This technique allows us to rule out possible numbers from being in a cell. This
may result in a cell only having one possible number in it. To make this easier
to understand, the possible numbers that can be in each cell have been filled in.
By looking at the possible numbers that can be put into a the 3x3 block, you may
find a number that only appears in one row or column of that block. If a number only
appears in one row of the block, we can remove that number from the other cells in
that row, that are not in the block. Because the block has to have that number in,
and so does the row, the only place it could go on the row is in the cells in that block
that contain the number.
If we were to place the number anywhere else on that row, we would not be able
to put it in that block, because the block can only have the number on that row.
Therefore the block forces the number to appear in those specific cells, which means
that it cannot appear anywhere else on the row.
This is sort of the reverse of row/col and block
intersection method, except it operates on the other cells in the row or column,
rather than the other cells in the block.
1 3 8 9
2
6
1 8 9
1 5 9
1 5 8 9
1 3 9
7
4
1 3 4 7 9
3 5 7 9
1 4 5 7
6
2 5 7 9
1 2 4 5 7
1 2 3 9
8
1 2 5
1 4 5 8 9
5 7 9
1 4 5 7 8 9
1 2 4 5 8 9
2 5 7 9
3
1 2 5 6 9
2 5 6 9
1 5 6 9
1 4 7 9
1 4 5 9
1 5 7 9
2 3 7 9
8
2 3 5 7 9
6
1 3 4 9
1 2 3 7 9
1 7 8 9
6 7 9
3
2 7 9
4
2 6 7
5
2 7 9
1 2 7 8
4 5 6 8 9
5 6 7 9
2
3 5 6 9
1
5 6 7 9
3 4 8 9
3 7 9
4 7 8 9
2 3 4 9
3 4 6 9
2 3 9
5
1 3 4 6
1 2 3 7 8
1 2 3 7 8 9
1 3 6 9
1 2 3 7 8 9
2 3 4
1
2 4 5 6
2 3 4 7 8
2 3 6 7
9
2 3 7 8
2 3 5 6 7
2 5 6 7 8
7
8
5 6 9
1 2 3 6
2 3 6
1 6
1 2 3 5 6 9
4
1 5 6 9
Example 1: Specific row in a block Looking
in this block, remove number from these cells
Looking at the top left block, we can see that the number 5 only appears in row 2
in that block, in cells [r2,c2] and [r2,c3]. Because that number has to appear in
that block, and it can only appear in one of those two cells, the number can't be
anywhere else on that row. We can therefore remove the number 5 from the other cells
in this row that aren't in this block, cells [r2,c5], [r2,c6], [r2,c7] and [r2,c7].
5
1 3
1 2
1 2 4
8
9
1 3 4
6
7
1 6 7
8 9
1 6 7
1 4 5
4 5
3
2
4 5 8 9
1 4 5
1 2 3 9
1 8
4
1 2 5
7
6
1 3 5 9
1 8
3 5 9
6
1 5 9
3
1 7
2
8
7 9
5 7 9
4
5 9
7
8
3 4 5
6
4 5
3 5 9
1
2
1 5
4
2
1 3 5 7
9
3 5 7
8
6
3 5 7
1 2 7
1 7
1 2 5 6
1 2 3 7 9
4
1 2
8
3 7 9
5 6
1 5 6 7
2 5
9
8
2 3
1 7
4 5 6 7
3 4 5
4 5 6 7
4
3
8
6
5
7 9
7 9
2
1
Example 2: Specific column in a block Looking
in this block, remove number from these cells
Looking at the middle right block, we can see that the number 1 only appears in
column 7 of that block. Because that number has to appear in that block, and it can only
appear in one of those two cells, the number can't be anywhere else in that column. We
can therefore remove te number 1 from the other cells in this column, that are not
in this block, cells [r1,c7], [r2,c7] and [r3,c7].
