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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. Figure 19 — 1 can be in four locations. Excluding the shared squares, the numeral 2 can only be in one square shaded green of the row see Figure Figure 22 — Only one place for a 9 in this column.
Using the alternation method does not find another entries either. We choose one of them, the leftmost column, to be next with the new technique see Figure Figure 23 — Next column to try the only once in a class technique.
Starting with 1, we find a singular possibility in the square shaded green of the top left sector see Figure Figure 24 — With only two locations open in the column, 1 can be in only one.
The alternation method fills five more entries see Figure However, in this situation we are at an impasse, none of the methods find any more entries.
A new method is necessary to continue. Figure 25 — Five more entries found. Notice this row shaded yellow in the example puzzle below see Figure It has only two open squares and both of them are shared by one sector.
This jumps out visually to be a candidate for the next logic to demonstrate. Figure 26 — Only two in two possible.
Because there are only two open squares in the yellow row, both of the remaining numerals in that row must occur in those squares.
Also, only these two numerals can be in these two squares, even if the rest of the sector is empty.
In the example, the numerals 4 and 5 must occur in the two remaining squares shaded green of the row. Therefore, they cannot occur in the other two open squares of that sector shaded red.
Sometimes this logic finds a singular possibility by itself. However, only two numerals remain 1 and 9 and they must be in the last two locations of the sector.
Unfortunately, because this technique did not find an entry, we will need another new technique to solve the puzzle. A sector can be subdivided into three rows and three columns.
I will call them sub-sectors. This means the numeral can be projected from the sub-sector without actually knowing where it is in the sub-sector.
Ths logic can be useful. Figure 27 — 1 ang 9 are used in column projection. We notice that the projection intersects a row shaded yellow with only two open squares.
Since 1, 2, and 3 are represented already, we start with the numeral 4 and we see that it can not exist on the bottom row in red.
Figure 28 — Only one location that can contain a 4. After finding the 4, the alternation method will find the rest of the solution see Figure I leave that as an exercise.
Figure 29 — The alternation method can solve this puzzle now. With just a few techniques, a solver can find success with all but the most difficult of Sudoku puzzles.
With these techniques and some practice, the novice solvers can jump start to a higher skill level. A solver using these techniques can find many hours of enjoyment and mental exercise using deductive reasoning.
Although these techniques may be new to some, they still may be considered as less than clever. Others may consider the deductive logic, shown here, as obvious or simplistic.
For those who may feel this way, I leave you with this quote:. Sherlock was saying that, after he explains the details of his logic, it no longer appears ingenious.
In all cases, each step was simple or elementary. Pin It. Home Download Purchase Advertise Here Search. By Dr Arf Strategy For me, the greatest appeal in solving Sudoku puzzles is the thought process used.
Brute Force At each open grid position of a Sudoku puzzle, a solver can mentally eliminate numerals by applying the basic rules of Sudoku. Row and Column Projection Here is the method I use when starting a new puzzle.
The theoretical approach of advanced Sudoku strategies is relatively easy to understand and to apply. The biggest difficulty is to find the right patterns on the grid and to know which technique to use in each case.
Nevertheless, only experts reach the levels in which they are required and at that point knowing and being familiar with these strategies becomes a requirement to progress in the hardest levels of these puzzles.
The X-Wing The X-Wing method is one of the most basic advanced Sudoku strategies. Example In this example, the number 5 forms the necessary pattern to apply the X-Wing strategy.
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!
See picture below. The number has already been used in the square. It also cannot be used in the column of the square below it because it has been prefilled there too.
That leaves you with only one option. The bottom left. This is how the process of elimination strategy works. Always remember columns and rows matter too.
Strategically eliminating possible moves is the best way to start your game. This is a technique slightly the opposite of what you just read about.
With crosshatching, you start by focusing on one 3x3 square and filling it in with the numbers needed.
Crosshatching can be especially useful for brand new Sudoku players who are overwhelmed with an entire grid to fill. The downfall is that you could find yourself going back to correct a lot of errors as the puzzle gets more filled in.
There are definite ways to solve the puzzle. You might be able to guess and get a lucky right answer, but in general yes, sudoku is solved without guessing.
Instead of guessing use strategic thoughtful moves. Guessing will not improve your game skills or chances of winning.
When it comes to sudoku the best strategy is going to be the one that makes the most sense to you. Move on to the next strategy or combine several to get the puzzle solved.
Some strategies are more difficult to master than others. Some strategies are meant for advanced players while others are great for beginners.
Try not to get stuck on one specific strategy. Something is bound to help. Illustration Of A Naked Pair As you can see each cell highlighted has 2 possible numbers.
This strategy is based on looking at the puzzle and deciding which numbers are the only possibility for a specific cell. In a naked pair, you know you have 2 possible numbers that will be able to work in the pair, but you have yet to figure out which will go where.
If you know the naked pair has either a two or a six as the possible answer, check to see where those numbers are used already.
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.