The New Sudoku Players' Forum

[SuDokuKid]

I was reading this: http://fredm.pbwiki.com/ and it states:

Cleaning up chains:

If a chain exists, then all additional possibilities in the chain can be discarded.
Chains of 2 numbers require 2 cells, chains of 3 numbers 3 cells and so on.
Example:
{4, 5, 6, 9}, {4, 9}, {5, 6, 9}, {2, 4}, {1, 2, 3, 4, 7}, {1, 2, 3, 7}, {2, 5, 6}, {1, 2, 7}, {8}

This group has a 3-number chain for the numbers (1, 3, 7): {1, 2, 3, 4, 7}, {1, 2, 3, 7}, {1, 2, 7}. Clearly the three numbers can only be in these three cells and no other numbers are possible. We can therefore simplify those cells to read: {1, 3, 7}, {1, 3, 7}, {1, 7}.

Why is the {1, 2, 7} included in the chain when the numbers in the 3-number chain are {1, 3, 7}?

Then the 2 is excluded.

[CathyW]

Otherwise known as a hidden triple - the 1, 3 and 7 can only go in those three cells (they are not candidates in any other cells), therefore you can remove the 2 and 4.

HTH

[Myth Jellies]

Just for grins and giggles, whenever there are N=8 undetermined cells, your hidden triple is always accompanied by a naked quint (8 - 3 = 5). Whenever there is a hidden something it is always coupled with a naked N - something.

[cho]

It's safe to say any number n unresolved cells in a group forms a naked set(n), so if you isolate x cells by whatever means that creates set(x) there will remain a (n-x) set.

cho

[Shazbot]

Example:
{4, 5, 6, 9}, {4, 9}, {5, 6, 9}, {2, 4}, {1, 2, 3, 4, 7}, {1, 2, 3, 7}, {2, 5, 6}, {1, 2, 7}, {8}

This group has a 3-number chain for the numbers (1, 3, 7): {1, 2, 3, 4, 7}, {1, 2, 3, 7}, {1, 2, 7}. Clearly the three numbers can only be in these three cells and no other numbers are possible. We can therefore simplify those cells to read: {1, 3, 7}, {1, 3, 7}, {1, 7}.

Why is the {1, 2, 7} included in the chain when the numbers in the 3-number chain are {1, 3, 7}?

I'm not going to pretend to understand those last 2 explanations. As indicated by CathyW, there's a hidden triple - the three numbers 1 3 7 can only go in 3 cells in that row, regardless of any other numbers also in the cells. It also doesn't matter that ALL THREE numbers don't appear in all of those cells - just that the combination is limited to them. So those three numbers MUST occupy those three cells in some sequence, and any extra numbers can be excluded. Following is the list again, with the remaining numbers in bold, so you can see where the hidden triple is, and the extras in those groups can be removed...

{4, 5, 6, 9}, {4, 9}, {5, 6, 9}, {2, 4}, {1, 2, 3, 4, 7}, {1, 2, 3, 7}, {2, 5, 6}, {1, 2, 7}, {8}