## nice loops question

Advanced methods and approaches for solving Sudoku puzzles

### nice loops question

nice loops are an extension of simple colouring. the simplest nice loops have two colouring chains interacting, but you can have ones with three or four colouring chains. Now with fish and hidden and naked sets we don't need to consider anything larger than size 4, is the same true for nice loops? ie if you have a nice loop with 5 colouring chains, is it complemented by another nice loop with 4 or less colouring chains?
ab

Posts: 451
Joined: 06 September 2005

### Re: nice loops question

ab wrote:if you have a nice loop with 5 colouring chains, is it complemented by another nice loop with 4 or less colouring chains?

No! For example, there may be no "complement" at all.
ronk
2012 Supporter

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

### Re: nice loops question

ronk wrote:No! For example, there may be no "complement" at all.

That sounds very definitive. Do you have an example?
ab

Posts: 451
Joined: 06 September 2005

### Re: nice loops question

ab wrote:
ronk wrote:No! For example, there may be no "complement" at all.

That sounds very definitive. Do you have an example?

A continuous x-cycle for an x-wing after the eliminations have been made.
Code: Select all
`2517489633946527..6781394525..983.4.18342759694.516.3.83.2.4..54.58.13.971.3.5..4 2   5   1   | 7   4   8   | 9   6   3 3   9   4   | 6   5   2   | 7   18  18 6   7   8   | 1   3   9   | 4   5   2-------------+-------------+------------ 5   26  267 | 9   8   3   | 12  4   17 1   8   3   | 4   2   7   | 5   9   6 9   4   27  | 5   1   6   | 28  3   78-------------+-------------+------------ 8   3   69  | 2   679 4   | 16  17  5 4   26  5   | 8   67  1   | 3   27  9 7   1   269 | 3   69  5   | 268 28  4 .  .  . |  .  .  . |  .  .  . .  .  . |  .  .  . |  .  .  . .  .  . |  .  .  . |  .  .  .---------+----------+---------- .  .  . |  .  .  . |  .  .  . .  .  . |  .  .  . |  .  .  . .  .  . |  .  .  . |  .  .  .---------+----------+---------- .  .  9 |  .  9  . |  .  .  . .  .  . |  .  .  . |  .  .  . .  .  9 |  .  9  . |  .  .  . -[r7c3]=9=[r7c5]-9-[r9c5]=9=[r9c3]-9-[r7c3]=`
ronk
2012 Supporter

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