## Nice Loop with Discontinuity...What is wrong?

Post the puzzle or solving technique that's causing you trouble and someone will help

### Nice Loop with Discontinuity...What is wrong?

I am baffled with the cells labeled... a,b,c,d,e. According to what I understand, I have a discontinuity at cell (c) on (8). Nice loop rule2 states the following: "if adjacent links are links with a strong inference, a candidate can be fixed in the cell at the discontinuity."

That is what it looks like to me that I have at cell (c) only an (8) cannot be placed at (C)

Help needed. Thanks for your help.

Code: Select all
` *-----------* |...|6.3|4..| |.9.|.5.|.7.| |52.|.87|..6| |---+---+---| |452|...|1..| |.8.|...|627| |...|...|...| |---+---+---| |..6|.3.|79.| |.3.|76.|...| |1..|..9|5..| *-----------*  *-----------------------------------------------------------* | 8     1     7     | 6     9     3     | 4     5     2     | | 6     9     34    | 124   5     24    | 38    7     18    | | 5     2     34    | 14    8     7     | 9     13    6     | |-------------------+-------------------+-------------------| | 4     5     2     | 389e  7     6     | 1     38d   89    | | 3     8     19    | 459   14    45    | 6     2     7     | | 7     6     19    | 2389  12    28    | 38    4     5     | |-------------------+-------------------+-------------------| | 2     4     6     | 58a   3     158   | 7     9     18    | | 9     3     5     | 7     6     18b   | 2     18c8  4     | | 1     7     8     | 24    24    9     | 5     6     3     | *-----------------------------------------------------------*`
Gee

Posts: 50
Joined: 18 March 2007

Gee wrote:According to what I understand, I have a discontinuity at cell (c) on (8).

Nice loop rule2 states the following: "if adjacent links are links with a strong inference, a candidate can be fixed in the cell at the discontinuity."

That is what it looks like to me that I have at cell (c) only an (8) cannot be placed at (C)

Code: Select all
` *-----------------------------------------------------------* | 8     1     7     | 6     9     3     | 4     5     2     | | 6     9     34    | 124   5     24    | 38    7     18    | | 5     2     34    | 14    8     7     | 9     13    6     | |-------------------+-------------------+-------------------| | 4     5     2     | 389e  7     6     | 1     38d   89    | | 3     8     19    | 459   14    45    | 6     2     7     | | 7     6     19    | 2389  12    28    | 38    4     5     | |-------------------+-------------------+-------------------| | 2     4     6     | 58a   3     158   | 7     9     18    | | 9     3     5     | 7     6     18b   | 2     18c8  4     | | 1     7     8     | 24    24    9     | 5     6     3     | *-----------------------------------------------------------*`

what makes this a "Nice Loop" ?
admittedly i don't have a definition for that term --
still, just looking at the 5 cells you marked, i see no useful conclusion

Pat

Posts: 3691
Joined: 18 July 2005

### Re: Nice Loop with Discontinuity...What is wrong?

Gee wrote:I am baffled with the cells labeled... a,b,c,d,e. According to what I understand, I have a discontinuity at cell (c) on (8). Nice loop rule2 states the following: "if adjacent links are links with a strong inference, a candidate can be fixed in the cell at the discontinuity."

That is what it looks like to me that I have at cell (c) only an (8) cannot be placed at (C)

Help needed. Thanks for your help.

First off, you need to set [r4c9]=9 in your PM. This leaves the following chain/loop

Code: Select all
` +--------------------------------------------------------------+ |  8     1     7     |  6     9     3     |  4     5     2     | |  6     9     34    |  124   5     24    |  38    7     18    | |  5     2     34    |  14    8     7     |  9     13    6     | |--------------------+--------------------+--------------------| |  4     5     2     | e38    7     6     |  1    d38    9     | |  3     8     19    |  459   14    45    |  6     2     7     | |  7     6     19    |  2389  12    28    |  38    4     5     | |--------------------+--------------------+--------------------| |  2     4     6     | a58    3     158   |  7     9     18    | |  9     3     5     |  7     6    b18    |  2    c18    4     | |  1     7     8     |  24    24    9     |  5     6     3     | +--------------------------------------------------------------+ # 31 eliminations remain (8) a - b = c - d = e ( - a )  => a<>8`

Here, you have strong links on each side of (c), but the chain/loop indicates that you have a strong inference on one side and a weak inference on the other.

