Mastering Sudoku: A Guide to Using the Notes in Solving Puzzles

Sudoku is a popular puzzle game that challenges players to fill a 9×9 grid with numbers from 1 to 9.

But have you ever wondered about the role of notes in Sudoku?

We will explore the importance of using notes in Sudoku, how to effectively incorporate them into your strategy, and valuable tips for mastering this technique.

We will also discuss common mistakes to avoid when using tips and tricks in Sudoku.

Let’s dive in and enhance your Sudoku skills!

What Are the Notes in Sudoku?

Notes are the small notations or candidate numbers that users can write inside cells of a Sudoku grid. Each cell is typically large enough to hold all 9 digits from 1 to 9, but notes use only a fraction of each cell. By jotting down candidate numbers in cells, a user dedicated to completing a Sudoku puzzle is ascertaining where numbers can be placed in a certain row, column, or block at large.

If the cells of a row, column, or block contain a note in which a number is written in only one cell, one knows for certain that the respective number belongs there. As a user completes or grows out of using note-taking tactics in Sudoku, there is a chance to engage in and develop other advanced techniques to solve the Sudoku puzzle. Solving without notes increases time productivity but also may deliver more satisfaction from using one’s brain without the note-taking training wheels.

Why Use Notes in Sudoku?

• Use notes in Sudoku to remind yourself which numbers are possible in a cell (or cells), reduce the number of possible numbers in a cell to better focus on specific strategies, and narrow down the location for a number to a certain range in order to cut off other search spaces. Using notes in Sudoku allows you to follow specific patterns which assist in motivation and retention for regular practice, ultimately improving your performance and efficiency.

How to Use Notes in Sudoku?

Notes, or pencil marks, refer to using small numbers in empty cells to track possible numbers. This is done by toggling during the game on a visible note-taking feature through which you can input all the possible numbers that can appear in each empty cell. The following six-step process identifies how to use notes most effectively in Sudoku.

1. Activate notes on the website or app you are using.
2. Mark all numbers you are sure about where to put.
3. If a number cannot be placed anywhere on the board, note them all in.
4. If a number can only be placed in a certain cell, fill in the answer and delete it from notes in other cells.
5. When a number appeared in a row or column three times, delete it from the notes on that row or column.
6. Occasionally remove notes to referring to empty cells which have fewer candidate numbers.

Understand the Notation System

The notation system in Sudoku is a way to help you write down and stay organized regarding the possibilities for all 81 cells while sustained through a series of deductions using elimination and lock-marking strategies.

Cells that cannot possibly hold a given number are sometimes referred to as locked cells or sometimes locked candidates if the number being researched is still a candidate for other numbers. Some sources say to first mark that all clues are sans before re-investigating clues that unbeknownst to the solver were incorrectly identified as sans at the outset of a puzzle. An efficient notation system will allow you to take cryptic notes on patterns and shark-fin problems beyond what is solvable with notations restricted to cells, zones, or specific numbers.

Use Pencil Marks in the Grid

Inolving pencil marks in the grid does not require you to write down the notes meaning in the top and bottom rows or cells, but instead notice the possible note entries that can go both horizontally and vertically in the individual cells, rows, or columns. Doing this allows you to easily update pencil marks across both rows and columns or visualize potential candidates with greater ease.

Fill in All Possible Numbers

This means if you are not 100% sure a number can be added to a cell, put the number in as a note. If you suspect a number may be placed and even with that number, the potential addition of that number decreases the possibility of another number being there, all other corners with only that number as a note may too quickly fill up. This can be put to a test in the example later in point 4.

Fill in all possible numbers. Volker Jantzen, an Alabama-based mathematician, outlines the following steps in his article How to Solve Sudokus.

Update Notes as You Solve

When you are left with only two possibilities in a cell for a number, you have completed what Norvig calls Simple Coloring, which refers to the white number and the gray number being in opposite positions. This gives you a new piece of information to propagate throughout the grid until it is no longer usable.

Note cells 1 and 6 in the bottom right and top left corners of the Sudoku puzzle. Since only one of these two cells can be a 1 according to Simple Coloring, we know neither of these two cells can be 1. This further tells us that the puzzle requires a 1 in the bottom right to avoid multiple solutions. For more insights, check out this guide to using hints in the popular puzzle game.

By this I’m referring to manual note-keeping when you write actual numbers in the grid option is eliminating a note when it is no longer valid (such as in simple coloring above).

Another part of Norvig’s Simple Coloring is placing the alternate number in a cell color other than white. I have always colored mine gray, which has caused confusion when discussing note-keeping with others. To allow you to collaborate more easily, you should instead choose to color such notes black or another color that is easily distinguishable from gray. Google Sheets is a good free tool which provides enough different colors for all note colors that can be used.

