## Between Uniqueness and BUG: BUG Lite

Advanced methods and approaches for solving Sudoku puzzles
ronk wrote:
Havard wrote:I tried to construct a BUG-lite grid on this puzzle (...)
Code: Select all
`7     3     26*   | 26*   4     9     | 1     8     515*   9     16*   | 8     7     56+2* | 3     4     2628*   58*   4     | 3     1     56*   | 7     26*   9------------------+-------------------+------------------28*   18*   12*   | 7     9     4     | 6     5     39     6     7     | 5     2     3     | 8     1     43     4     5     | 1     6     8     | 2     9     7------------------+-------------------+------------------4     7     3     | 26*   5     1     | 9     26*   815*   15*   8     | 9     3     26    | 4     7     266     2     9     | 4     8     7     | 5     3     1`

The fundamental rule for both BUG and BUG-Lite grids is the same, the deadly pattern has each candidate appearing exactly twice in each row, col, and box. While the BUG involves the entire grid, the BUG-Lite involves only a portion.

Yes, but if you examine my BUG-Lite, you will see that each candidate appears exactly twice in each row, col and box. The additional constraint which I obviously have not caught from reading this thread, I think is that all occurences of a single number in the pattern can not appear in more than n boxes, where n is the number of candidates divided by two. In other words: This BUG-Lite pattern is not valid because there are 8 6's, and 8 2'6 in the pattern, but they are distributed over 5 and 6 boxes respectively. If it were to be a valid BUG-Lite, they could not have been distributed over more than 4 boxes (8/2=4) Any thoughts?

Havard
Havard

Posts: 377
Joined: 25 December 2005

or to make it even clearer, what is wrong with this BUG-Lite-pattern?:
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`            26*   | 26*               |        15*         16*   |             56*   |               28*   58*         |             56*   |       26*     ------------------+-------------------+------------------ 28*   18*   12*   |                   |                   |                   |                   |                   | ------------------+-------------------+------------------                   | 26*               |       26*    15*   15*         |                   |                  |                   | `

Havard
Havard

Posts: 377
Joined: 25 December 2005

Havard wrote:or to make it even clearer, what is wrong with this BUG-Lite-pattern?

Among other things ... boxes 3, 8, and 9 each need another instance of both digits 2 and 6.

[edit: did not intend to repost the grid]
Last edited by ronk on Sat May 06, 2006 9:15 pm, edited 1 time in total.
ronk
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Location: Southeastern USA

ronk wrote:
Havard wrote:or to make it even clearer, what is wrong with this BUG-Lite-pattern?:
Code: Select all
`            26*   | 26*               |        15*         16*   |             56*   |               28*   58*         |             56*   |       26*     ------------------+-------------------+------------------ 28*   18*   12*   |                   |                   |                   |                   |                   | ------------------+-------------------+------------------                   | 26*               |       26*    15*   15*         |                   |                  |                   | `

Havard

Among other things ... boxes 3, 8, and 9 each need another instance of both digits 2 and 6.

Thanks. How does the (all occurences of single digit)/2 >= (nr of boxes where that digit is) - rule sound to you?

Havard
Havard

Posts: 377
Joined: 25 December 2005

Does these ones look good?

(From MJ's MUG-puzzle a bit back in this thread)
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`148   48    5     | 7     14    2     | 3     9     614    6     2     | 9     3     14    | 5     7     89     7     3     | 8     6     5     | 4     1     2------------------+-------------------+------------------3     1     9     | 2     8     6     | 7     4     55     28*   6     | 14    7     14    | 28*   3     948    28+4* 7     | 5     9     3     | 6     28*   1------------------+-------------------+------------------26    9     8     | 346   24    7     | 1     5     3427    5     4     | 13    12    8     | 9     6     3767    3     1     | 46    5     9     | 28*   28*   4714*   8     5     | 7     14*   2     | 3     9     614*   6     2     | 9     3     14*   | 5     7     89     7     3     | 8     6     5     | 4     1     2------------------+-------------------+------------------3     1     9     | 2     8     6     | 7     4     55     2     6     | 14*   7     14*   | 8     3     98     4     7     | 5     9     3     | 6     2     1------------------+-------------------+------------------26*   9     8     | 36+4* 24*   7     | 1     5     34*27*   5     4     | 13*   12*   8     | 9     6     37*67*   3     1     | 46*   5     9     | 2     8     47*`

Havard
Havard

Posts: 377
Joined: 25 December 2005

Havard wrote:How does the (all occurences of single digit)/2 >= (nr of boxes where that digit is) - rule sound to you?

