BUG+1 Question

Everything about Sudoku that doesn't fit in one of the other sections

BUG+1 Question

Postby daj95376 » Sat Nov 11, 2006 6:46 am

Code: Select all
 *-----------*
 |...|.9.|8.1|
 |392|..8|...|
 |...|...|.2.|
 |---+---+---|
 |.3.|6..|5.2|
 |6..|.4.|..3|
 |1.9|..3|.4.|
 |---+---+---|
 |.8.|...|...|
 |...|8..|465|
 |4.3|.5.|...|
 *-----------* # original

Code: Select all
# reduced to BUG+1 at [r7c6]
#
# <1> occurs three times in buddy cells to [r7c6]
# <4> occurs twice       in buddy cells to [r7c6]
# <6> occurs twice       in buddy cells to [r7c6]
#
# Simple Sudoku says [r7c6]=4 ... and it solves puzzle!!!
 *--------------------------------------------------*
 | 5    4    67   | 23   9    26   | 8    37   1    |
 | 3    9    2    | 14   17   8    | 67   5    46   |
 | 78   1    68   | 35   67   45   | 39   2    49   |
 |----------------+----------------+----------------|
 | 78   3    4    | 6    18   17   | 5    9    2    |
 | 6    2    78   | 59   4    59   | 1    78   3    |
 | 1    5    9    | 27   28   3    | 67   4    68   |
 |----------------+----------------+----------------|
 | 29   8    5    | 49   26  #146  | 39   13   7    |
 | 29   7    1    | 8    3    29   | 4    6    5    |
 | 4    6    3    | 17   5    79   | 2    18   89   |
 *--------------------------------------------------*

Why isn't [r7c6]=1 correct???
Last edited by daj95376 on Sat Nov 11, 2006 10:49 am, edited 1 time in total.
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Postby wapati » Sat Nov 11, 2006 7:58 am

I cannot get SS to like this puzzle. Check your grid, both of them?
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Postby daj95376 » Sat Nov 11, 2006 8:59 am

On my computer, SS doesn't have any problems with my puzzle or the PM. Don't copy the (#) characters into SS.

I checked to see if I eliminated too many <4> values by accident. I couldn't find an anomaly. Here's the full solution up to the BUG+1.

Code: Select all
r4c3    =  4     Hidden Single
r8c5    =  3     Hidden Single
  c7    -  67    Naked  Pair
  c1    -  578   Naked  Triple
r7c3    =  5     Hidden Single
r9c2    =  6     Hidden Single
    b4  -  78    Naked  Pair
  c2    -  25    Naked  Pair
r8      -  17    Naked  Pair
    b1  -  1     Locked Candidate (1)
r7c6    <> 29    Unique Rectangle Type 1
r4c8    =  9 (2) Forcing Chain/Net on [r7c1]
r7c9    =  7 (2) Forcing Chain/Net on [r7c1]
r5c7    =  1     Naked  Single
r5      -  78    Naked  Pair
r9c6    <> 1     XY-Chain on [r4c6]
r1c1    =  5     [r1c1]=7 => [r7c7]=EMPTY    (hidden,naked) = ( 0,31)
r2c8    =  5     Hidden Single
r1c2    =  4     [r1c2]=7 => [r7c8]=EMPTY    (hidden,naked) = ( 0,28)
r3      -  1678  Naked  Quad
    b3  -  6     Locked Candidate (1)
r3c3    <> 17    Unique Rectangle Type 1
r3c2    =  1     Hidden Single
r8c2    =  7     Naked  Single
r8c3    =  1     Naked  Single
  c38   -  7     X-Wing
r6c5    <> 7     Templates (A)
r5c6    <> 2     XY-Chain on [r1c6]
r5c4    <> 2     XY-Chain on [r1c4]
r5c2    =  2     Hidden Single
r6c2    =  5     Naked  Single
r7c4    <> 2     XY-Chain on [r1c4]
r9c4    <> 2     XY-Chain on [r1c4]
r9c6    <> 2     XY-Chain on [r1c6]
r9c7    =  2     Hidden Single
r3c4    <> 4     XY-Chain on [r3c6]
r9c4    <> 9     XY-Chain on [r5c4]
r2c4    <> 7     XY-Chain on [r2c7]
    b2  -  7     Locked Candidate (1)
r7c4    <> 1     XY-Chain on [r2c4]
r7c5    <> 1     XY-Chain on [r2c5]
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Re: BUG+1 Question

Postby ronk » Sat Nov 11, 2006 12:27 pm

daj95376 wrote:Why isn't [r7c6]=1 correct???

