This time we review the implications of Sudoku Snake’s naked double loop attack on Easter Monster. It is posed as an independent method of attack, i.e. one that is not dependent of the EM distribution of given clues.  But is it really?

Snake makes no mention of the distribution of 1267 given clues in Easter Monster.  Instead, he  describes a loop of  connected chutes, and names it the Naked Double Loop. A chute is an intersection of a box and a line. Each chute  contains candidates of exactly four numbers.  Chutes are connected by two numbers they have in common.

To paraphrase the Snake’s trace of the EM example:

In c2, NWc2 is connected to SWc2 via numbers 4 and 8.  In the NW box, the numbers 2 and 7 connect NWc2 to NWr2, which is connected to NEr2 via numbers 3 and 8, connecting to NEc8 via (1,1 and 6, connecting to SEc8 via 3 snf 9, to SEr8 via 2 and 7), to SWr8 via 4 and 5), and back to SWc2 via 1 and 6. The elimination rule for the naked double loop is that any candidate not in  a chute of the loop, but having  one of the connecting numbers of the chutes in its unit, is eliminated.   As Snake says, it’s hard to explain.

Now you can checkpoint the removals of the Easter Monster opening salvo, and verify your understanding of the naked double loop elimination rule, all at the same time.  The eliminations are the 1267 candidates in the corner cells of the corner boxes and the other candidates in the 1267-free lines between the corner boxes.

Sudoku Snake claims credit for the naked double loop, saying that “it can not be researched elsewhere”.  I disagree.   I can give him credit for the name,  and for something else.   His site suggests that the naked double loop works without the EM configuration of given clues, or even its four boxes. More on that later

I’m also skeptical of the Snake’s proof of the elimination rule. My readers know the Sue de Coq very well, and may prefer this proof:  Since the loop chutes contain exactly four connecting values, they are Sue de Coq chutes with no alternatives missing. The identical alternatives in two “married” SdC chutes in living in the same unit share the connecting numbers, denying them to any other cells of the unit. For example, in the NW box we have NWr2= 9(2+7)(3+8) and NWc2 = 9(2+7)(4+8).  In r2 there is NEr2 = (1+6)(3+8).  In NW, the corner outside corner boxes are denied 2 and7.  And in r2, middle cells are denied 3 and 8.  The naked double loop is an oligarchy of married Sue de Coqs and they have cornered the market. In your bv scan, look out for married Sue de Coq chutes.  I’ve seen them in lines. They could possibly lead you to a naked double loop, aka SK loop, aka opening volley.