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solving techniques


Using the following technique you can place a candidate in the cell or remove some possible candidates.

1) Visible unique candidate

2) Hidden unique candidate

3) Block interaction with Row or Column

4) Row or Column interaction with Block

5) Visible doublets triplets etc

6) Block Block interaction

7) Hidden doublets triplets etc

8) Xwing

9) Swordfish




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1) Visible unique candidate


If there is only one possible candidate for a cell then it is a candidate to that cell. They are easy to spot and you dont need a pencil in. The easy puzzle will only have visible unique candidates.


visible unique candidate

In the above example, I have marked few possible candidates with green square. In each of these cell there is no other possible candidates. So these possible candidaes must go into the cell. check out whether 9 is a visible unique candidate.







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2) Hidden unique candidate


If the possible candidate does not repeat in the interactive row, column or block, then that possible cadidate is a candidate for that cell. In the interactive cells we can remove that as a possible candidate from the list.


hidden unique candidate

In the above example, I have marked a possible candidate with green square. It is unique to that block. So, it is a candidate to that cell. Now we can safely remove 2(red square) from the interactive cells as a possible candidate.







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3) Block interaction with Row or Column


If a possible candidate in a block is contained completely in a row or column of that block, then the occurance of the candidate as possible candidates in the other part of the row or column can be removed.


block interaction with row or column

In the above example, the possible candidate 3 in the block(marked by yellow square) appears completely within second row of the block, So 3 can be removed as a possible candidate from the second row(possible candidates removed are marked by red square).







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4) Row or Column interaction with Block


If a possible candidate in a row or column is completely contained in a block then the occurance of that candidate as possible candidate can be removed from other part of the block.


row or column interaction with block

In the above example, the possible candidate 5 in column three is completely contained in block four(marked by yellow square). Now the candidate 5 can be removed as a possible candidate in other parts of the block(candidates removed are marked by red square).







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5) Visible doublets triplets etc


If in a group of cell belonging to a row, column or a block has same number of possible candidates and if they are identical, then these possible candidates can be removed from other part of the row, column or a block.


visible doublets

In the above example, possible candidate 5 and 9 in the block(marked by yellow border) and row(marked by green line) forms a group(total number of candidates in the group is 2) and the group is found in two cells. So, 5 or 9 must be presented only in these two cells. Now, we can remove 5 or 9 as possible candidate in cells except those from the affected column and row.







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6) Block Block interaction


If a possible candidate in two blocks belongs to two row or cell, then the candidate can be removed as a possible candidate from the row or cell excludin the two block.


block block interaction

In the above example, possible candidate 4 ispresent in only two cell in two blocks(marked by yellow border) and they fall under the same column. In the affected column a 4 must presented either in block1 or block3, So, 4 as possible candidates can be removed from the cells(marked by red color) in block2 of the affected columns.







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7) Hidden doublets triplets etc


If in a group of cell belonging to a row, column or a block has identical candidates and they do not appear in any other part of the cell, also the number of the identical candidate is equal to the number of cell group then other possible candidates except the identical candidates can be removed from the cell group.


hidden doublets

In above example, the possible candidates 6 and 9 forms a hidden group because they are not present in other cells and number of candidates in the group(2) is equal to number of cells occupied(2). Now all other possible candidates can be removed in these cells because either 6 or 9 can be the only candidate there.







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8) Xwing


If a possible candidate in two row or two column only occurs at two cell and they form corners of a parallelogram(square/rectangle), then that possible candidate can be removed from the cells in the affected row and column excluding the block where the corner is located.


xwing

In the above example, the possible candidate 2 is present only in two cells in row 1 and 9 and they fall under the same column. Now, In the affected columns a 2 must be present in either of these two cells, which mean 2 as a possible candidates can be removed from all other cells(marked by red color) in the affected columns.







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9) Swordfish


This is just an extension of xwing and very rarely occurs. If a possible candidate in three columns occur only two times and they fall under three rows with minimum two candidates on each row, then you can remove this as a possible canddiate from other parts of the row(replace row->column and column->row is also true).


swordfish

In the above example, the columns(marked by green line) has 4 as possible cadidate in only two cells and they fall under three rows with minimum two cell in each row(row: 2, 5 and 9). Now, in these each row 4 must be in any of these two cells, So, we can remove the 4 as possible candidates from all other cells(filled by red color) in these rows.



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