Because there are exactly two 1s in each row, col, and box. Look at the 9s instead.

Your puzzle may not fit the formal BUG+1 definitions, but it surely is one. The extra candidate is just not in the polyvalued cell ... a rarity I suspect.
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Postby RW » Sat Nov 11, 2006 1:11 pm

daj95376 wrote:
Code: Select all
# reduced to BUG+1 at [r7c6]
#
# <1> occurs three times in buddy cells
# <4> occurs twice       in buddy cells
# <6> occurs twice       in buddy cells
#
# Simple Sudoku says [r7c6]=4 ... and it solves puzzle!!!
 *--------------------------------------------------*
 | 5    4    67   | 23   9    26   | 8    37   1    |
 | 3    9    2    | 14   17   8    | 67   5    46   |
 | 78   1    68   | 35   67   45   | 39   2    49   |
 |----------------+----------------+----------------|
 | 78   3    4    | 6    18   17   | 5    9    2    |
 | 6    2    78   | 59   4    59   | 1    78   3    |
 | 1    5    9    | 27   28   3    | 67   4    68   |
 |----------------+----------------+----------------|
 | 29   8    5    | 49   26  #146  | 39   13   7    |
 | 29   7    1    | 8    3    29   | 4    6    5    |
 | 4    6    3    | 17   5    79   | 2    18   89   |
 *--------------------------------------------------*

Why isn't [r7c6]=1 correct???

Ronk is right, <1> doesn't occur three times in buddy cells, the 9s do. This is indeed a very strange situation, where your extensive use of chains has created a BUG+1 grid where the '+1' isn't in the polyvalued cell. I'm not quite sure how these grids should be dealt with, in case there's more of them coming up. In this case, apparently the +1 cell is r7c4, but why that one? It has 2 buddies in the box and row, but only 1 in the column. Both r8c6 and r9c6 has 2 buddies in the box and column, but only one in the row.

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Postby daj95376 » Sat Nov 11, 2006 2:35 pm

Just before logging in today, it hit me that there may be more to a BUG than the bi-value constraint. So, I went back to the definition and discovered a bi-location constraint as well.

Jeff: A Bivalue Universal Grave (BUG) is any grid in which all the unsolved cells have two candidates, and if a candidate exists in a row, column, or box, it shows up exactly twice.

I have egg all over my face for not checking the definition -- and 9s -- first. Sorry, I need to update my BUG module!!!

Thanks ronk and RW for catching the anomaly!!! Yes, this is the first time that the bi-value constraint was insufficient for my solver.

ronk and RW: I was not clear in my use of the term buddy cells. What I meant to say is that <1> occurs in three buddy cells to [r7c6]. Likewise for the <4> and <6> values being in two buddy cells to [r7c6]. Normally, this would have been sufficient to force [r7c6]=1. Right? (I've updated my previous posts to reflect this.)
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Postby RW » Sat Nov 11, 2006 6:20 pm

daj95376 wrote:What I meant to say is that <1> occurs in three buddy cells to [r7c6]. Likewise for the <4> and <6> values being in two buddy cells to [r7c6]. Normally, this would have been sufficient to force [r7c6]=1. Right?

No, I don't think it's normally sufficient to force the +1 value. It must appear in two "buddy cells" of each unit. In this case there's only one buddy for the <1> in all 3 units. As there is also only one buddy for the <4> and <6>.

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Postby daj95376 » Sat Nov 11, 2006 8:32 pm

RW wrote:
daj95376 wrote:What I meant to say is that <1> occurs in three buddy cells to [r7c6]. Likewise for the <4> and <6> values being in two buddy cells to [r7c6]. Normally, this would have been sufficient to force [r7c6]=1. Right?

No, I don't think it's normally sufficient to force the +1 value. It must appear in two "buddy cells" of each unit. In this case there's only one buddy for the <1> in all 3 units. As there is also only one buddy for the <4> and <6>.

RW

Okay, I think I understand where I'm going wrong. Thanks for all the help!
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Re: BUG+1 Question

Postby ronk » Mon Nov 13, 2006 12:18 am

ronk wrote:Your puzzle may not fit the formal BUG+1 definitions, but it surely is one. The extra candidate is just not in the polyvalued cell ... a rarity I suspect.

