Nice Loop: use cell twice?

kyriako · Posted: Sat Jun 14, 2008 6:41 pm Post subject: Nice Loop: use cell twice?

Hello Sudoku Friends,

when snaking around a Sudoku, it may happen that you hit a cell which is already being used by the loop. Is it allowed to use it a second time and continue?
Does it make sense at all?

Guenter(Kyriakos).

Steve · Posted: Sat Jun 14, 2008 7:28 pm Post subject:

Yiasou!

As far as the logic is concerned, no difficulty arises if a nice chain crosses itself, using a node (or nodes) several times. If you think about it, you can go round a continuous nice loop as often as you like without disturbing its meaning.

Whether it is helpful is another matter: I do not think any fresh elimination will arise as opposed to dealing with each sub-loop separately.

Steve

hobiwan · Posted: Sun Jun 15, 2008 1:22 pm Post subject:

I just posted possible examples here. They provide additional eliminations and seem to be valid (to me at least). Whether they are sensible (or useful) is another question.

kyriako · Posted: Sun Jun 15, 2008 6:31 pm Post subject: one more question

Yassu and thank you Steve for the explanation.

Would you suggest to examine the continuous sub-loop first before going ahead?

I have still another question, which you have probably already answered with your comment:
in the samples that I have seen so far, the traces form either kind of a "loop" or they
cross each other. Is it allowed to use a unit(like a row) several times?

Hello hobiwan and thank you for the samples.

I'm not familiar with this kind of code: what is the meaning of a character
in a cell, e.g. "b34" ?

Guenter(Kyriakos).

Steve · Posted: Sun Jun 15, 2008 6:53 pm Post subject:

The three I checked are valid right enough. However, I doubt if, properly speaking, they made any additional elimination.

Take the second loop marked with two asterisks for the third grid. It runs:

r3c9 =4= r3c5 -4- r6c5 =4= r5c6 =6= r5c7 -6- r1c7 =6= r1c2 =7= r7c2 =8= r7c1 =6= r7c5 -6- r4c5 =6= r5c6 =4= r1c6 -4- r1c8 =4= r3c9

You rightly conclude that r3c9 contains 4.

Now extract its middle loop

r5c6 =6= r5c7 -6- r1c7 =6= r1c2 =7= r7c2 =8= r7c1 =6= r7c5 -6- r4c5 =6= r5c6

This places 6 in r5c6. As for the rest of the loop, whether you use the head

r3c9 =4= r3c5 -4- r6c5 =4= r5c6

or the tail

r5c6 =4= r1c6 -4- r1c8 =4= r3c9

6 in r5c6 places 4 in r3c9.

There is a sort of equation, I suppose: long loop + singles = short loop + singles.

Steve

hobiwan · Posted: Sun Jun 15, 2008 8:30 pm Post subject: Re: one more question

Steve · Posted: Sun Jun 15, 2008 10:07 pm Post subject:

Günter

I spent so long transferring my previous note from the word processing program to the text box that your last post beat me to it and I have only just noticed it.

I am not certain I understand your fears but I’m pretty sure they’re groundless. Perhaps it will help to go back to basics. Take a small part of a chain, say

-1- r1c1 -2- r1c9 when written in nice loop notation.

This is just shorthand for two statements:
(1) If r1c1 does not contain 1, r1c9 does not contain 2:
(2) If r1c9 contains 2, r1c1 does not.
The fact that these statements can be made depends entirely on the grid. They are not affected by anything else. In particular, they are unaltered whether or not r1c1 appears elsewhere in the chain you build up around it. As far as I am concerned there is only one rule for chains: join the links logically and nothing else matters.

If this doesn’t set your mind at ease, perhaps you could provide an example of a chain with which you feel uncomfortable and I shall try to do better.

Steve

daj95376 · Posted: Sun Jun 15, 2008 10:58 pm Post subject: Re: one more question

kyriako · Posted: Mon Jun 16, 2008 6:34 pm Post subject: Thank you

Hello Steve and hobiwan,

Thank you for your hints. I will study the samples thoroughly. This will sure give me more certainty on the subject. In any case, I find the nice loop strategy fascinating.

Regards,
Guenter(Kyriakos)

Henk · Posted: Fri Jun 20, 2008 9:23 pm Post subject:

Hi,

If you are really interrested in nice loops (and other forcing chains) you should try this puzzle. Just try to find as many as you can, its has lots of them.
..1...5..8..4.5..32.......6..6.9.4..4..231..8..8.4.3..6.......99..1.3..4..2...1..

hobiwan · Posted: Sat Jun 21, 2008 6:06 pm Post subject:

kyriako · Posted: Sat Jun 21, 2008 7:02 pm Post subject: Nice Loop implementation

Thank you Friends,

Henk, I will have a look at your puzzle. Thank you.

hobiwan, what kind of solver do you use?

Meanwhile, I have included this strategy in my own solver.
Free download here:
http://homepages.compuserve.de/meinelg

Regards,
Kyriakos.

hobiwan · Posted: Sun Jun 22, 2008 8:22 pm Post subject: Re: Nice Loop implementation

daj95376 · Posted: Sat Jun 28, 2008 7:10 pm Post subject:

kyriako · Posted: Sun Jun 29, 2008 8:13 pm Post subject: Nice Loop: use cell twice?

Hello daj95376,

meanwhile I handle the situation of hitting an occupied cell by stepping back and branching elsewhere. If this doesn't end up successfully, the program would step further back, finally landing at the cell in question, from where it proceeds in a different direction.
This way, I believe, I cover all possibilities without too many unnecessary links.

Perhaps a silly question:
the code that you present here, have you typed it manually or is there a program producing this kind of code?

Guenter(Kyriakos).