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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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 Posted: Mon Apr 28, 2008 9:24 pm Post subject: A question . . . |
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. . . for the cognoscenti. Have a look please, at M4195526 (52) | Code: |
+----------------+--------------+-------------+
| 4 8 13579 | 135 2 157 | 6 13 359 |
| 2 359 1359 | 8 145 6 | 7 134 359 |
| 6 35 1357 | 135 9 1457 | 8 1234 235 |
+----------------+--------------+-------------+
| 5 1 2 | 4 6 8 | 3 9 7 |
| 79 4 6 | 19 17 3 | 5 28 28 |
| 3 79 8 | 59 57 2 | 4 6 1 |
+----------------+--------------+-------------+
| 789 679 4 | 26 13 19 | 29 5 38 |
| 89 2 59 | 7 345 459 | 1 38 6 |
| 1 3569 359 | 26 8 59 | 29 7 4 |
+----------------+--------------+-------------+
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I'm not asking how to do it, for it's easy enough: this is about multi (>2) - digit DPs to which I haven't given much thought. Have a look at r79. If c2 were both 69s we'd have a 69/26/29 DP. So OK to do a sort of type 4 and remove the 9s from c2r79?
What about r13? Any mileage in considering 135/13/35? Or maybe a combination of 1/3/5/7? |
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storm_norm
Joined: 18 Oct 2007
Posts: 1741
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| Posted: Tue Apr 29, 2008 12:06 am Post subject: |
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something like this?? maybe... 
consider columns 4,6,8...
column 4 rows 1,3 would be the {3,5}
column 6 "" would be the {1,5}
column 8 "" would be the {1,3}
| Code: | +----------------+--------------+-------------+
| 4 8 13579 |#135 2 #157 | 6 #13 359 |
| 2 359 1359 | 8 145 6 | 7 134 359 |
| 6 35 1357 |#135 9 #1457 | 8 #1234 235 |
+----------------+--------------+-------------+
| 5 1 2 | 4 6 8 | 3 9 7 |
| 79 4 6 | 19 17 3 | 5 28 28 |
| 3 79 8 | 59 57 2 | 4 6 1 |
+----------------+--------------+-------------+
| 789 679 4 | 26 13 19 | 29 5 38 |
| 89 2 59 | 7 345 459 | 1 38 6 |
| 1 3569 359 | 26 8 59 | 29 7 4 |
+----------------+--------------+-------------+ |
this is only theoretical...so bear with me
so you would have a 6 cell DP on {1,3,5}
but if the cells containing {3,5} in col 4 must have a 1 in one of the cells to break up the DP then the 1 in r5c4 can't be there.
similarily... in r13c6... the cells must contain {4,7} to break up the DP therefore it acts like a naked pair and eliminates the 4 in r8c6
and...
in r3c8, you can eliminate 1 and 3 to break up the DP
something like that??
I can't tell if the 7 can be used, maybe in col 3 somehow.
edit: now that I looked at it again, you can also break up the theoretical DP by removing the 1's in r13c6 because they would have to go in r13c4 |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Tue Apr 29, 2008 12:46 pm Post subject: Re: A question . . . |
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| Victor wrote: | | If c2 were both 69s we'd have a 69/26/29 DP. So OK to do a sort of type 4 and remove the 9s from c2r79? |
Yes, quite right. Seen from the other side, only a 9 in r26c2 can destroy the DP, because no other DP digits are available in the 3 columns. | Quote: | | What about r13? Any mileage in considering 135/13/35? Or maybe a combination of 1/3/5/7? |
Note, that for bivalue DP's each number must be exactly 2 times in each row, column and box (and thats all you need). So storm_norm's pattern is not deadly. But e.g. this is a DP:
| Code: | +-------------+-----------+-----------+
| . . . | 35 . . | . . 35 |
| . 35 . | . . . | . . 35 |
| . 35 . | 35 . . | . . . |
+-------------+-----------+-----------+
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I cant see a DP with trivalue cells in the grid. E.g. this would be one (some of the digits may be missing also):
| Code: | +-------------+-----------+-----------+
| . . 135 | 135 . . | . . . |
| . . 135 | 135 . . | . . . |
| . . 135 | 135 . . | . . . |
+-------------+-----------+-----------+
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Wed Apr 30, 2008 4:46 pm Post subject: |
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Thanks Ravel. I guess that one way to look at multi-digit DPs is to note that the subset within a box must be locked (closed). (I suppose that this is one way in which one could explain why an apparent UR with the 4 cells in 4 boxes is invalid.)
Here, the 135s aren't closed: another cell in that box must have an influence on them.
Presumably you can have multi-digit DPs running round corners, as you've often posted with cells with the same two candidates. E.g. | Code: |
+--------+-------+--------+
| 13 . . | . . . | . 35 . |
| . . . | . . . | . 35 . |
| . . 13| . . . | . . |
+--------+-------+--------+
| . . . | . . . | . . . |
| 15 . 15| . . . | . . . |
| . . . | . . . | . . . |
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E.g. if these were all actually naked apart from one which had an extra number, that would fix that cell (and thus solve all 6).
Or your 35 example could have 3 digits say 13, 35, 15 with the identical pairs in their own box/column and be a valid DP: | Code: |
+--------+--------+--------+
| . . . | . 13 . | . 15 . |
| . 35 . | . . . | . 15 . |
| . 35 . | . 13 . | . . . |
+--------+--------+--------+
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(No doubt this has all been explained / exemplified / discussed elsewhere: but i haven't read such stuff.) |
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Asellus
Joined: 05 Jun 2007
Posts: 865
Location: Sonoma County, CA, USA
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| Posted: Thu May 01, 2008 7:12 am Post subject: |
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Victor,
The patterns you have shown are not DPs. The DP "subsets," as you call them, must be locked within every house in which they are involved: rows and columns as well as boxes.
Look at the discussion in this thread for some comments that may help you figure out the larger and more complex DP patterns. |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Thu May 01, 2008 8:59 am Post subject: |
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Thanks Asellus, that was silly of me. I do get it now.
MOral (for me): think before you write! |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Thu May 01, 2008 10:11 am Post subject: |
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PS. Well, having thought a bit more, I sort of get it. Take the 3-digit example quoted by Ravel as a DP:
| Code: | +-------------+-----------+-----------+
| . . 135 | 135 . . | . . . |
| . . 135 | 135 . . | . . . |
| . . 135 | 135 . . | . . . |
+-------------+-----------+-----------+ |
The subsets are locked within boxes & columns but not rows. So couldn't values in box 3 have an effect on this pattern?
Offhand, I'd have thought that a 3-digit DP would need as a minimum to be in 3 boxes, etc. But a quick glance at MUG references suggests that this isn't right. |
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ravel
Joined: 21 Apr 2006
Posts: 536
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| Posted: Thu May 01, 2008 12:43 pm Post subject: |
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In box 3 the 3 numbers finally must be somewhere in different rows, so you always will end up with something like this:
| Code: | +-------------+-----------+-----------+
| . . 35 | 35 . . | 1 . . |
| . . 15 | 15 . . | . 3 . |
| . . 13 | 13 . . | . . 5 |
+-------------+-----------+-----------+
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This obviously has 2 solutions. |
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Victor
Joined: 29 Sep 2005
Posts: 207
Location: NI
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| Posted: Thu May 01, 2008 11:37 pm Post subject: |
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| Thanks Ravel. !st time I read of a MUG was when Steve R posted about one, and that made sense - seemed obvious even. I've read a little more, but it doesn't seem so easy now. Thanks for your help anyway. |
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