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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.
It uses material from the Sudopedia article. Also like Sherlock, one particular type of deductive reasoning is used, that being the process of elimination.
Actually in Sudoku, a numeral a single digit number is never improbable. Therefore, Sudoku is even more elementary than a Holmes mystery.
At each open grid position of a Sudoku puzzle, a solver can mentally eliminate numerals by applying the basic rules of Sudoku. If, by the process of elimination, there is only one possible numeral, then it must be the entry that will solve the puzzle.
By brute force a solver can, one at a time, analyze each open square. If it has one possible numeral, the solver enters that numeral and then goes on to examine another open square.
If there is more than one numeral possible and all but one cannot be eliminated, the solver skips that square and tries another.
However, at the start of a difficult puzzle, few open squares will have a single possibility. In fact, many puzzles will have only one or two at the start.
Sometime at the start of a puzzle, using just the basic rules, there are no squares with a single possibility.
In that case, more complex logic is required just to begin. Also, even when there exists a square at the beginning, where only one digit is possible, often as the grid is filled, new locations with only one possibility cease to occur and open squares with only one possibility run out.
Again, to continue, only more complex logic can work. Using brute force becomes very tedious when there are many open squares and few having a single possibility.
Brute force has its drawbacks for sure. However, as the solution puzzle progresses and more empty squares are filled, it may become necessary and preferable to employ a brute force method.
In fact, in some situations brute force becomes easy. 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. Unfortunately, applying it requires very high levels of concentration and the outcome can be uncertain.
When it does work, it gives the player the solution for one cell. To apply a simple forcing chain, there must be cells with only two candidates in the grid.
The player picks one and begins testing the changes to puzzle when applying each of the two digits in that cell. The goal is to find if there is a cell that would bear the same result whichever digit is used.
If so, that will safely be the solution for it. In this example, the top highlighted cell with the candidates 1 and 2 was used to apply the forcing chains technique.
When testing for both digits, the player finds that the outcome for the highlighted cell with candidates 5 and 7 is always 5. Therefore, this digit will be the solution for that particular cell.
Note that when testing for number 1, the player could also have made a chain by going right to the cell with 1 and 4 as candidates.
The chain would be longer, but the result is the same. Out of the advanced Sudoku strategies, the forcing chains method is usually a last resort as the chains can be very long and complicated and they do not always produce results.
The XY-Wing is a strategy to remove candidates. It can be applied when there are three cells in the grid, each with only a pair of candidates that share at least one digit among them e.
With a bit of mental effort, the player can picture a Y when connecting them, with one cell working as the stem and the remaining as the branches.
The next step is to trace lines in each row and column of the cells to form a square or rectangle. If any of the shared digits are candidates within the lines connecting the cells or at an intersection point, they can be safely removed.
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.
If any of the cells on the red paths contained one candidate shared by the cells on the extremities of the lines, it could be eliminated, but this is not the case.
However, the cell at the intersection of both branches of the Y contains a shared digit by both number 1 , allowing the player to eliminate it as a candidate to that cell.
Any Sudoku puzzle must have only one possible solution. However, at the most extreme levels, the players might find themselves with two.
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.
The cells that cannot have a five are highlighted in red. Again, this is a highly advanced and somewhat complicated strategy to use for solving your puzzle.
Start in numeric order and go up from there. If you have 1 as a candidate in any of those areas you now know you can eliminate it as a possibility.
In the image above you can see this more clearly. The 2 has been taken and cannot be reused in that row, square, or column. For a Sudoku game you really just need 9 symbols, and numbers just happen to be the most popular version.
You could just as well use shapes and still present the same type of puzzle with the same rules and the same outcome.
In fact, there are Sudoku versions where letters or symbols are used instead of numbers just to change things up.
However, Sudoku does require mathmatically logical thinking. Sudoku is solved with logical reasoning heavily based on concepts used in mathematics.
In most cases, there is only one solution for a Sudoku puzzle. However, if the puzzle is blank there are definitely multiple solutions. In the most extreme case where a puzzle has zero prefilled number clues, Wikipedia states there could be up to 6,,,,,,, solutions.
So, while in general every puzzle only has one solution, if you did want to do a completely blank Sudoku puzzle, yes, there are definitely many solution options.
While there seems to be some disagreement on this within the Sudoku fan community, most agree that a true Sudoku puzzle is never unsolvable.
They state that a real Sudoku puzzle has one and only one solution. If you work on a puzzle that is unsolvable, it is either an error in printing, or not a true Sudoku puzzle.
It is another type of game based on a Sudoku type of grid. There are websites and publications dedicated to purposely creating unsolvable puzzles, but those are by design.
Your best bet is to erase everything and start with a clean slate. If you really wanted to challenge yourself you could start by erasing rows or columns with repeated numbers, but that could lead to more frustration.
It might be the fresh perspective you need to get the puzzle solved successfully. While every puzzle does have a solution, not every puzzle is solved by every person.
Sudoku is a puzzle game that requires skill building. The puzzle may only have one solution but how you get there is up to you.
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