The New Sudoku Players' Forum

by **PIsaacson** » Mon Oct 27, 2008 1:06 pm

Dear StrmCkr,

Forgive me in advance for asking here:

Is your constraint theory similar to subset counting, or more like Allan Barker's base/cover link-set logic (which I'm still trying to comprehend). Thanks to working on distributed-disjoint-subsets, which you greatly helped me with suggestions/advice, subset counting at least makes sense to me from a programming pov. Trying to figure out how to find all base/cover sets of (what seems like) potentially anything gives me headaches.

by **udosuk** » Thu Oct 30, 2008 7:05 pm

ronk wrote:
udosuk wrote:
Code: Select all
+----------+----------+-------------------+ | . . . | . . . | . . . | | . . . | . X . | . 29 . | | . . . | . . . | . . . | +----------+----------+-------------------+ | . . . | . . . | . 12589 . | | . . . | . 29 . | 12589 12589 12589 | | . . . | . . . | . 12589 . | +----------+----------+-------------------+ | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +----------+----------+-------------------+ X <> 2,9

(The mechanism is similar to Empty Rectangle but not quite the same.)

If there is no ER, where is your strong link

The grouped strong link is at r46c8+r5c789 (or alternatively, r456c8+r5c79), which disallows r2c8+r5c5 to be both 2s or both 9s, thus eliminating r2c5 from being 2 or 9.

Compared to the following ER:

Code: Select all: +----------+----------+-------------------+ | . . . | . . . | . . . | | . . . | . 29 . | . Y . | | . . . | . . . | . . . | +----------+----------+-------------------+ | . . . | . . . | . 12589 . | | . . . | . 29 . | 12589 12589 12589 | | . . . | . . . | . 12589 . | +----------+----------+-------------------+ | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +----------+----------+-------------------+ Y <> 2,9

Alternatively, we can view the ER above as a grouped turbot fish:

Grouped strong link: r456c8+r5c79 must have 2
Strong link: r25c5 must have 2
Weak link: r5c5 & r5c79 can't both contain 2
If r5c5<>2, r2c5=2
If r5c79<>2, r456c8 have 2
=> r2c8 can't be 2

Same argument on digit 9.

:idea:

by **daj95376** » Thu Oct 30, 2008 7:18 pm

My guess is that udosuk is talking in terms of the classic Empty Rectangle solving technique, and ronk is thinking in terms of the Empty Rectangle pattern. Apples and oranges!!!

by **ronk** » Fri Oct 31, 2008 2:39 am

udosuk wrote:The grouped strong link is at r46c8+r5c789 (or alternatively, r456c8+r5c79), which disallows r2c8+r5c5 to be both 2s or both 9s, thus eliminating r2c5 from being 2 or 9.

Thanks, I finally see your POV. For a locked set ("LS"), all candidates must ultimately be placed exactly once. That makes for an interesting nice loop expression:

r2c5 -2- r5c5 -9- LS:(r5c789 =9|1458|9= r456c8) -9- r2c8 -2- r2c5 ==> r2c5<>2

Note: To be read right-to-left also, r5c8 is included twice.

Personally, I would just apply the locked set in box 6, and use the resultant ERs in two w-wings ... as (I believe) you suggested earlier.

by **udosuk** » Fri Oct 31, 2008 4:49 pm

ronk, I see your usage of "locked set" in here but it's not the necessary condition - you only need the two candidates (2 & 9) to be locked in those 5 cells as a condition.

For example, the following also works:

Code: Select all: +----------+----------+-------------------------------+ | . . . | . . . | . . . | | . . . | . X . | . 29 . | | . . . | . . . | . . . | +----------+----------+-------------------------------+ | . . . | . . . | 1345678 123456789 1345678 | | . . . | . 29 . | 123456789 123456789 123456789 | | . . . | . . . | 1345678 123456789 1345678 | +----------+----------+-------------------------------+ | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | +----------+----------+-------------------------------+ X <> 2,9

by **StrmCkr** » Fri Oct 31, 2008 5:34 pm

ronk, I see your usage of "locked set" in here but it's not the necessary condition - you only need the two candidates (2 & 9) to be locked in those 5 cells as a condition

correct

heres a hybrids with more degernation.

