## Hidden Pair in a Chain

Everything about Sudoku that doesn't fit in one of the other sections

### Hidden Pair in a Chain

Assuming that basic techniques have already been applied.

Code: Select all
` +-----------------------------------------------+ |   .   .   .   |   .   .   .   |   .   .   .   | |   .   .   .   |   .   .   .   |   .   .   .   | |   .   3W  .   |   .   .   .   |   .   .   .   | |---------------+---------------+---------------| |   .   .   .   |   .   .   .   |   .   .   .   | |   .   .   .   |   .   .   .   |   .   .   .   | |   .   .   .   |   .   .   .   |   .   .   .   | |---------------+---------------+---------------| |   .   .   .   |   .   .   .   |   .   .   .   | |   /   3X  /   |   /   /   /   |  37Y 37Z  /   | |   .   .   .   |   .   .   .   |   .   .   .   | +-----------------------------------------------+ Chain Segment:   ... = 3r3c2 - 3r8c2 = hp(37)r8c78 - ???`

It follows that <7> is locked in r8c78 and must have been eliminated elsewhere in [r8] and [b9]. It can't contribute any eliminations from the Hidden Pair.

There is an SL for <3> in [r8], and a simpler chain segment -- ... = 3r3c2 - 3r8c2 = 3r8c78 - 3[b9] -- exists for eliminations of <3> in [b9].

Thus, I'm left with the only realistic eliminations (in the chain) associated with the Hidden Pair being the candidates Y and Z.

Agree/disagree ?

_
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

### Re: Hidden Pair in a Chain

daj95376 wrote:Thus, I'm left with the only realistic eliminations (in the chain) associated with the Hidden Pair being the candidates Y and Z.

Agree/disagree ?

Agreed, in your scenario no more and no less than a conventional hidden pair.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

### Re: Hidden Pair in a Chain

Moreover to be able to continue the chain you need a candidate x in the 2 cells with a strong inference
.. = 3r3c2 - 3r8c2 = (hp37-x)r8c78 = ..
This candidate always must build a hidden pair x7 in the other direction
.. =(hpx7-3)r8c78=3r8c2 .. or
.. =(hpx7-hp37)r8c78=3r8c2 ..
eleven

Posts: 1816
Joined: 10 February 2008