Intermediate techniques to solve Sudoku puzzles
Candidates
To solve more than easy Sudoku puzzles is essential to know the candidates system.
A candidate number is that one which is a possible solution for a certain cell taking into account the rest of numbers from its row, column and region.
Isolating this region we can see that the remaining numbers are 1, 2, 3, 4 and 5, so these numbers are the candidates for the empty cells.
To reject more candidates from each of the empty cells is necessary to check the corresponding row and column.
Hidden single
If a cell has a set of candidates which one of them is only candidate for this cell and no other cell from its same row, column or region, that number is the solution for that cell.
In region 6 we see that there is only one cell which has the number 7 as a candidate, I6, so, although it has more candidates, we can assert that the number 7 is the solution for that cell.
Intersection
If there is a region in where there is a candidate only in the cells of a certain row or column, we reject that number as a candidate for the rest of its row or column. In the same way, if a candidate appears in the cells of a certain row or column only inside a region, we can reject that number as a candidate for the rest of cells from that region.
Observing region 5 we see that candidate 4 appears only in the cells of column E, so one of these two cells will have number 4 as a solution, which implies that the rest of that column can’t have number 4 as a solution, and so we can reject it as a candidate from the rest of cells that have that candidate, E2 and E8.
Naked pairs/triples/quads
If two cells from the same row, column or region only have 2 candidates and they are the same, we can reject these 2 numbers as candidates for the rest of the row, column or region.
The same technique is valid for triples candidates, despite of is not necessary that the 3 candidates appear in the 3 cells but works for some combinations, and quads.
Possible combinations for a naked triple:
· [123] [123] [123]
· [123] [123] [12]
· [123] [12] [23]
· [12] [23] [13]
Observing column C we see that candidates 3 and 6 appear as the only candidates in cells C1 and C9, so these 2 cells will share that numbers as a solution, which implies that we can reject the numbers 3 and 6 as candidates from the rest of the cells of the column, C4 in this case.
Hidden pairs/triples)
If 2 cells from the same row, column or region have 2 of their candidates equal and this 2 numbers don’t appear in the rest of the cells from that row, column or region as candidates, we can reject the rest of the candidates from that 2 cells.
Observing column C we see that candidates 4 and 8 only appear in cells C4 and C6, so these cells will share that 2 numbers as the solution, which implies that we can reject numbers 3 and 6 as candidates for cell C4.