## Forming MUGs from BUG-Lite composites

Advanced methods and approaches for solving Sudoku puzzles

### Re: Forming MUGs from BUG-Lite composites

ronk wrote:gsf's program shows that placements for this pattern ...

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` .     12345 12345 | 12345 .     12345 | .     12345 .    .     .     .     | .     .     .     | .     .     . .     12345 12345 | 12345 .     12345 | .     12345 .   -------------------|-------------------|------------------- .     .     .     | .     .     .     | .     .     .`

... produce only two essentially-different unavoidable sets corresponding to BUG-Lites. Note the absence of URs.

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` . 1 2 | 3 . 4 | . 5 .                . 1 2 | 3 . 4 | . 5 . . . . | . . . | . . .                . . . | . . . | . . . . 3 4 | 5 . 2 | . 1 .                . 3 4 | 2 . 5 | . 1 .-------+-------+-------              -------+-------+------- . . . | . . . | . . .                . . . | . . . | . . .`

r13c36 in first pattern?

Btw. These patterns with two rows in one band are the deadly pattern counterpart to the reverse BUG-lite that I defined a few years ago.
RW
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### Re: Forming MUGs from BUG-Lite composites

Yes I agree that RW's perspective is interesting and useful.

As before, considering the external cells that must hold member digits this diagram shows one possible way that Luke's pattern can be reduced legitimately to leave ordered BUG-Lite pairs.
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`| /   12   34   | 51   /   23   | /   45   /   || (5) .    .    | .    (4) .    | (3) (2)  (1) || /   21   43   | 15   /   32   | /   54   /   |------------------------------------------------| .   (34) (12) | (23) .   (15) | .   (13) .   |`

The ordering of the digits in row 2 is arbitrary as they are all equivalent.
This leaves a requirement for two external digits in each of columns to reduce the pattern to bivalues.
In column 8 (13) are forced as external digits, but there are options regarding how the external cells can be set to hold (1234) in columns 2 & 3 and (1235) in columns 4 & 6. If they are set so that two columns hold the same digit pair we get two BUG-Lites with 4 & 6 cells, otherwise we get a 10-cell BUG-Lite as shown.
David P Bird
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### Re: Forming MUGs from BUG-Lite composites

Rounding off the giant MUGs, here's the six candidate...
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`*------------------*-------------------*------------------*| .  abcdef abcdef | abcdef  .  abcdef | .  abcdef abcdef || .    .      .    |   .     .    .    | .    .      .    || .  abcdef abcdef | abcdef  .  abcdef | .  abcdef abcdef |*------------------*-------------------*------------------*`

...and an example from Sudoku UK's Weekly Extreme #286.

Code: Select all
`.------------------.-------------------.-----------------.| 3     6      27  | 29    1249   5    | 49    147   8   ||*1258 *1258   4   | 2689  1269   7    | 369   16    369 ||*178  *178    9   | 68    146    3    | 2     1467  5   |:------------------+-------------------+-----------------:|*29   *29     6   | 5     8      4    | 7     3     1   ||*1578 *1578   578 | 3     269    269  | 4689  25    469 || 4     58     3   | 269   7      1    | 689   25    69  |:------------------+-------------------+-----------------:| 6     23489   1  | 7     239    289  | 5     48    34  ||*2589 *2589+3 258 | 4     23569  2689 | 1     68    7   ||*578  *578+34 578 | 1     356    68   | 346   9     2   |'------------------'-------------------'-----------------'`

MUG(125789) r234589c12 ==>(4)r9c2=(3)r89c2
(Aside: Is there a way to use this in conjunction with (34)r7c9?)

The seven candidate MUG has already been established here.

Not being much of a theorist, could generalizing the larger one chute MUGs might look like this?

4 digits, 2 rows 3 boxes, 4 columns
5 digits, 2 rows 3 boxes, 5 columns
6 digits, 2 rows 3 boxes, 6 columns
7 digits, 2 rows 3 boxes, 7 columns

Luke
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### Re: Forming MUGs from BUG-Lite composites

Luke451 wrote:...and an example from Sudoku UK's Weekly Extreme #286.

Code: Select all
`.------------------.-------------------.-----------------.| 3     6      27  | 29    1249   5    | 49    147   8   ||*1258 *1258   4   | 2689  1269   7    | 369   16    369 ||*178  *178    9   | 68    146    3    | 2     1467  5   |:------------------+-------------------+-----------------:|*29   *29     6   | 5     8      4    | 7     3     1   ||*1578 *1578   578 | 3     269    269  | 4689  25    469 || 4     58     3   | 269   7      1    | 689   25    69  |:------------------+-------------------+-----------------:| 6     23489   1  | 7     239    289  | 5     48    34  ||*2589 *2589+3 258 | 4     23569  2689 | 1     68    7   ||*578  *578+34 578 | 1     356    68   | 346   9     2   |'------------------'-------------------'-----------------'`

MUG(125789) r234589c12 ==>(4)r9c2=(3)r89c2

Sorry, don't understand your syntax here, but are you suggesting some kind of elimination/placement based on that MUG?

The MUG suggests r89c2 must hold at least one of the digits 34. But you get this same info just by looking at c2, so this one is unfortunately not that useful.

Luke451 wrote:The seven candidate MUG has already been established here.

That seven candidate MUG is my Reverse BUG-lite example from 2006 (first posted here).

Luke451 wrote:Not being much of a theorist, could generalizing the larger one chute MUGs might look like this?

To generalize larger one chute MUGs you would need to include MUGS in 3 rows as well. This is not quite as easy...
RW
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### Re: Forming MUGs from BUG-Lite composites

RW wrote:
Luke451 wrote:MUG(125789) r234589c12 ==>(4)r9c2=(3)r89c2

Sorry, don't understand your syntax here, but are you suggesting some kind of elimination/placement based on that MUG?

No. not a placement, just a strong link. I was fishing for help in making it useful. I really just wanted confirmation that it indeed is a MUG.

I will look into the reverse BUG-Lite idea, thanks for the link, and thanks to everyone for reviving this thread.

Luke
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Location: Southern Northern California

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