Tips for Using Notes in Sudoku

Tips for using notes in Sudoku:

1. Start small and count up.
2. Use notes to preview larger moves.
3. Use notes to simplify and speed up your game.

The most effective way to use tips to stop guessing and solve puzzles with strategy in Sudoku is fairly simple:

1. Start with pencil marks of potential numbers for each cell.
2. Every time you fill in a cell, erase the incorrect timing of the notes.
3. Keep your pencil marks up to date.

If you are relatively new to using notes in Sudoku, or if you realize you might be spending more time than is reasonable on the notes, Lawrence offers a suggestion of counting interactions. Stop using the notes, even if you have not yet found the correct solution for every cell, after on average every fourth fill-in, and then only updating here and there. To keep track, you could simply clip a writing utensil onto paper for every time you cycle through 4 updates and reset the count whenever you complete updating notes on all cells of the game board.

Start with Easy Puzzles

It is crucial to begin your Sudoku journey with easy puzzles such as those in the New York Times Easy Sudoku to become comfortable with the note making mental framework. According to Kevan Choset of the US Puzzle Team, this is because easy puzzles offer the simplest starting point for learning the mechanics of their solution. He points out that after zeroing in on a single possibility for an empty cell, one can eliminate all other possibilities in the same cell’s rows and columns. Extreme or very hard puzzles usually require multiple combinations of possibilities and greater creativity to solve, which makes using notes for keeping track of all of these possibilities exceedingly useful for both the player and the developer.

Easy puzzles such as those in the New York Times Easy Sudoku can be solved much faster than medium, hard or expert puzzles, which allow novice players the luxury of learning notes without wasting too much time. Timing of note-taking is part of training one in seeing possibilities abstracted from the puzzle to see quickly where solving progress is being made and where progress has stalled. Starting with easier puzzles offers an advantage in this sense. A brief venture into easy puzzles initially, maintained for about a week, should speed the ability to identify patterns and logical shortcuts in more difficult games where they provide more help and need to refer back to rule basics is less necessary.

Use Different Colors for Different Numbers

Even with the method of elimination and multiple notes, certain things of which one is certain while solving sudoku puzzles. We call these certainties. Two of the certainties are discovered through the examination of the solved numbers correctly. These are the advanced sudoku notes with which one can find all the mistakes in any sudoku, following which they have efforts in the rows and columns until they are left with just the lower left box.

At this point one will be left with an easy puzzle that can even be solved without these advanced notes. It could also be that nothing has advanced, and they are left looking for the number 1.

Sudoku savant Grant Fikes combines advanced notes cell color-coding of the penis grid, axial subsets, and multiple solutions in order to tackle this entity and advantageously acquire the correspondingly numbered solutions. To sum up, complex color grids use advanced notes to help induce logical eliminations of potential values. Starting from simple note-keeping Fikes walks through his system associating all squares in a primary block based on the bottom left, associating all blocks to the left, top, and right that do not intersect by color or main number even with/a sex grid, increasing until all cells are associated with exactly one other with advanced notes. This system will assist until solution.

Practice Regularly

Use the notes in Sudoku to practice regularly. Persistent and methodical practice is key for improving your note-taking and Sudoku-solving skills as well as to encourage the development of patience and focus with structured and organized thinking. Progress is not usually quick, but supports improvement when practiced as little as once per week combined with applying your new skills to harder Sudoku puzzles. This helps to beef up your new notions into logical memories, helps build expectations for how to sort out tricky puzzles, and how to arrange effective logical resolutions.

Moving up to more difficult and larger puzzles can also serve as challenging practice, along with working towards better and faster times. In fact, persistent practice is often the single most critical determinant of effective Sudoku-solving. The Archbishop’s School shared David J. Bodycombe’s analysis, which shows that average time required to complete standard 9×9 Sudoku puzzles is much faster for respondents who solved a Sudoku puzzle within 7 days of the first time they tried to solve a Sudoku puzzle. Additionally, over 50% of respondents who obtained an ‘Experts’ level time of 5 – 6 minutes on average, said they used a simple notepad. This demonstrates that regular practice with the notes function can be used to develop increased mental and physical abilities in Sudoku games.

