## A simple chain that is not so simple for me.

Advanced methods and approaches for solving Sudoku puzzles

### A simple chain that is not so simple for me.

The puzzle below on "5's" looks like a very easy "solve. There are 9 cells with a 5 in them and 8 of them seem to hsve strong links. That leaves just one 5 that is not linked. The following cells are colored blue: r1c1...r3c4...r9c3...r7c7. These cells are colored green: r3c3...r7c1 r1c4...r9c7.. Note that these all seem to me to be strong links. Could someone please tell me where my thinking is flawed? Thank you ever so much.

*--------------------------------------------------*
| 57 1 567 | 25 9 8 | 24 467 3 |
| 4 3 2 | 1 7 6 | 9 8 5 |
| 9 8 567 | 25 3 4 | 1 67 27 |
|----------------+----------------+----------------|
| 2 9 4 | 6 8 3 | 7 5 1 |
| 8 7 1 | 4 5 2 | 3 9 6 |
| 6 5 3 | 9 1 7 | 8 2 4 |
|----------------+----------------+----------------|
| 57 6 9 | 8 4 1 | 25 3 27 |
| 3 4 8 | 7 2 5 | 6 1 9 |
| 1 2 57 | 3 6 9 | 45 47 8 |
*--------------------------------------------------
Gee

Posts: 50
Joined: 18 March 2007

### Re: A simple chain that is not so simple for me.

Gee wrote:There are 9 cells with a 5 in them and 8 of them seem to hsve strong links. That leaves just one 5 that is not linked. The following cells are colored blue: r1c1...r3c4...r9c3...r7c7. These cells are colored green: r3c3...r7c1 r1c4...r9c7.. Note that these all seem to me to be strong links. Could someone please tell me where my thinking is flawed?

A strong link occurs when there are exactly two candidates (of the same digit) in a row, col, or box. That means there is no strong link between r1c1 and r1c4 ... and no strong link between r1c1 and r3c3.

There are two conjugate chains -- chains of conjugate links -- that I've colored A-a and B-b below. There are no deductions possible.
Code: Select all
`A5  .  5 | b5  .  . |  .  .  . .  .  . |  .  .  . |  .  .  . .  . b5 | B5  .  . |  .  .  .---------+----------+---------- .  .  . |  .  .  . |  .  .  . .  .  . |  .  .  . |  .  .  . .  .  . |  .  .  . |  .  .  .---------+----------+----------a5  .  . |  .  .  . | A5  .  . .  .  . |  .  .  . |  .  .  . .  . A5 |  .  .  . | a5  .  .`

BTW you should be asking for help in the Help with particular puzzles forum.
ronk
2012 Supporter

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

### Simple Chain

Thanks Ronk. I am really new to Sudoku and appreciate your help. I will write any other questions I have to the group you mentioned. gee
Gee

Posts: 50
Joined: 18 March 2007