I'm unable to eliminate a candidate to yield a BUG grid, so now think daj's grid is not actually a BUG+1.
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Re: BUG+1 Question

Postby daj95376 » Mon Nov 13, 2006 1:15 am

ronk wrote:
ronk wrote:Your puzzle may not fit the formal BUG+1 definitions, but it surely is one. The extra candidate is just not in the polyvalued cell ... a rarity I suspect.

I'm unable to eliminate a candidate to yield a BUG grid, so now think daj's grid is not actually a BUG+1.

Correct! It only appears to be a BUG+1. Once I reviewed Jeff's thread on BUGs, and merged it with what your and RW were saying, I realized that I'd completely misunderstood BUG+1.

After correcting my solver, this puzzle -- and several others that I tested -- suddenly weren't BUG+1 anymore.

Thanks again to you and RW for getting me past my confusion on BUG+1 !!!
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Postby tarek » Tue Nov 14, 2006 1:28 am

The grid that daj posted is a nice example of a BUG trap or a pseudoBUG...........

as it is easy to see the only trivalue cell in the grid...none of its candidates occurs 3 times in that cell's row/column/box

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Postby Eioru » Sat Oct 18, 2008 12:48 am

Code: Select all
I list some puzzles with BUG I found.
The number is the rest empty cells(>34) when BUG is appeared.

75.6.3.946248.9.35....54...46..9..83....3.9..93.....52.........18.9.5.2724.3.1.69   43
78.4.3.9119.7.5.64.........978....42.....2.7.26..74.858........64.1.7.385372.8.19   42
29.5.863115.6.9.47......5..37.1...84.8.39...662...4.53..2......94.2.3.1581.9.7.62   40
28.91.43.61473.59.39......172..9.81.54.38.72........5.47.85.96.95.26.14......9..5   39
32.7.1.4949.523.78.......2.56.....142.....9.691.....37.49......15.4.8.92832957461   38
45.98.12.83.26.75.........861....54.39..4.26...4..68..28.47931.143658972.....2.8.   38
16985.34.42.91.68..7.......24..6893.95....826..6.....461.27.45.7924851635.4......   37
42.9.3.1616.5.4.37....1.4..21..45.83..4.32...53..9..42.4..59...68.4.139595.368.74   36
26.3.819438.2.9675..9...28349..8.536......42.65..3..19....2..6.92.8.735117.5.3.42   35


Did other puzzles have more empty grids than these?
Last edited by Eioru on Sat Oct 18, 2008 12:40 am, edited 1 time in total.
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Postby ronk » Sat Oct 18, 2008 4:10 am

Eioru wrote:I list some puzzles with BUG I found.
The number is the rest empty grids(>34) when BUG is appeared.

I didn't put forth much effort, but I found none. What set of techniques is required to reveal your BUG+1 patterns:?:

BTW what you're calling "grid" is almost universally called "cell."
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Re: BUG+1 Question

Postby hobiwan » Sun Oct 19, 2008 2:53 pm

daj95376 wrote:After correcting my solver, this puzzle -- and several others that I tested -- suddenly weren't BUG+1 anymore.

Well, lucky you! This is what my solver gives me:
Code: Select all
.-----------.----------------.------------.
| 5   4  67 | 23  9    26    | 8   37  1  |
| 3   9  2  | 14  17   8     | 67  5   46 |
| 78  1  68 | 35  67   45    | 39  2   49 |
:-----------+----------------+------------:
| 78  3  4  | 6   18   17    | 5   9   2  |
| 6   2  78 | 59  4    59    | 1   78  3  |
| 1   5  9  | 27  28   3     | 67  4   68 |
:-----------+----------------+------------:
| 29  8  5  | 49  26  -1-4-6 | 39  13  7  |
| 29  7  1  | 8   3    29    | 4   6   5  |
| 4   6  3  | 17  5    79    | 2   18  89 |
'-----------'----------------'------------'

Bivalue Universal Grave + 1 => r7c6<>1246

I still try to figure out where the r7c6<>2 comes from:D

Thanks anyway for the nice test case...
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Postby daj95376 » Sun Oct 19, 2008 4:52 pm

My solver returns a short XY-Chain for [r8c6]<>9. While reviewing the PM, it appears that this elimination might also be the result of an ALS using [r27c4]=149 and [r9c46]=179. Am I even close:?:
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