The New Sudoku Players' Forum

[ab]

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?

[ronk]

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.

[ab]

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

That sounds very definitive. Do you have an example?

[ronk]

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]=