If you find two cells in a row that only have two possible numbers, and
both of those cells have the same two numbers in, they they form a number pair.
Because they both have the same two numbers in, and because they are in the same
row, if one cell is number a, then the other cell has to be number b, and vice
versa.
This means that, whichever cell has number a in, the other one will have number
b in. Because they're in the same row, and because they only contain two numbers,
these two numbers can't appear anywhere else in this row.
4
6
5 8
1 7
5 7 8
2
1 9
3
1 5 9
2 5 8
3
1
4 5 8
9
6
2 4 5
7
2 5
2 5
7
9
3
1 4
1 5
1 2 4 5
6
8
2 6 9
2 8 9
4 6 8 9
2 3 9
2 8 9
3 4 8 9
5
1
7
1
2 4 5 8
2 5 8 9
6
2 4 5 8
7
2 9
2 4 8
3
4 5 8
3
7
1 4 5 8
1 4 9
1 2 5
4 6 8
4 9
2 6
8
4
1 3 6 9
2 3 6
2 5
3 5 6
1 6 7 9
7 9
1 6 9
2 9
2 6
2 9
7
1
4
3
5 6 8
5 8 9
7
5
1 3 6
9
8
3 6
1 6
2
4
Example 1: Number Pairs Number pair cells,remove from these cells
If we look at row 7, there are two cells that contain two numbers,
cells [r7,c4] and [r7,c6]. Both of these cells can only be either 2, or 9,
therefore the numbers 2 or 9 can't appear anywhere else in this row, so
we can remove 2 from [r7,c5] and 9 from [r7,c3].
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
2 3 9
1 8
4
2 5
7
6
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: Number Pairs Number pair cells,remove from these cells
If we look at column 3, there are two cells that contain two numbers,
cells [r1,c3] and [r8,c3]. Both of these cells can only be either 1, or 1,
therefore the numbers 1 or 2 can't appear anywhere else in this column, so
we can remove 1, and 2 from [r7,c3].
