Eliminate Candidates




This technique is so basic, that it is barely even worth mentioning. For completeness' sake I do, though.

Basically all we do here, is eliminate all candidates that can be seen by a fixed number that has the same value.

In this grid every number is possible for the center cell. In other words: the cell contains all candidates 1-9.

As soon as there are other fixed (single) values in the grid that "see" the cell via row, column or box, the respective candidates can be eliminated from that cell.

In this example the candidates 1, 5 and 9 are eliminated from the center cell. They are no longer possible there, because the Sudoku rules say that there must not be the same two numbers within a row, column or box.

  • The center cell sees the 1 via row.
  • The center cell sees the 5 via box.
  • The center cell sees the 9 via column.

When to look for this

This technique comes first into play when we start writing down cell candidates, which might be relatively late in the solving process.

From that point onwards, every time you find a solution of a cell, you should immediately check whether this solution sees any cells where you have candidates notated. In those cells, the candidates with the same value can be immediately eliminated.

Take this grid for example.

Imagine we find the solution of a cell, for example via Hidden Single:

We can see that the 8 in the bottom left box prevents another 8 from being in the bottom row. That leaves only one cell in the bottom right box to contain an 8.

Now as soon as we write down that cell's solution (8), we immediately start to look what other cells it sees via row, column or box.

Those candidates can be immediately eliminated.

Of course this is an easy example where the candidates do not matter that much. A trained eye will immediately see that there must be a 9 at the top, and a 5, 6 and 2 in the bottom center box.

In those cases, where eliminating a candidate instantly yields a fixed solution, this step can of course be skipped. For all other cases you should always immediately erase the affected candidates, so you don't forget.