Help for Box-Line interactions
 

The Box-Line method uses two similar approaches. Firstly, if an unsolved number in a row or column occurs only in a box, then because that number must eventually occupy one of those cells, other occurrences of the number in the row or column outside the box can be eliminated. In the first grid (from Top95, #7, after naked and hidden singles), the 1s in the red cells (column 6) are the only ones in box 8, and one of these must be true. Therefore the other 1s in column 6 can go.


The second approach takes advantage of the fact that when an unsolved number occurs in a row or column within a box, and there are no other occurrences of the number in the row or column, then other occurrences of the number inside the box may be deleted. In the example, following on from above, the 3s in the red cells are the only ones in row 1, so one of these must be a 3. Therefore the other 3s in box 3 can go.


In the example, there are a further six box-line occurrences to follow.

With each elimination of numbers, the hidden singles and naked singles processes are repeated. Then the whole process is repeated until no further eliminations are possible. Top95 puzzles which are solved at the box-line level are #2, #3, #23, #24, #27, #36, #43, #44