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Top Nine Most Often Used Strategies for Solving Expert Sudoku Puzzles

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The Swordfish This strategy helps to eliminate a candidate from cells too. Example In this grid, number 4 is a candidate to two cells in three different rows, allowing the player to use the Swordfish technique.

Forcing Chains Forcing chains is one of the easiest advanced Sudoku strategies to understand. Example In this example, the top highlighted cell with the candidates 1 and 2 was used to apply the forcing chains technique.

The XY-Wing The XY-Wing is a strategy to remove candidates. Example In the example above, the stem cell contains the digits 2 and 9 highlighted in orange and connects to the branches, each with one of these digits as candidates purple squares.

Unique Rectangle Type 1 Any Sudoku puzzle must have only one possible solution. Example In this table, the player faces a possible deadly pattern with the candidates 2 and 3, in which the placement of those digits can become indifferent in the end and result in two possible solutions for the puzzle.

Nishio The Nishio strategy takes its name from professional puzzle player Tetsuya Nishio who is credited with inventing it.

Sudoku Genius. Classic Numbers Puzzle. Sudoku Unique Rectangle: Types and Patterns. The Best Sudoku Books to learn and enjoy these brain teasers.

Sudoku X-Wing technique: when and how to use. Sudoku Swordfish strategy explained. We have more online games for you.

Play now! Solitaire Word Search Mahjong Online All Rights Reserved. Puzzles: Easy Medium Hard Evil Impossible. Mutant Fish Fish patterns with mixed sets of constraints.

Kraken Fish A fish pattern with indirect connections to a candidate which can be eliminated. This article is licensed under the GNU Free Documentation License.

So, knowing how to determine a numeral by brute force is required. The pertaining squares are shaded in yellow see Figure 1.

The numerals 1, 2, 5, and 9 occur in the pertaining row, column and sector yellow squares. This leaves 3, 4, 6, 7, and 8, or five possibilities for the upper left hand square.

We cannot eliminate all but one and cannot determine the proper numeral from this analysis. Figure 1 — Brute force analysis of the upper left hand square.

The next square to the right is not much better see Figure 2. The numerals 1, 2, 3, 5, 6, and 9 occur in the pertaining area, leaving 4, 7, and 9, or three possibilities.

Figure 2 — Brute force analysis of the next square. To illustrate the situation, a map of the number of possibilities at each position, shows where a square that has a single possibility may exist.

By counting the possible numerals at each grid location and placing that count in the corresponding location, a map of possibilities is constructed.

Figure 3 — The map of possibilities of the example puzzle. It can be seen using this map, by applying the brute force method systematically, the solver would analyze 18 squares, before the first entry is found.

The solver could start at the upper left and examine each square, one at a time, across and down, applying the process of elimination see Figure 4.

Figure 4 — Applying brute force to each open square systematically. Great, we have our first entry at last.

Figure 5 — Brute force analysis to determine the first entry. Figure 6 — The map of possibilities with a new location where only one numeral is possible.

Each new entry reduces the overall possibilities. Each entry can lead to the discovery of other entries by changing what is possible. Each deduction leads to the next.

Like in a mystery, one clue leads to another. A solution is a sequence of deductive steps. If the solver applies the brute force method repeatedly in this example, the solver is stymied after only four entries.

The map of possibilities shows no squares where only one numeral is possible see Figure 7. Brute force will no longer work. Figure 7 — The example puzzle grid and map of possibilities after four entries.

Clearly the brute force method is lacking. It is tedious and frustrating. It may be the first strategy learned, but should not be the first strategy used when starting a new puzzle.

This is at the other extreme of the tedium spectrum. Finding the one missing numeral in a row, column or sector is easy.

For example, if there is only one open square in a row, the solver can look across the row for a existing numeral 1 in the filled positions.

If found, the solver looks for a 2. If found, the solve looks for 3 and so on. If a numeral cannot be found in the row, then is must be the numeral in the last open square of the row.

Another time to use brute force is when at an impasse stymied. It is sometimes useful to try brute force to overcome the impasse and continue solving the puzzle.

If there are only two or three open squares in a row, column or sector, it may work and the solution may progress again. Also at impasse, it sometimes can be visually detected that a particular location may be a candidate for a brute force analysis.

As the solver becomes acquainted with more complex techniques, the solver is less likely to be willing to endure the tedium, and will consider brute force at an impasse only as a last resort.

And unfortunately, It seldom succeeds. Here is the method I use when starting a new puzzle. By projecting particular rows and columns, that contain the same numeral, into a target sector, a single position in the target sector, where that numeral can occur, can sometimes be visually identified.

It is a mental construction and is best explained visually. Figure 8 — Projecting rows that contain a 2 to the right. The 2 is entered to the grid.

Naked pairs do not have to align within the grid. They can be naked pairs and be scattered within the square too.

No matter where they fall the point of the strategy is that you know there are only 2 possible numbers that can be placed in those cells and that you need to use the process of elimination to find the right one.

This same idea can also be applied to what more advanced players will call naked triplets or threes and naked quads.

Example of how hidden pairs can distort the true options for a cell. This is a great way to open up your grid and get a good feel for where to place numbers.

The hidden pair strategy is a way to eliminate clusters of numbers from two cells which leaves you with simple options for the rest of the cells.

Then look through your square, columns, and rows to rule out those numbers as options. In the above example, you can see that the hidden pair appears to have a multitude of options.

But if we apply the rule of looking through columns and rows we can see that the actual value of those cells is limited to being either a 6 or 7.

Again, this strategy can be used in triplets or quads but that could take more practice. If the numbers are aligned in the same column or row they are called a pointing pair.

The pointing pair tells you the number must be used in that line and can be ruled out from other possible cells. This is another strategy to help eliminate possibilities and make the entire puzzle more easily solved.

Are you noticing a theme with these strategies? Intersection removal is no exception to that line of thinking. If any number occurs as a possibility two or three times in any one unit row, square, or column you can then remove that number from any intersecting other units.

The key to using this strategy is to really fully understand what a unit is in the game. If the pair or triplet of numbers intersects with another row, column or square it can be eliminated as a possibility for that intersecting unit.

Another way to methodically use the process of elimination to get to the final result. This one just takes a little more focus on the entire grid than previous strategies mentioned.

Take a look at your rows and see if there are any pencil marks that are exactly the same in two spots.

Match up that row with another row that mirrors it. The pencil marks must be exactly the same in the same two spots.

You can see an example below to get a better idea. As you can see, the parallel rows create an X giving this strategy its name.

Looking at the example above you can now see that each of these rows has to have a 4 in it. You also know you can only place the 4 in either the slots that are dark blue, or light blue, since doing anything else would cause a repeated number in the row or column.

This will guide you to the right choice to erase and the right cell to place the X formation numeral. This is a strategy that takes a lot of thought but it does work very well.

It will help you develop the skills required to move beyond focusing on just one square or one row or column.

It helps you see the bigger picture. Remember how the X wing involved 2 possible numbers in two rows? The blue lines show you the slots where a 5 matches up and crosses the blue line itself.

In short, the blue lines are showing you where you have the possibility of placing a five. If there is not a somewhere that a blue and red line intersect, you can eliminate five as a candidate in that cell.

The blue lines will not tell you WHICH cell the five goes in, it just shows you what to eliminate. In the image, you can see that with this strategy the cells highlighted in blue are the ones that might have a five.

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