Code: Select all: *-----------------------------* | . . . | . . . | . . . | | . . . | . X . | . 29 . | | . . . | . . . | . . . | |-------+--------+------------| | . . . | . . . | . 289 . | | . . . | . 29 . | 289 8-9 . | | . . . | . . . | . . . | |-------+--------+------------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | *------------------------------*

the x is still removed as 29's and R5C8 aslo <>9

by **udosuk** » Fri Oct 31, 2008 6:04 pm

StrmCkr, as usual I think you're making things way more complicated than they should be.

StrmCkr wrote:
Code: Select all
*-----------------------------* | . . . | . . . | . . . | | . . . | . X . | . 29 . | | . . . | . . . | . . . | |-------+--------+------------| | . . . | . . . | . 289 . | | . . . | . 29 . | 289 8-9 . | | . . . | . . . | . . . | |-------+--------+------------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | *------------------------------*

the x is still removed as 29's and R5C8 aslo <>9

It is in fact just a simple intersection/locked candidate elimination:
8 @ r5,b6 locked @ r5c78
Naked pair: r24c8={29}
=> r5c8<>9

StrmCkr wrote:
Code: Select all
*-----------------------------* | . . . | . . . | . . . | | . . . | . X . | . 29 . | | . . . | . . . | . . . | |-------+--------+------------| | . . . | . . . | . 289 . | | . . . | . 29 . | 28 89 . | | . . . | . . . | . . . | |-------+--------+------------| | . . . | . . . | . . . | | . . . | . . . | . . . | | . . . | . . . | . . . | *------------------------------*

this one degernates completly

8 @ c8,b6 locked @ r45c8
=> r5c578=[928]
=> r24c8=[29]

:idea:

by **ronk** » Fri Oct 31, 2008 6:06 pm

udosuk wrote:you only need the two candidates (2 & 9) to be locked in those 5 cells as a condition.

Then it's already an ER.

Either you know it's an ER or you don't; make up your mind.

by **udosuk** » Fri Oct 31, 2008 6:12 pm

ronk wrote:
udosuk wrote:you only need the two candidates (2 & 9) to be locked in those 5 cells as a condition.

Then it's already an ER.

Either you know it's an ER or you don't; make up your mind.

The pattern in the block (b6 here) has the same pattern as an ER (namely r46c79 doesn't contain the two candidates involved), but the actual elimination mechanisms are different. In the (classical) ER, e.g. you use the strong link @ r25c5 (if there is one) to eliminate the candidate(s) from r2c8. In this move however you use the fact that r2c8+r5c5 are both from {29} to eliminiate the candidates from r2c5.

I think you need to distinguish between ER as a solving technique or a pattern.

by **ronk** » Fri Oct 31, 2008 6:18 pm

udosuk wrote:I think you need to distinguish between ER as a solving technique or a pattern.

You can think what you want ... but I'm done with this word game.

by **StrmCkr** » Thu Dec 18, 2008 5:28 pm

alirghty i found one for udosuks examples from the top1465
#129

Code: Select all: *-----------* |.13|5..|...| |...|.7.|4..| |...|...|...| |---+---+---| |1..|...|.89| |2.4|.6.|...| |7..|...|...| |---+---+---| |.8.|1..|...| |6..|...|2..| |...|9.3|...| *-----------*

Code: Select all: *-----------------------------------------------------------------------------* | 48 1 3 | 5 9 248 | 78 267 2678 | | 589 256 256 | 268 7 128 | 4 12359 12358 | | 4589 24567 2567 | 2468 3 1248 | 1589 1259 1258 | |-------------------------+-------------------------+-------------------------| | 1 36-5 56 | 247 45@ 2457 | 3567 8 9 | | 2 359 4 | 78 6 5789 | 1357 157 157 | | 7 569 8 | 3 1 59 | 56 24 24 | |-------------------------+-------------------------+-------------------------| | 3 8 279 | 1 245@ 6 | 579 4579 457 | | 6 45@ 19 | 47@ 8 57@ | 2 139 13 | | 45 27 127 | 9 245@ 3 | 1578 14567 145678 | *-----------------------------------------------------------------------------*

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