoku players have suggested not starting with easy puzzles. Starting with Sunday puzzles in newspapers may provide intermediate sudoku players with a good balance between advanced solving strategies and simplicity in the face of the urge to guess.

Use Online Resources for Help

Solving sudoku puzzles using online resources without guessing is a little difficult, however, some websites and tools keep track of the possible numbers you can put into a cell and help you use them efficiently. One such tool, Cracking the Cryptic, provides a key for tracking possibilities within a cell using the notation system that truncates grid values from the full range to only those most beneficial to the solver.

Seeing this system at use may help you find a natural way to think about grid values which does not involve guessing. If you find the proper value, you have done well, and if not, you may consider other values which still answer your question without the brute force of guessing. For such levels of practice and advice, the full Old Faithful video of Cracking the Cryptic from June 2021 appears to be blocked on YouTube.

Cracking the Cryptic helps you learn not to guess by providing the notation to track possible values used in cells in a visual manner to minimize guessing. Around half the puzzles are from trusted authors providing new and great challenges. Solving methods are also shown for each video but each one is a stand-alone that is not part of a learning progression.

Frequently Asked Questions

How to Not Guess in Sudoku?

1. What is the main key to solving Sudoku without guessing?

The main key to solving Sudoku without guessing is to use logic and elimination techniques to carefully fill in the missing numbers.

2. Is guessing ever necessary in Sudoku?

No, guessing is not necessary in Sudoku. In fact, guessing can often lead to incorrect solutions and frustration.

3. How can I avoid guessing in hard Sudoku puzzles?

To avoid guessing in hard Sudoku puzzles, try breaking down the puzzle into smaller sections and use logic and elimination techniques to solve each section individually.

4. What are some common strategies to prevent guessing in Sudoku?

Some common strategies to prevent guessing in Sudoku include using the “naked singles” and “hidden singles” techniques, as well as looking for patterns and using pencil marks to keep track of possible numbers.

5. What should I do if I get stuck and feel like I have to guess?

If you get stuck and feel like you have to guess, take a break and come back to the puzzle later with a fresh perspective. You can also try using a different strategy or asking a friend for help.

6. Can I still enjoy Sudoku even if I don’t want to guess?

Absolutely! Sudoku is a fun and challenging puzzle game that can be solved using only logic and deduction. Avoiding guessing can make the experience even more satisfying.