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BUG Pattern

 
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA
PostPosted: Thu Jul 20, 2006 11:52 pm    Post subject: BUG Pattern Reply with quote
I am curious how "big" the BUG pattern usually is. The first BUG pattern I found (earlier this week) was big (I think). While I solved it, I needed help explaining why I solved it because there are so few matched pairs and the basic explanations I read didn't make the logic readily discernable. It has a twenty-two cell finish. It was also a pretty good puzzle getting to that point. I put it below, in case anyone is interested. In any event, my question is, is that an uncommonly big BUG?

000107000
006090700
070206080
701000204
040000050
502000903
010504090
005020300
000603000

You can also print it by going to the June 20 Super Hard from the link below:

http://www.brainbashers.com/sudoku.asp

PS: This explanation would have helped me:

You cannot have a situation where there are only two cells in any row, column or block that can host each of the remaining numbers. Two candidates in the the three-candidate cell will always violate the rule in a valid puzzle.

I'm sure it could be more artfully worded, but I think you catch my drift.
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ravel



Joined: 21 Apr 2006
Posts: 536
PostPosted: Fri Jul 21, 2006 8:00 am    Post subject: Reply with quote
Nice puzzle.
I can only confirm, that the BUG is uncommonly big, in average there are much less cells unresolved, when a BUG+1 arises (maybe 12 or 15 ?). But i dont know any statistics.

[Edit:] In the other forum i found this one posted by tso in this thread.
Code:
 . . . | 7 . 3 | . 5 .
 . . . | 2 1 . | . . .
 3 . 6 | . 8 . | . . .
-------+-------+------
 6 . 9 | . . . | . 2 5
 . . 3 | . . . | 6 . .
 5 4 . | . . . | 8 . 3
-------+-------+------
 . . . | . 3 . | 7 . 1
 . . . | . 6 7 | . . .
 . 1 . | 9 . 5 | . . .

  18   29   18   | 7    49   3    | 24   5    6
  47   5    47   | 2    1    6    | 9    3    8
  3    29   6    | 5    8    49   | 124  14   7
 ----------------+----------------+-------------
  6    8    9    | 3    7    14   | 14   2    5
  12   7    3    | 48   5    28   | 6    14   9
  5    4    12   | 6    29   19   | 8    7    3
 ----------------+----------------+-------------
  24   6    5    | 48   3    28   | 7    9    1
  9    3    24   | 1    6    7    | 5    8    24
  78   1    78   | 9    24   5    | 3    6    24

You need an xy-wing, x-wing and the elimination of 4 in r5c9 with turbot fish (coloring) to get there. (There are other turbot fishes around, which would lead to different grids)

btw: this is the only puzzle i had so far with a BUG+2 (2 cells with 3 candidates, eliminating the same one from both would lead to a BUG).
Code:
 +-------+-------+-------+
 | . . . | 9 . . | . . . |
 | . . 2 | . . 4 | 9 6 8 |
 | . 5 . | . . 6 | . . . |
 +-------+-------+-------+
 | 7 . . | 2 . 3 | . . . |
 | 6 8 3 | 7 . 9 | 5 4 . |
 | . . . | 4 . . | . . 7 |
 +-------+-------+-------+
 | . . . | 6 . . | . . 5 |
 | . . . | 8 . 2 | . . 6 |
 | . . . | . . . | 4 3 . |
 +-------+-------+-------+
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AZ Matt



Joined: 03 Nov 2005
Posts: 63
Location: Hiding under my desk in Phoenix AZ USA
PostPosted: Fri Jul 21, 2006 8:41 pm    Post subject: Another Big BUG Reply with quote
Today's (July 21) BrainBasher's Super Hard has a twenty-cell BUG pattern that has triple, quad, and even quint sets.

Perhaps big BUGs aren't all that uncommon.
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David Bryant



Joined: 29 Jul 2005
Posts: 559
Location: Denver, Colorado
PostPosted: Fri Jul 21, 2006 10:40 pm    Post subject: Finding BUGs Reply with quote
AZMatt wrote:
000107000
006090700
070206080
701000204
040000050
502000903
010504090
005020300
000603000

I didn't find a BUG in this one. After locating the X-Wing on "4"s I reached this position.
Code:
  9     25    8     1     4     7     56    3     26
  13    25    6     38    9     58    7     4     12
  13    7     4     2     35    6     15    8     9
  7     3     1     89    58   589    2     6     4
  6     4     9     37    37    2     18    5     18
  5     8     2     4     6     1     9     7     3
  2     1     3     5     78    4     68    9    678
  4     6     5    789    2     89    3     1     78
  8     9     7     6     1     3     4     2     5

At this point I noticed that r7c7 = 8 is impossible, because it forces two "5"s into row 3:

A. r7c7 = 8 ==> r5c7 = 1 ==> r3c7 = 5
B. r7c7 = 8 ==> r7c5 = 7 ==> r5c5 = 3 ==> r3c5 = 5

With r7c7 = 6 the rest of the puzzle crumbles.

Most "BUG" puzzles are like this one, in my experience. I often fail to find the "BUG" pattern because I start using double-implication chains as soon as I see a large number of bi-valued cells emerging. Anyway, when I have found "BUG"s, they've tended to run between 9 and 30 unresolved cells, with most of them falling in the 11 - 15 range. dcb
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