Mastering Sudoku: A Guide to Using Hints in the Popular Puzzle Game

Sudoku, the popular number puzzle game, can be both challenging and rewarding.

We explore the rules of Sudoku, the different levels of difficulty, and how to solve puzzles step by step.

We also discuss using hints to help you along the way, from highlighting possibilities to revealing single numbers.

Whether you’re a beginner or a seasoned player, these tips will guide you towards mastering the art of Sudoku.

What is Sudoku?

Sudoku is a logic-based number-placement puzzle. It is a game played by individuals to hone their skills of deduction, logic, and problem-solving. In Sudoku, each puzzle is divided into small 3×3 boxes each containing a 3×3 set of squares, for a total of 81 squares in a 9×9 grid. The goal is to fill all the squares with numbers from 1 to 9 such that each row, every column, and each of the nine small 3×3 boxes contains all of the numbers from 1 to 9 once and only once.

Originally a number game, Sudoku evolved over the years with versions containing letters, shapes, colors, or even images. The hallmark of all these variations is that they all use the same grid structure and have the same goal of arranging unique sets of characters into rows and blocks.

The simple rules of Sudoku make it a challenging and engaging pastime to hone concentration, memory, and logic. Invented separately by Leonard Euler in the 18th century and later in the 1970s by Dell Magazines of Pennsylvania, Sudoku became a worldwide fad by the mid-2005s. Sudoku literally means a single number or a number that is unique in Japanese. The game became wildly popular and made newspaper headlines and television programs. Many Sudoku players used the hints within the puzzles to guide them through the solution. This practice eventually evolved into a more engaging and esoteric game mode in which numbers are left out or filled in on the board, depending on the unique difficulty mode selected.

What are the Rules of Sudoku?

The rules of sudoku are simple. The classic 9×9 sudoku grid starts completely blank, and the player must add numbers in the empty cells directly or indirectly using the numbers that are already on the grid. Only the numbers 1 to 9 can be used. The goal is to have each row, column, and 3×3 sub-box contain each of the 1 to 9 numbers exactly once. That is, no two cells that are in the same row, column, or sub-box are allowed to contain the same number, 1 to 9.

When inputting the numbers for the first time or later during the game, if a number that is being input causes duplicate numbers in the row, column, or region it is in, the puzzle is NOT solved. Simply put, the sudoku rules do not allow any duplicate numbers in the row, column, or 3×3 region where the number is placed.

These rules can be easily learned in the How to play sudoku section of Fixing and Completing Guide’s Sudoku Web Twenty and Fifteen, written by Mike Heater. (Note: This refers to the guided section of his book, not web pages.)

What are the Different Levels of Sudoku?

The different levels of sudoku refer to the amount of initial numbers provided for the player. The five levels of sudoku are Very Easy, Easy, Medium, Hard, and Expert. The World Puzzle Federation Standard for sudoku of every 9×9 puzzle is that each of the digits 1 to 9 are provided by the puzzle distributor to both give and receive hints. The following is the WFPB standard for minimal givens for each of the five sudoku difficulty levels.

How to Solve a Sudoku Puzzle?

To solve a Sudoku puzzle one creates a collection of possible values that each cell can be, and then uses the constraints provided by the orthogonal and sub-grid lines to iteratively reduce the candidate values assigned to each cell down to a single value, reflecting the final solved value.

Solving a Sudoku puzzle requires creating a collection of possible values that each cell can be and then using constraints to reduce these possible values, and this process may involve hints to facilitate this reduction in some cases more than others. Solving a Sudoku puzzle is a specialized case of solving an important class of mathematical problems, those in which a solution can be constructed by the set of constraints that reduce the available choices.

Start with the Easy Spots

Use hints in Sudoku by using the easy spots to guide your next moves, solving blocks using mistake mediation, and using calculated opportunities under peacetime. At the beginning of a puzzle, take the time to scan the grid for blocks where a cell can be solved. In the image above, Cell 9 can only be a 6 and among all the incomplete cells in the block, it can be filled in immediately. Other hints might exist in this block which can be identified by noting which cells can only be one number. Regularly update your pencilmark grid to ensure you are on track and to identify any recalculated opportunities for moves.

