The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..3|...|4..|
 |..7|.8.|53.|
 |...|25.|..1|
 |---+---+---|
 |.2.|1..|.6.|
 |..5|6.8|3..|
 |.6.|..4|.1.|
 |---+---+---|
 |8..|.62|...|
 |.52|.7.|6..|
 |..1|...|7..|
 *-----------*
..3...4....7.8.53....25...1.2.1...6...56.83...6...4.1.8...62....52.7.6....1...7..



Play/Print this puzzle online

[SpAce]

Code: Select all

.------------------.---------------.-----------------------.
| 5    89    3     | 79   1    679 |    4      289   2689  |
| 2    1     7     | 4    8    69  |    5      3     69    |
| 49  c489   6     | 2    5    3   |   c89     7     1     |
:------------------+---------------+-----------------------:
| 37   2    a4[89] | 1    3-9  57  | ad[8(9)]  6     458-9 |
| 1   b49    5     | 6    2    8   |    3      49    7     |
| 37   6     89    | 57   39   4   |    2      1     589   |
:------------------+---------------+-----------------------:
| 8    7     49    | 359  6    2   |    1      459   349   |
| 49   5     2     | 389  7    1   |    6      489   3489  |
| 6    3     1     | 589  4    59  |    7      2589  289   |
'------------------'---------------'-----------------------'

(98=4)r4c73 - r5c2 = (48-9)r3c27 = (9)r4c7 => -9 r4c59; stte

[SteveG48]

Code: Select all

 *-----------------------------------------------------------*
 | 5     8-9   3     |c79    1     679   | 4     289   2689  |
 | 2     1     7     | 4     8     69    | 5     3     69    |
 | 49    489   6     | 2     5     3     | 89    7     1     |
 *-------------------+-------------------+-------------------|
 | 37    2     489   | 1     39    57    |b89    6     4589  |
 | 1    a49    5     | 6     2     8     | 3    b49    7     |
 | 37    6     89    |c57    39    4     | 2     1    b589   |
 *-------------------+-------------------+-------------------|
 | 8     7     49    | 359   6     2     | 1     459   349   |
 | 49    5     2     | 389   7     1     | 6     489   3489  |
 | 6     3     1     | 589   4     59    | 7     2589  289   |
 *-----------------------------------------------------------*


9r5c2 = (985)b6p159 - (5=79)r16c4 => -9 r1c2 ; stte

[eleven]

Similar to SpaCe:

Code: Select all

 *-------------------------------------------------------------*
 |  5    89    3     |  79    1    679   |  4    289    2689   |
 |  2    1     7     |  4     8    69    |  5    3      69     |
 | #49   489   6     |  2     5    3     | b89   7      1      |
 |-------------------+-------------------+---------------------|
 |  37   2   c#49+8  |  1     39   57    |ca89   6      4589   |
 |  1    49    5     |  6     2    8     |  3    49     7      |
 |  37   6     89    |  57    39   4     |  2    1      589    |
 |-------------------+-------------------+---------------------|
 |  8    7    #49    |  359   6    2     |  1    459    349    |
 | #49   5     2     |  389   7    1     |  6    489    3489   |
 |  6    3     1     |  589   4    59    |  7    2589   289    |
 *-------------------------------------------------------------*

Almost remote pair 49.
9r4c7 = r3c7 - 9r3c1 == 89r4c37

[Edit: see below]

[SpAce]

Hi eleven,

Almost remote pair 49.

That's perhaps a bit misleading name. You do have an almost-RP but I don't think it's really used as such (normally at least). More like a teleporting and transformation mechanism?

9r4c7 = r3c7 - (9=4)r3c1 == 89r4c37

Can't have adjacent strong links. If you replace the latter '==' with '->' the logic should work (both ways). Not standard Eureka, perhaps, but who's managing the standard? We are, I'd think! I've been wanting to add the implication symbol for a while now anyway. I don't think it breaks the AIC logic or spirit at all, if used correctly and sparingly (I think I've previously argued against it, but looks like I've changed my mind). Of course it adds a new detail to the learning curve.

The same idea using an X-Chain teleport:

(98=4)r4c37 - (4=9)r7c3 -> (9)r4c7 => -9 r4c59

Without the implication we need an extra link and node:

(98=4)r4c37 - (4=9)r7c3 - r8c1 == (9)r4c7 => -9 r4c59

...or one fewer:

(98=4)r4c37 - (4)r7c3 == (9)r4c7 => -9 r4c59

[eleven]

You are right, it was incorrect.
I had it the way 9r4c7 = r3c7 - 9r3c1 == 89r4c37, but then thought, the (9=4) would make it clearer. Sorry for my sloppy AIC usage.
And yes, it's not really, what usually would be called an almost remote pair, where the remote pair and the extra candidate(s) lead to a common elimination.
And of course the RP could be replaced by a simple chain. However i saw it and looked, what i could do with it.

[SpAce]

I had it the way 9r4c7 = r3c7 - 9r3c1 == 89r4c37, but then thought, the (9=4) would make it clearer. Sorry for my sloppy AIC usage.

Not a problem. I'm sure no one thought you didn't know better! Besides, I already guessed how it happened, because you're right that the (9=4) term does make it clearer. However, with that we actually have another option that I didn't think earlier. You could follow with a derived weak link:

9r4c7 = r3c7 - (9=4)r3c1 -- (4=89)r4c37 => -9 r4c59

And yes, it's not really, what usually would be called an almost remote pair, where the remote pair and the extra candidate(s) lead to a common elimination. And of course the RP could be replaced by a simple chain. However i saw it and looked, what i could do with it.

Again, not a problem at all. I like to see creative ways to use grid elements and to present the logic. For example, Dan's recent compact expressions gave food for thought. Here's one (overly compact) way to use his approach here:

(4|9)r8c1 -> (9)r4c7|(89)r4c37 => -9 r4c59

Not really what I would recommend, as it hides all the intermediate logic, but it's an interesting perspective. It does show the essential ingredients, which should be enough for an advanced player to figure out the rest. Here's the same idea with a different starting truth and fuller logic:

(9)r38c1 - (9)r3c7&(94)r74c3 = (9)r4c7|(89)r4c37 => -9 r4c59

Both of them are basically compact krakens, not AICs, so that's how they should be read (which is not necessarily obvious). They're very easy to turn into valid AICs, however. Just add a contradiction node to the beginning:

[!] = (9)r38c1 - (9)r3c7&(94)r74c3 = (9)r4c7|(89)r4c37 => -9 r4c59

In practice, that contradiction node can be left out, because it's implied if the starting node is a known truth, but it makes it easier to read for someone used to normal AICs which have an OR relationship between the start and the end nodes (the reversed chain makes more sense then too). One problem with omitting it is that some people start some of their AICs with assumptive weak links (which I hate), so there's room for confusion if it's not immediately clear which style is being used.

You've sometimes used that "compact kraken" style as well. I've been eager to rewrite them as AICs (mostly because I like such exercises), but for practical purposes I don't think that's necessary or always even a good idea. Sometimes the alternate expression is way simpler.