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| Bob Hanson
| Joined: 05 Oct 2005 | Posts: 187 | : | Location: St. Olaf College | Items |
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Posted: Sun Dec 04, 2005 12:16 am Post subject: simple intersection picture of Sudoku |
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I offer here a simple picture of all
basic methods. The picture is one of
INTERSECTING sets. The principle behind
all these methods is simply that if
a candidate is located only in the
intersection area of one of two overlapping
sets, then it is solely in the
intersection area of the other set as
well.
The statement is this:
If a candidate k is possible in area A^B (A intersect B)
and not elsewhere in A, then k can be eliminated from
any other position in B as well.
Code: |
---------------
| A |
| |
| |
| ---------------
| | k | |
| | A^B | k |
| | k| k |
--------------- |
| k |
| k |
| k B |
---------------
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implies
Code: |
---------------
| A |
| |
| |
| ---------------
| | k | |
| | A^B | |
| | k| |
--------------- |
| |
| |
| B |
---------------
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Methods involving more than one candidate simply
require more than one A and/or more than one B.
Code: |
method A B candidate
singles row col k
col row k
block cell k
locked block row k
candidates block col k
tuples row (col)n (k)n
col (row)n (k)n
block (cell)n (k)n
X-wing (row)2 (col)2 k
swordfish (row)3 (col)3 k
n-grid (row)n (col)n k
uniqueness? (row)n (col)n (k)n
--------- 4x4 Sudoku or larger ---------
n-locked (block)n (row)n k
candidates (block)n (col)n k
uniqueness? (block)n (row)n (k)n
(block)n (col)n (k)n
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[edited 12/4/2005 ot add uniqueness -- not sure on this] _________________ Bob Hanson
Professor of Chemistry
St. Olaf College
Northfield, MN
http://www.stolaf.edu/people/hansonr
Last edited by Bob Hanson on Sun Dec 04, 2005 7:53 am; edited 2 times in total |
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| dukuso
| Joined: 14 Jul 2005 | Posts: 424 | : | Location: germany | Items |
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Posted: Sun Dec 04, 2005 4:23 am Post subject: |
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wondering, how this translates into exact (cover) speak.
trying:
Let C1,C2 be sets of columns and R1 a set of rows,
if R1/\N(C1)/\N(C2) != {}
and R1/\(N(C1)-N(C2))={}
and r in N(C2)-N(C1) then r can be removed
but R1,C1,C2 must probably have some properties...
(hope I can edit and improve this later) |
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| Bob Hanson
| Joined: 05 Oct 2005 | Posts: 187 | : | Location: St. Olaf College | Items |
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| dukuso
| Joined: 14 Jul 2005 | Posts: 424 | : | Location: germany | Items |
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