Look for Single-Number Rows, Columns, and Boxes

In major publications, the next key hint after keeping grids in mind and crosshatching candidates is to look for rows, columns, and roughly 3 by 3 squares (boxes) that are restricted to one number. Some refer to these as naked singles as they are cells that have been stripped of all other complexity. One of these, for instance, would be that a 3×3 box is already filled with 8 numbers, leaving only one potential space for the last number in the box, which may allow for other spots to be solved.

According to mythology, the answer to the question of whether Tuesdays are the most productive days of the week, comes from a variant of Sudoku known as Super Sudoku. Instead of starting with the numbers 1-9 in the boxes on the left and upper part of the grid and then using those spaces as hints for the main Sudoku, one starts with the answers to these boxes before attempting to solve the main Sudoku. If you are doing Super Sudoku and you see a clue with only one possible number to place there, you need to numerically represent the number of the day of the week. For example, if ten days from the desired functionality Tuesday, March 18th – one will have to place six in that particular box.

Use the ‘What If’ Technique

The ‘What If’ technique in Sudoku describes the practice of trying different possible solutions to examine the implications of each. As was used in the example of the ‘locked pair’ above, the ‘What If’ technique is much more general; once you begin to employ it at a more advanced level, you will discover now often this technique can be used to come up with the next logical step.

The ‘What If’ technique is also sometimes useful in determining whether a cell can hold two potential values. This involves making alternate selections for the cell, and then going through the consequences for the constraints in the current situation. This is in effect a simple form of the ‘What If’ technique.

Eliminate Possibilities

As you find more hints to use in the base puzzle, replace candidates in your possibles puzzle that have been proven false by the hints in the base puzzle. If the sudoku puzzle you are working on is self-consistent and the possibles grid is updated correctly, you will eventually reduce the possibles down to exactly one number in each blank. This is the number for the specific sudoku board layout on that day.

Use the ‘Naked Pairs’ Technique

Naked pairs describes two open candidate numbers that are shared by only two unknown cells in the same row, column, or block. The main reason to use the naked pair technique is to gain symmetry in the Sudoku by setting more than 1 number. This leaves only two possible numbers to go in one of the cells of the Naked Pair. Here is a Sudoku example of all the cells in row 3 not containing 5 with only 3 and 7 left:

What are Hints in Sudoku?

Hints in Sudoku are blocks in the puzzle that are already solved for the player. The grid block has been set in place with the correct digit already. In most cases, only one hint can be received regarding a specific block. This retains the challenge of the conscious and methodological thinking Sudoku puzzles incorporate. Hints add guidance to the problem that might lead to the solving of a larger Sudoku puzzle. The more hints in a Sudoku puzzle, the easier the solution of the Sudoku is deemed. It is likely that as a sudoku is solved, those who might be stuck seek to ask a mentor or expert for hints. When they do not know what to do next in a more complex Sudoku puzzle, a hint can help them start again. Cheating by looking up the solution online without trying, by pressing the hint option numerous times, or just scanning through the answers are not viewed positively from a Sudoku functionality standpoint. They decrease mental exercise and disengage the buyer from the importance of this past time. Authors like Sy Kurane of Hard Sudoku and Sudokus.GR of the website sudokus.gr add hints to solve puzzles, make buying more intuitive and mentally engaging.

Highlighting Possibilities

In most digital Sudoku apps, cell hints give players the ability to enable every possible number in that cell regardless of whether or not it is viable. This can serve as a reminder of all the numbers not yet marked in as well as a mental relief from the stress of trying to remember how many remaining options there are. Players can then turn the irrelevant options off to make room for what is relevant.

Using the ‘Pencil Mark’ Technique

The ‘Pencil Mark’ technique for using hints in sudoku refers to the process of solving a cell by marking the possible candidates in that cell (i.e. the pencil marks) and using them to eliminate the same numbers frm the square, row, and column in which the cell is located. This brief video from Solve My Sudoku shows visually how to use the pencil mark technique effectively.

