## A simple Chain that doesn't work...Why

Advanced methods and approaches for solving Sudoku puzzles

### A simple Chain that doesn't work...Why

I am working on "9". I thought I had this type of thing firmly entrenched in my mind. Evidently not.

I will use colors to describe the problem.

I colored R2C2 Blue....R2C8 Green....R5C8 blue....R5C9 Green.

My thinking was I could exclude all the 9's in column 8 because I had a blue at R2C8 and a green at R5C8. Well I could....almost.... but the 9 in R8C8 would not exclude.

This is driving me bonkers because I don't know what was wrong with my logic. I have tried and tried but I don't know what was wrong with my logic. Hopefully, one of you could set me straight. Thanks for your help.

*--------------------------------------------------------------------*
| 2456 1 69 | 2468 2368 7 | 2589 2589 389 |
| 7 269 8 | 236 5 26 | 1 239 4 |
| 3 245 24 | 1 28 9 | 258 7 6 |
|----------------------+----------------------+----------------------|
| 2458 2458 24 | 2489 1289 124 | 3 6 7 |
| 268 268 1 | 5 7 3 | 4 289 89 |
| 9 3 7 | 2468 1268 246 | 258 1258 18 |
|----------------------+----------------------+----------------------|
| 1 2469 3 | 7 269 8 | 69 49 5 |
| 68 689 5 | 369 4 16 | 7 1389 2 |
| 2468 7 69 | 269 12369 5 | 689 1489 1389 |
*--------------------------------------------------------------------*
Gee

Posts: 50
Joined: 18 March 2007

### Re: A simple Chain that doesn't work...Why

Code: Select all
` *--------------------------------------------------------------------* | 2456   1      69     | 2468   2368   7      | 2589   2589   389    | | 7      269    8      | 236    5      26     | 1      239    4      | | 3      245    24     | 1      28     9      | 258    7      6      | |----------------------+----------------------+----------------------| | 2458   2458   24     | 2489   1289   124    | 3      6      7      | | 268    268    1      | 5      7      3      | 4      289    89     | | 9      3      7      | 2468   1268   246    | 258    1258   18     | |----------------------+----------------------+----------------------| | 1      2469   3      | 7      269    8      | 69     49     5      | | 68     689    5      | 369    4      16     | 7      1389   2      | | 2468   7      69     | 269    12369  5      | 689    1489   1389   | *--------------------------------------------------------------------*`

Gee wrote:I colored R2C2 Blue....R2C8 Green....R5C8 blue....R5C9 Green.

Seems like you didn't fully understand the correct application of the "simple colors technique". You can only (intentionally) color r2c8 & r5c8 in alternative colors if they are strong links (i.e. no other candidates of 9 on c8). From this position you cannot do that. The essential condition is you must be able to prove that exactly one of the 2 cells involved must contain the candidate (i.e. they can't be both being 9 or both not being 9). Here, r2c8 & r5c8 can both not being 9 with r2c2=r5c9=9. Then some other cells on c8 can be 9.

I'll show you a correct coloring application:

r2c8=blue <-> r2c2=green <-> r1c3=blue <-> r9c3=green

(Note that each of the 3 double arrows shown above are between cells that are strong links, like I described above.)

Therefore all cells seeing both r2c8 & r9c3 can't be 9, namely r9c8.

The 4 cells you quoted can actually be applied in a "multiple colors" move:

r2c2=blue <-> r2c8=green ; r5c8=pink <-> r5c9=amber

Since green & pink meet together here (r2c8, r5c8), all cells that see both blue & amber (r2c2, r5c9) cannot be 9. But it's totally useless here because all those cells (r2c9, r5c2) already don't contain any 9.
udosuk

Posts: 2698
Joined: 17 July 2005

### Re: A simple Chain that doesn't work...Why

udosuk wrote:The 4 cells you quoted can actually be applied in a "multiple colors" move:

r2c2=blue <-> r2c8=green ; r5c8=pink <-> r5c9=amber

Since green & pink meet together here (r2c8, r5c8), all cells that see both blue & amber (r2c2, r5c9) cannot be 9. But it's totally useless here because all those cells (r2c9, r5c2) already don't contain any 9.

However, there is a valid alternative multicolor exclusion on 9 at this point.
Code: Select all
` *--------------------------------------------------------------------* | 2456   1      69     | 2468   2368   7      | 2589   2589   389    | | 7      269(b) 8      | 236    5      26     | 1      239(g) 4      | | 3      245    24     | 1      28     9      | 258    7      6      | |----------------------+----------------------+----------------------| | 2458   2458   24     | 2489   1289   124    | 3      6      7      | | 268    268    1      | 5      7      3      | 4      289(p) 89(a)  | | 9      3      7      | 2468   1268   246    | 258    1258   18     | |----------------------+----------------------+----------------------| | 1     2469(g) 3      | 7      269    8      | 69     49     5      | | 68     689    5      | 369    4      16     | 7      1389   2      | | 2468   7      69(b)  | 269    12369  5      | 689    1489   1389-  | *--------------------------------------------------------------------*`

Coloring as above, since green sees pink, we can exclude 9 from any cell that sees both blue and amber, namely r9c9<>9.
Last edited by re'born on Thu Jun 21, 2007 7:00 am, edited 1 time in total.
re'born

Posts: 551
Joined: 31 May 2007

### Re: A simple Chain that doesn't work...Why

Thank you udosuk and re'born so much for your kindness in helping me understand the concept of "Simple Coloring". I truly appreciate your replies and help it has given me. Gee
Gee

Posts: 50
Joined: 18 March 2007