BTW: You have five cells with three strong links (on four cells) -- bc, cd, de. This is a Turbot Fish pattern, and the candidate can be eliminated in the fifth cell; i.e., cell (a).
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

thanks, daj95376, of course i should've noticed r4c9, that does change things!

Pat

Posts: 3691
Joined: 18 July 2005

The discontinuous nice loop (type-2) you wanted to make: c=b-a=e-d=c , does not work because of the candidate 8 in r6c4, which cannot be removed. To be a nice loop, the a - e link must also be a bi-value strong link, which is not possible for this puzzle.

Code: Select all
`+----------+------------------+--------------+| 8  1  7  | 6       9   3    | 4   5     2  || 6  9  34 | 124     5   24   | 38  7     18 || 5  2  34 | 14      8   7    | 9   13    6  |+----------+------------------+--------------+| 4  5  2  |e3(8)    7   6    | 1  d3(8)  9  || 3  8  19 | 459     14  45   | 6   2     7  || 7  6  19 | 239(8)* 12  28   | 38  4     5  |+----------+------------------+--------------+| 2  4  6  |a5(8)    3   158  | 7   9     18 || 9  3  5  | 7       6  b1(8) | 2  c1(8)  4  || 1  7  8  | 24      24  9    | 5   6     3  |+----------+------------------+--------------+`
Allan Barker

Posts: 266
Joined: 20 February 2008

I see that (9) can be placed in r4c9, which changed the complexion of things, and the PM’s you sent clarified things for me.

I do have a question of whether an AIC can be created on these cells. I don’t know how to properly apply the proper notation but I will express what I mean.

There is a strong inference on (8) between b and c. A weak inference on (8) between c and d. and a strong inference on (8) between d and e.

Therefore A<> 8 and r6c4 <> 8.

If this is not correct perhaps someone could correct my logic and AIC interpretation. . I do appreciate you replies and help. Thanks.
Gee

Posts: 50
Joined: 18 March 2007

Gee wrote:I see that (9) can be placed in r4c9, which changed the complexion of things, and the PM’s you sent clarified things for me.

I do have a question of whether an AIC can be created on these cells. I don’t know how to properly apply the proper notation but I will express what I mean.

There is a strong inference on (8) between b and c. A weak inference on (8) between c and d. and a strong inference on (8) between d and e.

Therefore A<> 8 and r6c4 <> 8.

If this is not correct perhaps someone could correct my logic and AIC interpretation. . I do appreciate you replies and help. Thanks.

Gee
My one piece of advice would be to forget forever the whole business of examining links to determine what deduction you can or can't make.
You can do all of that with simpler logic where you are in complete control !
Just remember that :
1. all chains without exception proceed with alternating links (which some call "inferences")
2. all deductions for all chains without exception and therefore including loops are made by confronting the first node and the last node.
By way of illustration in your example, consider the following chains :
8r8c6=8r8c8-8r4c8=8r4c3
ie b=c-d=e
Examine first and last nodes :
if b is false, then e is true
Confront that position : if follows that at least one of them must be true, so anything which they jointly see can be eliminated : in this case 8r6c6.
Now extend that chain :
8r8c6=8r8c8-8r4c8=8r4c3-8r7c4
ie b=c-d=e-a
Confront the first and last nodes :
if b is false, then a is false : nothing to be deduced.
Now consider the loop :
8r7c4-8r8c6=8r8c8-8r4c8=8r4c3-8r7c4
ie a-b=c-d=e-a
Confront the first and last nodes (and forget about examining links) : in this case they are the same node r7c4.
The chain shows that if "a" is true, then it is false. Well "a" is either true or false. When it is false, it is false (obviously), but when it is true it is false as the chain shows : only possible deduction : "a" is false ie 8r7c4 can be eliminated.
aran

Posts: 334
Joined: 02 March 2007

I wish to thank 7you all for your replies. Aran, you gave me a different perspective which I appreciate.

Thanks again.
Gee

Posts: 50
Joined: 18 March 2007