Common Mistakes When Using Notes in Sudoku

Here are the most common mistakes when using notes in Sudoku:

1. Incomplete markings: Failing to fill in all the valid numbers that exist for each empty cell before turning off notes and/or marking the correct number to be in that square. This ensures all possibilities are considered and that a mistake doesn’t blind you to the eventual tips for faster puzzle solving.
2. Overreliance: Using notes to fill in possible values before attempting to logic your way through them. This is important since it is possible that once completed the grid could be solved without using yellow areas if the logic is sound. To learn more, check out a step-by-step guide on mastering the puzzle.
3. Too many notes: Excessive notes can cloud analysis and be just as bad and misleading as too few notes. Try to keep notes as clean as possible by erasing options that can be eliminated with each step of the solving process. David J. Bodycombe in The Mammoth Book of New Sudoku suggests leaving 2-4 options in open cells, but if you only need 1, then that is the correct number.
4. Failing to update notes: If you fail to cross out notes as they become no longer valid after a block, line, or box has been completed, you are much more likely to make an error soon that will be very difficult to notice.

Not Updating Notes

Not updating notes is a mistake when using notes in the sense that they are no longer effective to help you solve a puzzle. The value of notes is that they are easy to update, so if they become counterproductive you can easily erase and rewrite them in a few more appropriate configurations. If you never update them, then they may evolve to be of little use during the course of the puzzle.

If you spend time meticulously filling them out at the beginning of the puzzle and then never touch them again, they will eventually be identical to the initial filling numbers which makes the entire point of the exercise a waste. Notes should be an active tool, constantly update them and erase old notes as you progress and for the puzzle to reach its most complete end state, particularly the BAST manageable end state of minimal filled-in numbers.

Using the Wrong Notation System

Strategy 2 is to use the wrong notation system for the wrong difficulty level of Sudoku. There are three main notation systems used in Sudoku. All three of them can be used in any Sudoku puzzle, but the difficulty of the puzzle decides which system to use. They are as follows:

System HTWG Konstanz Sudoku Notation System Color-Flash (Green-Red) Method

This is the title of the system implementation the Institute of Computer Science at Hochschule f r Technik, Wirtschaft und Gestaltung (HTWG) Konstanz in Germany developed for teaching their students to solve Sudoku 4×4 and 9×9 grids. This solves the whole puzzle at once but at the price of being a bit more chaotic on higher difficulty levels where a lot of boxes are not definitively solvable. These are boxes where more than one number is possible without reaching a contradiction. For a comprehensive guide on using math to solve Sudoku puzzles, check out this sudoku math tips.

This flashcard system where a note is only checked off when it becomes definitively not solvable is called a guide on how to use pencil. It is best suited for puzzles up to the meditative level of difficulty from 6.5 difficulty score down.

When you maintain separate rows and columns then it is usually easier to solve the Sudoku puzzle. You can often switch to and easily check the notes sections as you move about the puzzle on the grid. This makes it easier to not make errors.

Not Erasing Notes When They Are No Longer Valid

Erasing notes that are no longer valid is optional. Users can either keep the notes they made in squares with multiple solutions or jot down new possibilities in those same squares. If a user continually finds themselves losing track of notations in certain cells, they should concentrate on erasing them.

Here is an example strategy in which you don’t erase invalid notes:

Number notes can get messy with all the multiple possibilities in many squares. But if tracking what is possible in each case helps you solve the puzzle (for example, if you remember one square in a block is either 2 or 5), then you can continue to keep them. Provided you don’t lose track, you likely will be able to solve the puzzle.

Conclusion

Using notes in Sudoku or Sudoku doodling is a useful tool for preemptive reasoning. During the game, users must practice adding notes on the entire grid every time they pencil mark. This helps in remembering if a number can exist in a particular square. If a player is putting in multiple value or random notes then this helps in resolving all options before analyzing possible scenarios. However, while this can be a useful tool for users, notes should only be used in Sudoku when necessary.

Frequently Asked Questions

How do I use the notes in Sudoku?

To use the notes in Sudoku, simply write potential numbers in the empty cells as small notations to help you solve the puzzle. These notes will help you keep track of possible solutions and can be erased as you solve the puzzle.

What are the benefits of using notes in Sudoku?

Using notes in Sudoku can help you approach the puzzle in a more organized and strategic manner. They can also help you avoid making costly mistakes and speed up your solving process.

When should I use notes in Sudoku?

It is recommended to use notes in Sudoku when you are stuck and unable to make progress. Notes can also be helpful when you need to make an educated guess or eliminate possible solutions.

How do I make sure my notes are accurate?

To ensure the accuracy of your notes, make sure to check for any duplicate numbers in a row, column, or 3×3 square. Double check your notes before making any final moves to avoid errors.

Is it necessary to use notes in Sudoku?

While notes can be beneficial in solving Sudoku, they are not necessary. Some players prefer to solve the puzzles without notes, relying on their logic and memory skills. It ultimately depends on your personal preference and solving style.

Can I use different symbols instead of numbers for my notes?

Yes, you can use different symbols or colors as notes in Sudoku instead of numbers. This can be especially helpful for players who have difficulty keeping track of numbers or want to add some variety to their solving experience.