I think that would be "equals" instead of "greater than or equals". But that's just one-third of the requirement that each digit occur exactly twice in each row, col, and box ... of the BUG-Lite pattern or the entire BUG grid.
ronk
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Location: Southeastern USA

ronk wrote:
Havard wrote:How does the (all occurences of single digit)/2 >= (nr of boxes where that digit is) - rule sound to you?

I think that would be "equals" instead of "greater than or equals". But that's just one-third of the requirement that each digit occur exactly twice in each row, col, and box ... of the BUG-Lite pattern or the entire BUG grid.

Yup! Get it now. Thanks!

(ps. do you think I am entitled to the "my-bug-is-bigger-than-yours"-award with this one? )
Code: Select all
`14*   8     5     | 7     14*   2     | 3     9     6 14*   6     2     | 9     3     14*   | 5     7     8 9     7     3     | 8     6     5     | 4     1     2 ------------------+-------------------+------------------ 3     1     9     | 2     8     6     | 7     4     5 5     2     6     | 14*   7     14*   | 8     3     9 8     4     7     | 5     9     3     | 6     2     1 ------------------+-------------------+------------------ 26*   9     8     | 36+4* 24*   7     | 1     5     34* 27*   5     4     | 13*   12*   8     | 9     6     37* 67*   3     1     | 46*   5     9     | 2     8     47* `

Havard
Havard

Posts: 377
Joined: 25 December 2005

Havard wrote:Does these ones look good?

Yes. The first is a BUG-Lite+1, as in 1 cell of the BUG-Lite pattern having extra candidate(s). The second is a BUG+1.

If one takes the stance that a BUG-Lite pattern can be of any size, then your BUG+1 can correctly -- but not precisely -- be considered a BUG-Lite pattern too.
Last edited by ronk on Sat May 06, 2006 9:50 pm, edited 1 time in total.
ronk
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That's it! I'm off Bug-hunting! I'll report back on any funny specimen later!

Havard
Havard

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Joined: 25 December 2005

Havard wrote:ps. do you think I am entitled to the "my-bug-is-bigger-than-yours"-award with this one?

Nope. Myth Jellies posted one with 23 cells here.
ronk
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Not too happy about the +3... We should at least have different classes for the different BUG-lites.

so... MJ has a solid lead in the BUG-lite+3 department! The competition is on to find the biggest BUG-lites there is!

Honour and eternal glory to the ones how can produce the biggest BUG's in the categories:

BUG-Lite+1
BUG-Lite+2
BUG-Lite+3

The only rule is (one I recently tried to break myself) that the BUG-Lite can NOT also be a "ordinary" BUG of the same type (+1 etc)

Havard
Havard

Posts: 377
Joined: 25 December 2005

Havard wrote:Honour and eternal glory to the ones how can produce the biggest BUG's in the categories:

BUG-Lite+1
BUG-Lite+2
BUG-Lite+3

"Most simultaneous BUG-lite reductions in a grid"

I'd like to make a submission to the category I just started myself

top1465 #206
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` *--------------------------------------------------------------------* |x58     4      6      | 9      3     x28     | 1      7     x25     | | 9      2      7      | 4      5      1      | 8     #36    #36     | |x58     1      3      | 6     x28     7      | 4     x25     9      | |----------------------+----------------------+----------------------| | 3      59     1      | 57     6      48     | 2      89     47     | | 2      6      8      | 1      79     349    | 5      39     47     | | 7      59     4      | 35    x28    x28+39  |#36    #13689 #1368   | |----------------------+----------------------+----------------------| | 6      8     x25     | 37     1      39     | 79     4     x25     | |*14    *37     9      | 2     *47     5      |#367   #1368 #*13+68  | |*14    *37    x25     | 8     *47+9   6      | 379   x25    *13     | *--------------------------------------------------------------------*`

First 2 complicated (and useless) reductions:

* BUG-lite+2 in r89c1259, extra candidates in r8c9 and r9c5:
2 strong links give if r8c9=1 => r9c5=4 => r8c9<>1

# BUG-lite+"a lot" in r268c789
only possibilities to place either candidate 3 or 6 outside the pattern are 3 in r5c8, r9c7 and r9c9 - r8c5 can see all these cells => r8c5<>3

Then there is of course the 12 cell BUG-lite+1 (marked with x) that removes 2 and 8 from r6c6 and solves the puzzle.

RW
RW
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