Cage Splitting With chaining strategies, there is definitely a theme going through them.
Sudoku solving techniques Advanced techniques Before starting on the advanced techniques, make sure you have looked at the basic techniques first. The technique takes two rows and finds four empty cells perpendicular to form a rectangle. The cells must be related to each other using a common value that is held as a candidate for each of the empty cells, there must only ever be two empty cells on each of the two rows that house that certain common value.
Either top-left and bottom-right or top-right and bottom-left of this pattern will hold the true candidates, any other empty cells in the columns connecting the X-Wing can have the common value withdrawn from their candidate list.
The shadowed columns have all their candidate number 1's removed. This time we get two rectangle patterns in our puzzle. When you have three empty cells along a row and a column you get an L shape. The two outside cells hold a candidate number that is the same as one of the centre cell candidate numbers.
The two cells also hold one other matching candidate number each. When you follow the two outside cells along either their column or row you will find another cell that will force the pattern into a square.
If this empty cell holds the matching candidate number then it can be removed from that cells candidate list.
The XY-Wing technique also has other patterns that work in the same kind of way. If either 4 ot 5 is the correct number for that cell we can follow the L-shape to its other points, where the 4 or the 5 from those cells would be removed, leaving an 8.
This tells us that the shadowed cell must have candidate number 8 removed. This means that one of the cells must hold the true candidate number, for this to work we must colour each of the two cells different colours, one of the coloured cells could also have the same relationship with another cell along another row, column or block, we can then colour the new cell with the opposite colour of the previous cell, so we get a kind of chain forming of opposite colours.
When we have two opposite coloured cells in relation with a common cell forming an L shape we know that one of those cells must be the true candidate number, This then allows us to remove the candidate number from the new cell. From here we found cell C, which links nicely with cell B and then finally cell D which also has candidate 1.
One cell must only have two candidates and one candidate must always be the same as the next link in the chain. We take the first link in our chain and systematically go through pretending that one of our candidate numbers is the true one, this will move through each link in the chain whittling down the candidates to one possible true answer like trial and error.
When we reach a dead end, we start over and we do exactly the same thing again with the second candidate number following the path until it reaches another dead end should be on the same cell as the last guess. Now if the two values that were found in our final cell were matching, we know that our cell has to be that value.
We then start from Cell A and fill in all the values if 2 was indeed the correct answer, we also in turn fill in all the correct answers for all the cells if number 2 was the correct answer.
We find that our shadowed square always returns the same value 2. Meaning that whichever route you take that shadwed cell E will always be a 2. For each candidate you ask the question: Will placing this number here stop me from completing the other placements of this number?
If yes then the candidate can be eliminated.The sudoku solves with singles after that move. Locked candidates moves can eliminate up to 6 candidates as can be seen in the example on the right: In box 8 candidate 1 is locked in row 7 and can therefore be eliminated from the intersection of boxes 7 and 9 with row 7.
Sudoku Solving Tactics. If you're here, you're probably familiar with the rules of Sudoku: fill in the empty cells in the grid with the numbers 1 through 9 so that no row, column, or .
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First enter the numbers of the sudoku directly in . Sudoku Instructions - candidate reduction methods Please note: This section will be more relevant to you and easier to follow when you have acquired the Sudoku Instructions program and the free course in sudoku..
In some sudoku puzzles there are too many possible digits in each square - there are too many candidate digits. To solve the problem it may be necessary to eliminate some of the. Free web sudoku site unlike any other.
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