R8C1<>6 =>R1C1=6 => R3C9=6
R8C1 = 6 => R8C456789 <> 6 => either R7C7 or R9C7 = 6 => R1C7 <>6 => R3C9=6
There.
Stuartn
http://www.brightonandhove.org/sudolinks.htm
Wolfgang wrote:oops, i didnt enter the 6 in the 5 other boxes:
R8C1<>6 =>R1C1=6 ?
... => either R7C7 or R9C7 = 6 => ...
this was the question: is that a forcing chain?
6 6 6 | 6 6 6 | 6 . .
. . 6 | 6 6 6 | . . .
. . 6 | 6 6 6 | . . 6
---------+---------+---------
6 6 6 | 6 6 6 | 6 6 6
6 6 6 | 6 6 6 | 6 6 6
6 6 6 | 6 6 6 | 6 6 6
---------+---------+---------
. . . | 6 6 6 | 6 . .
6 . . | 6 6 6 | 6 6 6
. . 6 | 6 6 6 | 6 . .
Wolfgang wrote:Bunnybuck wrote:There is also another trick to colouring, whereby you start case1 with one of the pair of candidate in a unit, finish the chain, and start case2 with a candidate of a different pair of which has NOT been used.
... when from (n in A) follows that (n in B), it does not follow from (n not in A), that (n not in B). I.e. if it is possible that (n not in A) and (n in B), you cannot conclude anything further.
. . . | . . . | . . .
2 . +2 |(2) . (2)| . . .
. [2] . | 2 . 2 | . . .
---------+---------+---------
. -2 . | . +2 . | . . .
. . . | . . . | . . .
+2 . . | . -2 . | . . .
---------+---------+---------
. [2] . | 2 . 2 | . . .
2 . 2 | 2 . . |+2 . .
. +2 . | . . . |-2 . .
So your sample with the 2's also is not correct. Eg it is possible that 2 is in r7c2 (which you eliminated)
- Code: Select all
. . . | . . . | . . .
. . 2 | . . . | . . .
. . . | . . 2 | . . .
---------+---------+---------
. . . | . 2 . | . . .
. . . | . . . | . . .
2 . . | . . . | . . .
---------+---------+---------
. 2 . | . . . | . . .
. . . | 2 . . | . . .
. . . | . . . | 2 . .
[/quote][x&y] is the intersection of units x and y.
[R9&C3]=6 => [B1&C3]<>6 => [B1&R1]=6 => [B3&R1]<>6 => [R3&C9]=6
[R8&C1]=6 => [B9&R8]<>6 => [B9&C7]=6 => [B3&C7]<>6 => [R3&C9]=6
Bunnybuck wrote:Hence if we were to complete the entire logic chain with (2) included, it would be as follow:
2 in r8c7 => 2 in r9c2 => 2 in r6c1 => 2 NOT in r4c2
Bunnybuck wrote:Now if we combine the contrapositive of the simplified equation, ie. 2 in r4c2 => 2 NOT in r8c7 together with (1), we will have:
2 in r4c2 => 2 in r8c7
. . . | 3 . . | . 3 .
. . . | . . . | . . .
. . . | . 3 . | . 3 3
------+-------+------
3 . . | . 3 . | . 3 .
3 . . | . . 3 | . . 3
3 . 3 | . 3 . | . . .
------+-------+------
. . 3 | . . 3 | . . .
3 . 3 | 3 . . | . . .
. . . | . . . | . . .
Nick70 wrote:Surely you mean 2 in r4c2 => 2 NOT in r8c7
Bunnybuck wrote:2 in r8c7 => 2 in r9c2 ...
Your pattern DOES seem possible, however there MUST be some clues as a result of the position of 2s in block(1,3) and block(2,3), which will eliminate the possibility of this pattern.
. . . | . . . | . . 2
. . 2 | . . . | . . .
. . . | . . 2 | . . .
---------+---------+---------
. . . | . 2 . | . . .
. . . | . . . | . 2 .
2 . . | . . . | . . .
---------+---------+---------
. 2 . | . . . | . . .
. . . | 2 . . | . . .
. . . | . . . | 2 . .
Nick70 wrote:B6R5=3 => B5R5<>3 => B5C6=3 => B2C6<>3
Wolfgang wrote:i like the notation, but i am still confused, what a forcing chain is and what not. Do you have a notation that makes use of pairs also ? Something for
r3c9=7 => r3c1={8,9}
with r1c2={8.9}
-> r2c1<>9
Wolfgang wrote:i could not find a good definition for (simple, double, multiple ..) forcing chains.
Wolfgang wrote:Are some "auxiliary logical steps" allowed?
Wolfgang wrote:Must one node follow directly from the preceding alone or maybe from all steps before (eg when you have A{1.2}B{1,3}C{1,2,3}, how do you call a forcing chain A=1->B=3->C=2)?