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Searching for Nearly Full Entities

Sometimes you're stuck with scanning. Then you can fall back to another method that is particularly useful if many cells are filled.

It goes like this: you look for 3x3-sub grids, rows or columns that already contain many numbers (six or seven numbers are a good point to start).

If there are eight numbers given in an entity, it is simple to find the missing number.

An example Sudoku

The figure above show the same Sudoku as show in section "Scanning".

In the third row only two cells are left blank. We mark these cells.

The third row is nearly full, only two numbers are missing (Two and Seven).

Now we try to exclude some of the possibilities. Therefore we search for Twos and Sevens in the columns crossing the empty cells.

Because of the Two in the lower right corner, in the rightmost cell there can only be a Seven. Only one place remains for the Two.

In the lower rightmost corner there is a Two. Nowhere else in that column there may be another Two, so in our selected row at the rightmost position there must be a Seven.

Now eight numbers are filled in in our row, the last free cell has to be occupied with a Two.

We found two numbers with our search.