Well, I think I have to do it very detailed, so I repeat the statements by Ronk with a comment from the NLN notation:

[r9c8]=1=[r9c4]=2=[r8c4]-2-[r8c7]-4-[r9c8], => r9c8<>4

if r9c8 is not 1, then r9c4 is 1 "[r9c8]=1=[r9c4]"

if r9c4 is 1, then r9c4 is not 2 "1=[r9c4]=2"

if r9c4 is not 2, then r8c4 is 2 "[r9c4]=2=[r8c4]"

if r8c4 is 2, then r8c4 is 2 "2=[r8c4]-2" (I a added this redundant line)

if r8c4 is 2, then r8c7 is not 2 "[r8c4]-2-[r8c7]"

if r8c7 is not 2, then r8c7 is 4 "2-[r8c7]-4"

if r8c7 is 4, then r9c8 is not 4 "[r8c7]-4-[r9c8]"

So if you generalise all the link statements it becomes like this:

[cell1]=a=[cell2] means if cell1 is not a then cell2 is a

[cell1]-a-[cell2] means if cell1 is a then cell2 is not a

It seems, that for this nice loop you can revert the direction of the loop. Is this always possible? My verbal interpretation of this is:

if r9c8 is 4, then r8c7 in not 4 "[r9c8]-4-[r8c7]"

if r8c7 is not 4, then r8c7 is 2 "4-[r8c7]-2"

if r8c7 is 2, then r8c4 is not 2 "[r8c7]-2-[r8c4]"

if r8c4 is not 2, then r8c4 is not 2 "2-[r8c4]=2"(This may not be allowed)

if r8c4 is not 2, then r9c4 is 2 "[r8c4]=2=[r9c4]"

if r9c4 is 2, then r9c4 is not 1 "2=[r9c4]=1"

if R9C4 is not 1, then r9c8 is 1 "[r9c4]=1=[r9c8]"

The reversed NLN is:

[r9c8]-4-[r8c7]-2-[r8c4]=2=[r9c4]=1=[r9c8], => r9c8<>4

The deduction starts at r9c8=4 and ends at r9c8=1 - a contradiction, so r9c8<>4.

I think my misconception was, that I was focused on, that the NLN should express the logic of the links and cells. But the NLN notation does not focus on the logic of the puzzle, but it focus on the result of the deduction. You may say that you can always interpret the parts like this:

"a=[cell]" as "then cell=a"

"a-[cell]" as "then cell<>a"

So the signs "-" and "=" refer to the deduction results and not so much on the links general performance on information transfer.

I have got this other Puzzle from LB:

- Code: Select all
` 17 9 6 | 5 34 8 | 37 2 14 `

3 4 2 | 7 69 19 | 5 8 16

5 8 17 | 2 346 14 | 37 9 146

-------------------+-------------------+-------------------

148 17 148 | 3 49 249 | 6 5 27

9 2 45 | 46 7 456 | 1 3 8

6 37 35 | 8 1 25 | 9 4 27

-------------------+-------------------+-------------------

247 5 347 | 1 8 34 | 24 6 9

248 6 489 | 49 5 7 | 248 1 3

148 13 13489 | 469 2 346 | 48 7 5

Here you got a Nice Loop like this:

[r1c5]-4-[r3c6]-1-[r3c3]-7-[r1c1]-1-[r1c9]-4-[r1c5] => [r1c5] <> 4

The links from r3c3 to r1c5 is strong (bidirectional) links with bilocation behavior. But the links are expressed by "-" only.

The notes above is very detailed, but it is my experience, that you have to be very carefull with logic deductions. Hopefully in this way you can quote my misconceptions and correct me.

/Viggo