Block/block interaction

Bo · Posted: Fri Nov 04, 2005 2:13 pm Post subject: Block/block interaction

The technique block/block interaction essentially says:
If there are two blocks which have the same candidate
in two, shared columns, but not in the 3rd column, then
in a 3rd block this candidate can be removed for those
shared columns.
(The technique is also valid when columns are replaced by rows.)

But there is also another technique saying that if a block (A) has
a candidate in one of its columns and this candidate do
not exist in that column for the other blocks, then the same candidate
in other columns of block A can be removed.

If this latter technique is used, it will always find the candidates to
remove by the block/block interaction technique, because:
1. In block/block interaction, the third column of the blocks having
the common candidate, does not have the candidate (that was in the
prerequisite).
2. In the 3rd column of the 3rd block, this candidate must exist (there
is no other alternative.)

Provided that this latter technique is used (name?) then the
block/block interaction technique is really superflous.
It is not the other way around, the latter technique is not superflous
if block/block interaction is used.

It would be nice if this relationsship between the techniques could be
reflected in the descriptions of solving techniques.

Regards
Bo

Ruud · Site Admin

The 2 techniques you describe are 2 complementary forms of the same technique. There are other techniques that have complementary counterparts, like subset.

I think the best common name would be: Line-Box Interactions.

The definition could be: When all candidates for a given digit within a house are confined to the intersection with another house, all candidates for that digit can be eliminated from the intersecting house, except those that lie within the intersection.

Ruud.

Bob Hanson · Posted: Sat Nov 05, 2005 3:17 am Post subject:

Yes, I agree, these are two aspects of the same thing, and they are both accounted for with no special treatment by "hypothesis and proof":

Bob Hanson · Posted: Sat Nov 05, 2005 4:09 am Post subject:

By the way, the forward logic for this would be:

dukuso · Posted: Sat Nov 05, 2005 9:39 am Post subject:

>If there are two blocks which have the same candidate
>in two, shared columns, but not in the 3rd column, then
>in a 3rd block this candidate can be removed for those
>shared columns.
>(The technique is also valid when columns are replaced by rows.)

>a candidate in one of its columns and this candidate do
>not exist in that column for the other blocks, then the same
>candidate in other columns of block A can be removed.

>When all candidates for a given digit within a house are
>confined to the intersection with another house, all candidates
>for that digit can be eliminated from the intersecting house,
>except those that lie within the intersection.

in exact-cover-speak:
r in R;c in C-N(r);N(N(r))>N(c) => Sol(A)=Sol(A-r)

this is shorter, more exact, covers all the above cases and some others.

see:
http://www.setbb.com/phpbb/viewtopic.php?t=395&sid=42618d4be0d03b99a98f53809ed4bb13&mforum=sudoku

xyzzy · Posted: Sat Nov 05, 2005 3:45 pm Post subject:

Bob Hanson · Posted: Sat Nov 05, 2005 9:37 pm Post subject:

sure, I like that. It's also nice to remember what we are trying to do -- eliminate nodes.
Thanks -- as I prepared this message, using

1.. .5. ..9
... 1.. .3.
..8 ... 2..
.5. ..4 ...
4.. .6. ..8
... 3.. .1.
..2 ... 5..
.3. ..5 ...
7.. .9. ..2

http://www.stolaf.edu/people/hansonr/sudoku/?LOAD=DEFAULTPROOF

(a very nice little puzzle!)

I noticed that the logical statements it was spitting out were not consistent with what was actually being done. Too many binary possibilities for my brain! But it's fixed.
_________________
Bob Hanson
Professor of Chemistry
St. Olaf College
Northfield, MN
http://www.stolaf.edu/people/hansonr