This is an extension of hidden pairs. Where
hidden pairs looks for two numbers that only appear in two cells, hidden 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. Unlike number chains, these cells can have other
numbers in them, but the numbers that form the chain cannot appear anywhere else
in that house.
A hidden pair is a
hidden chain of two numbers,
appearing in only two cells. A small hidden chain would be three numbers appearing
only in three cells and no others in that house. The cells may have other numbers in
them, but the numbers that are part of the chain cannot appear in any other cells.
Because these numbers have to appear somewhere in this house, and the only places
that they can appear are the cells in the chain, these cells cannot contain any
other numbers, so we can remove the numbers not in the chain, from the cells that
make up the chain.
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 only in N different cells in
one house, and these numbers appear
nowhere else in the house.
3 5 6 9
8
3 5 6
2
5 6
7
3 6 9
4
1
1 2 3 6 9
7
1 2 3 6 9
1 3 6 9
4
1 3 6 9
8
5
2 3 6 9
1 3 6 9
4
1 2 3 5 6 9
8
3 5
1 3 5 6 9
3 6 9
7
2 3 6 9
1 5 6 8
3
2 5 6 8
7
5 6
4
1 5
9
2 5
7
1 2 6
1 2 4 5 6
1 3 5 6 9
1 6
1 3 5 6 9
1 2 3 4 5
1 2
8
1 4
9
1 4 5
2
3 5
8
7
6
1 3 4 5
3 4 6 8
1
3 6 8
4 5 6
2
9
3 4 5 6
7
3 5 6
4 6
9
7
1 4 5 6
3
1 4 5 6
2 4 5 6
8
2 4 5 6
5
2
3 4 6
4 6
8
7
3 4 6 9
1
3 4 6 9
Example 1: Hidden Chain of 4 Hidden chain cells
If we look at the centre block, the numbers 3, 4, 5 and 9 only appear in
[r4,c6], [r5,c4], [r5,c6] and [r6,c4]. Because these are the only places
that these four numbers appear in and nowhere else, and they appear in four
cells, we can remove all the other numbers from those cells. This means we
can remove 1 and 6 from [r5,c4], 1 and 2 from [r6,c4], 1, 2 and 6 from [r4,c6]
and 1 and 6 from [r5,c6].
