This is an extension of number pairs. Where
number pairs looks for two numbers in two cells, number chains looks for 3 or more
numbers in 3 or more cells. The condition is that the the amount of numbers and the
amount of cells they're found in must be the same, eg 3 numbers in 3 cells, or 4
numbers in 4 cells. The other condition is that these cells must not have contain any
other numbers in them.
A number pair is a
number chain of two numbers,
appearing in two cells. A small number chain would be three numbers appearing in
three cells, with no other numbers in those cells. Between those three cells, they
have to contain those three numbers. This means that these three numbers can't
appear anywhere else, so we can remove those three numbers from all of the other
cells in that house.
This can be extended to 4 numbers in 4 cells, 5 numbers in 5 cells, and so on,
the rule being that only N different numbers appear in N different cells in
one house.
1
4
3 5
6 7
3 5
8
6 7
2
9
7
6
3 5
2 3 5
9
2 3 5
4
1
8
8
2 9
2 9
6 7
4
1
5
3
6 7
3 5
3 5 8
1
4
6
2
9
3 5 8
7
2 3 6 8 9
2 7
2 3 7 9
8 9
5
7 9
3 6 8
4
1
6 7
5 6 7 9
4
3
1
7 8 9
2
5 6
5 6 8
8
7
6
2
1
3 5
3 5
9
4
1
3
4
5 9
8
5 7 9
2 5
2 7
6
9
2 5
2 5
4
6 7
3 6 7
1
8
3 7
Example 1: Number Chain of 3 Number chain cells,remove from these cells
If we look at column 9, the numbers 3, 6 and 7 appear as the
only numbers in [r2,c9], [r8,c9], and [r9,c9]. Because there are only
three different numbers in these three cells, these three numbers can't appear
anywhere else in this column. Therefore, we can remove 6 from [r6,c9],
and 7 from [r5,c9].
2
1
4
6
8
5 7
3 7
3 5
9
3
6
9
1 2
2 5 7
1 2 7
8
5 7
4
8
7
5
4
3
9
1
6
2
4
5 6
1 2 5 7
1 3 7 8
3 5 6
1 2 5 7 8
3 8
9
5 8
2 5 6
9
3
2 5 6
4
2 6 8
7
1
6 8
5 6 7
8
1 6 7
3 5 6 7
9
1 6 7
3 5 6
2
4
1 8
2
3
5
4
6 8
9
7
1 6
1 6
7 8
5
9
2 7 8
2 7
4
3
1 6
9
4
6 7
6 7
1
3
2
5
8
Example 2: Number Chain of 4 Number chain cells,remove from these cells
If we look at the middle left block, the numbers 3, 5, 6 and 8 appear as the
only numbers in [r4,c2], [r5,c2], [r6,c1] and [r6,c3]. Because there are only
four different numbers in these four cells, these four numbers can't appear
anywhere else in this block. Therefore, we can remove 3 and 8 from [r5,c1],
5 and 8 from [r5,c3] and 5 from [r4,c3].