Revealing a Single Number

The simplest of the Sudoku hints is giving you the answer to a single cell or entire row, column, or box (square of nine) with all covered cells already filled in except for just one empty cell. The empty cell’s value is always between 1-9, and thus only 2 – (number already in column/row/box that the empty square occupies) are possible choices.

According to a Wolfram Mathematica Sudoku Solver blog on site `stackexchange.com`, for simple and hard Sudoku the number of provided hints can be as few as 17 to 21. Easy Sudoku can be solved in only a few minutes with as few as 21 givens, but many of them will then have multiple valid solution grids. This minimal range of 17 to 21 means players of easy Sudoku puzzles can simply replace any solution’s original hints with a fresh set to produce a singularity.

Solving a Box or Row

In this situation, unique rectangle type 3 rule inversion specifically applies. The UR becomes A2 (pos3-23). Since this pair is crucial, which’s removal would allow a second unique rectangle to be created, they must both have their mutual candidates removed. This then removes the final two occurrences of 4 in row 1, resulting in a dual solution.

Box/Row Situation Example: This example of solving a box or row is a situation developers have discovered with possible Sudoku hints. On further analysis, if the expanded hints showed that the value of the two corner 4s were dependent on the original hypothesis, making them especially crucial, they would show an additional alternative and eliminate this situation.

The other possibilities of corner solutions are found in remaining open tiles, yet they are all connected to partial uncompleted URs which rule them out. The expanded hint would show on 4 (88) that removing them eliminates a last instance of 4 in Box 8, thus a dual solution persists. The partially expanded hints show that finishing the UR handled by the upper left and lower right 4s would show that removing them rules out a 4 in row 8, and thus a dual solution.

The other possibilities of corner solutions are found in remaining open tiles, yet they are all connected to partial uncompleted URs which rule them out. The expanded hint would show on 4 (88) that finishing the UR handled by the upper left and lower right 4s would show that removing them rules out a 4 in row 8, and thus a dual solution.

How to Use Hints in Sudoku?

Hint in Sudoku can be used to solve a square manually or digitally. When solving Sudoku manually, hints are often used to solve targeted squares for which related squares have been resolved. You can easily use Sudoku hint software such as the one provided on GCHQ’s webpage to get assistance for solving a square of your choice by selecting the helper difficulty level. You can find the GCHQ page at the link provided in the written article.

Use Hints Sparingly

As using hints detracts from the cognitive challenge and overall quality of the Sudoku solving experience, they should be used reasonably. Folks that like easy hints and always use them when they become available are doing something of a greater disservice to their cognitive development by not developing the discipline specifically needed to regain focus and employ the difficulty progression methods without any automated guidance.

Seniors and younger children aid in helping make the Sudoku solving process more entertaining and less frustrating by utilizing unlimited hints. It can help in reducing memory loss among seniors and promotes healthy brain growth among children.

There are no set rules or recommendations for how to find or when to use hints, as accelerated progress can produce their own cognitive outcomes. The best guidance that individuals can follow is to track their own challenge response methodologies around the use of hints and modify their own usage and discipline tactics based on their understanding of these results.

LA Times Former puzzle editor Merl Reagle notes that some Sudoku apps track the number of clues a player receives, so they mistakenly think that the game is keeping score. All these apps are doing is showing you that you are blatantly incapable of solving an easy puzzle.

Start with Highlighting Possibilities

Use hints in sudoku by starting with highlighting possibilities. Refer to the Hints Strategy section to see some interesting results. When filling in large, open squares with 4-6 empty cells, that have many two square combinations possible, fill them in with light grey. This helps to identify ‘Naked Singles’ (squares with only one possible number), ‘Hidden Singles’ (squares with unique digits including their peers), X-Wing, Swordfish, and skyscrapers.

Try the ‘Pencil Mark’ Technique

Once you have made a few initial deductions, the ‘Pencil mark’ method will allow you to keep track of possible numbers in a specific cell or set of cells. Write small notes inside the Sudoku cell called the givens, penciling in the possible numbers until the cell’s correct number has been deduced. Clear the penciling when cells form a pair or trio for a number since no other cells could contain the number.

