## Forcing Chain Question

Advanced methods and approaches for solving Sudoku puzzles
sweetbix wrote:Thanks Jeff, is this a bivalue nice loop?

sweetbix:

There are two types of xy-type nice loops:

Code: Select all
`[12]---2---[23] |          | |          | 2          3 |          | |          |[24]---4---[34]`

The labels on the edges repeat -- 2234. You can remove the 2 from the cell connected to both edges with the label 2. The 2 is eliminated from the [12] cell by placing any value in any of the other three cells.

Code: Select all
`[12]---2---[23] |          | |          | 1          3 |          | |          |[14]---4---[34]`

The labels on the edges do NOT repeat -- 1234. No eliminations can be made within the 4 cells -- but you may eliminate 2s from the rest of the top row, 4s from the rest of the bottom row, 1s from the rest of the first column and 3s from the rest of the second column.

The nice loop in question is of the first type:

Code: Select all
` *--------------------------------------------------*  | .   [56]-------------(56)-------------[56]  .    |  | .    |    .    | .    .    .    | .    |    .    |  | .    |    .    | .    .    .    | .    |    .    |  |------|---------+----------------+------|---------|  | .    |    .    | .    .    .    | .    |    .    |  | .   (5)   .    | .    .    .    | .   (6)   .    |  | .    |    .    | .    .    .    | .    |    .    |  |------|---------+----------------+------|---------|  | .    |    .    | .    .    .    | .    |    .    |  | .    |    .    | .    .    .    | .   [68]  (8)  |  | .   [45]--------------(4)-------------[48]  .    |  *--------------------------------------------------*`

You can consider the label on the top edge as either 5 or 6, your choice. Either way, the labels repeat, eliminating the 5 from r1c2 and a 6 from r1c8.
tso

Posts: 798
Joined: 22 June 2005

Thanks tso, I understand it now.
sweetbix

Posts: 58
Joined: 10 December 2005

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