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 all the possible numbers in a row, you may find a number that only
appears in one of the 3x3 blocks that the row crosses. Because the number has to
appear in that row somewhere, and the only places it can appear are confined to one
block, then we know that the number can't appear anywhere else in that block.
This allows us to remove that number as a possibility for all the other cells in that
block. The number has to appear in the row, so we remove that number from all the
other cells in that block that aren't in that row.
3 9
6
3 9
1 4 9
1 7 9
8
2
3 5 7
3 4 5
1
2 7 8
4
3
2 7
5
6
7 8
9
2 7 8
5
7 8 9
6
2 4 9
7 9
4 7 8
3 4 8
1
8
1 2 5 9
1 5 9
1 4 9
1 9
6
7
2 3 5
3 5
4
3
7
8
5
2
9
6
1
2 5
1 2 9
6
3
1 9
7 9
2 5 8
2 8
4
5
1 8 9
1 9
1 3
1 3 8
7
6
4
2
7
1 4
3
2
1 4
6
5
9
8
4 8
4 6 8
2
9
4 8
5 8
1
7
3
Example 1: Row and Block Interaction Search row, remove number from these cells
Looking at row 1, the number 3 only appears as a candidate in the part of that
row that is inside the top left block, cells [r1,c1] and [r1,c3] Therefore, we could
remove 3 as a possibility from all the other cells in that block (which have been
highlighted). This means that we remove 3 from [r3,c2] and [r3,c3].
3
5
6
7
1 2 9
1 2 9
8
4
1 9
4 8
2
4 8
1 5 9
1 5 9
6
1 9
7
3
1
7
9
8
3
4
6
2
5
2 4
3
2 4 5
6
1 2
1 2 4 7
9
8
1 2 4 5 7
6
4 5
1
2 4 8 9
4 9
4 7 8 9
2 4 5
3
4 7
9
8
7
5
1 4
3
2 4
6
1 2
5
6
1 2 4 8 9
1 4
1 9
1 4 8 9
1 2 4
7
3
3
1 4 9
4 9
7
6
2
1 4 9
8
5
7
1 4 9
1 2 8
3
5
1 8
2 4
1 4 9
6
Example 2: Column and Block Interaction Search column, remove number from these cells
Looking at column 1, the number 1 only appears as a candidate in the part of that
row that is inside the bottom left block, cells [r8,c1] and [r9,c1]. Therefore, we
could remove 1 as a possibility from all the other cells in that block (which have
been highlighted). This means that we remove 1 from [r7,c3], [r8,c2] and [r8,c3].