Here is an example of how the pencil mark method works for a hard level. The right-edge column’s bottom cell has a single possibility; the top flexed T cell is either 1 or 6; the bottom right cell could be a 1 or a 9; and the bottom-most flipped T cell in the middle of the right edge must be a 9 or 5. We can remove a 5 and pencil in the 8 that can go in one of the three central-right 3×3 squares. Continuing the solution in the easy no-mistakes manner, we can pencil in the 5 at the right-middle via green, but as we reveal, it is the 5 that belongs in that cell. You can fill in the solution like this in a haphazard way, or you can carefully use penciling to keep track of potential number solutions until only one possibility is left, like this.

Move on to Revealing a Single Number

• If you are not certain of the location of an update, back up a move and reevaluate with the same policies.
• Mentally force out the impossible scenarios by forcing a piece into one location and seeing if your constraints are taken up elsewhere.

Why? Visualizing the same situation in multiple ways will often uncover something that was missed in the initial evaluation.

• Note the number of times each number needs to be placed in a solved, semi-solved, or blank cell and compare via elimination.

Moving onto revealing a single number is the final hint to be used in Super MacGyver mode. So you’ve run the am I Pagoda mode and nothing has stuck? Testing against different impossible chains found nothing, and eliminating which ones are possible and placing them alongside other possibilities solved nothing either? Well you’ve reached the final stage, which is simply adding one number and seeing what moves.

Best practices for revealing a single number:
1. Start with high minimums
2. Work progressively to reveal the easiest number you can place
3. Look easy and medium portions as well as hard portions to reveal the needed number
4. If the wrong number is needed to progress, you did something wrong in your errors which you need to back up and correct
5. Finish as many qualifiers in a solution as you can and compare other potential solutions until one is matched

Only through trial, error, logic, and a little subconscious use of your brain’s pattern-seeking mechanisms will you find out what number opens the dam to solving each individual problem of the Sudoku grid.

Use Hints to Solve a Box or Row

A row or box is another useful context in which to apply whittling thinking. If multiple cells in a box or a row have been narrowed down to just two or three possibilities, then if you evaluate that they can either be the digits one way or the other, then rule out the middle digits which can no longer be applied. An example of this is in the image below you can learn to solve when two of the three possible digits are forced. In this medium difficulty sudoku, if the two 4s were not there then there would still be three possible places for 4 with no way to know which is correct. But these 4s that should be ruled out creates a domino effect of certain placements: 4s can’t be placed in the e7 and f8 cells.

Frequently Asked Questions

How to Use Hints in Sudoku?

1. What are hints in Sudoku and how do they work?

Hints are helpful clues that can guide you towards solving a Sudoku puzzle. They show you which numbers are possible for a particular square, based on the numbers that have already been filled in the same row, column, and grid. You can use these hints to narrow down your options and make more informed choices when filling in the remaining squares.

2. How do I access hints in a Sudoku puzzle?

Typically, Sudoku puzzles have a button or option that allows you to access hints. This can be in the form of a “hint” button or a “check” button that also provides hints. You can also check the settings of your Sudoku app or game to see if there is a way to enable hints.

3. Can I use hints as a beginner in Sudoku?

Yes, absolutely! Hints are a valuable tool for beginners in Sudoku, as they can help you understand the logic behind solving the puzzle. They can also prevent you from getting stuck and feeling frustrated, making the learning process more enjoyable.

4. Is it cheating to use hints in Sudoku?

No, using hints in Sudoku is not considered cheating. It is a helpful feature that is designed to assist you in solving the puzzle. However, if you want to challenge yourself and solve the puzzle without any help, you can choose to ignore the hints.

5. How many hints can I use in a Sudoku puzzle?

This depends on the puzzle itself and the hint system that is available. Some puzzles may offer only a limited number of hints, while others may have unlimited hints. It is important to note that the more hints you use, the less challenging the puzzle will be.

6. Can I use hints in every Sudoku puzzle?

Generally, yes. However, there may be some variations in the hint system depending on the Sudoku app or game you are using. It is recommended to check the instructions or settings of each puzzle to see if hints are available and how they work.