Sudoku Solving Strategies And Techniques - A Beginners Guide To Sudoku Puzzles

Sudoku Strategy
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In the SudoCue program, the Markup tool shows all candidates in little numbers. As you've seen earlier in this guide, you can use the peers to tell something about the candidates of a cell.

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The aim is to eliminate enough candidates so that only one remains. Some of the naming in sudoku solving will trigger the parental controls of your browser, but there is nothing indecent with these naked singles. To figure out what goes into that cell, we will first have to establish what cannot go into that cell. In order to do this, we have to examine the peers. In this picture, the peers that contain a digit have been highlighted in red. In fact, there is only one digit not used by any peer. Can you see it? It is digit number 9. This is the only candidate left for R5C3. It is called a "Naked Single". Other terms used are "Forced Digit" and "Single Candidate". There is a famous line by Sherlock Holmes: "When you have eliminated the impossible, whatever remains, however improbable, must be the truth.

That, in essence, is the logic you use to solve a Sudoku. Eliminate the impossible digits until there is a single candidate remaining. You begin each cell with 9 candidates. When peers are filled, these candidates are eliminated one by one. At some point, 8 out of 9 digits are eliminated. The last candidate must be the correct digit. You can place it in the cell. This in turn will eliminate that digit in other peers.

Though Naked Singles are easy to explain, they are not easy to find in a Sudoku. There are 81 cells in the grid, of which maybe 30 have a digit placed. This means that you need to look at 50 cells, check the 20 peers, and count the number of candidates remaining. Each time you found a single, the situation has changed and you need to start all over again. Many Sudoku players use pencilmarks to keep track of the remaining candidates for each cell. Not only are they an important timesaver in your quest for naked singles, but they are essential when solving more difficult puzzles where you need more advanced techniques.

In SudoCue , you can use the Markup tool to maintain pencilmarks. This picture shows the same board with pencilmarks.

This time, it is not very difficult to spot the naked single. When you are using a computer program that shows candidates like this, you are, in fact, cheating. Some players have such strong objections to pencilmarks, that they never use them to solve a sudoku. If you like to read more about solving sudokus without pencilmarks, follow this link. Now check out the diagram.

Can you say which digit is most likely to go into R5C7? This is not very difficult. Digit 8 is a naked single in R5C7. Furthermore, row 5 has a single empty cell and digit 8 is the only one missing. When a house has 8 filled cells, the last cell can be filled with the missing digit. It is easily spotted by every player. You will not find them often in the early stages of solving the puzzle.

In the endgame however, you will encounter lots of Last Digits. Technically spoken, Full House is not a separate technique. It is both a naked single and a hidden single which will be our next subject. The number of cells that can be solved as last digit does have a strong influence on the difficulty of the sudoku, because they are so easy to spot and such excellent timesavers. You learned about Naked Singles and Last Digits.

How to Solve Sudoku Puzzles Quickly and Reliably

A hidden single exists when there is only one cell left in a house that allows a certain digit. This sounds more complicated than it actually is. Now check box 2 in the diagram. It does not contain digit 1, so one of the empty cells in box 2 must contain digit 1.

Now the cells that I marked in red come into play. These are the conclusions that we can draw from them:. Because R1C2 contains digit 1, no other cell in row 1 can contain digit 1. This eliminates R1C4 and R1C5. Because R5C4 contains digit 1, no other cell in column 4 can contain digit 1. This eliminates R1C4 again and R3C4. Because R8C6 contains digit 1, no other cell in column 6 can contain digit 1. This eliminates R2C6.

Here is the same board with pencilmarks. Unlike naked singles , pencilmarks will not immediately reveal a hidden single. You have to check the candidates for all empty cells in the house to find it. In this case, R2C5 has 4 candidates.

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Sudoku theory is evolving in many places at the same time. Communities are forming fast and terminology, once firmly established in a community, is not easily replaced with another.

Techniques for removing numbers:

This is why so many aliases exist for even the simplest Sudoku concepts. Please take another look at the pencilmark diagram.

Sudoku Solving Tip - X Wing Technique

R2C5 is also a hidden single in column 5. When you are scanning the grid, you have the chance to discover the hidden single both in the box or the column. This does have an effect on the difficulty. We are only looking for chutes that have exactly 2 placements for a digit.

Techniques for removing candidates:

More by the author:. Sudoku rules The sudoku rules are very simple: Fill sudoku so that each column, row and 3x3 box has exactly once the numbers from 1 to 9. An example of sudoku solved. It works by removing candidates. Consequently, one branch would be the 'x' and the other the 'y' leaving the 'stem' without a candidate, an invalid state. Rule of Necessity This rule can be applied to sudoku regions i.

These 2 placements eliminate 22 of the 25 remaining candidates in the chute, efficiently narrowing down the remaining options.