## Double-BUG???

Post the puzzle or solving technique that's causing you trouble and someone will help

### Double-BUG???

Related to this discussion, I have a question about the January 20 puzzle. I can usually figure out pretty quickly if a puzzle is a BUG+n or not and which ones the plus-candidates are, but this one is giving me a headache. Seems like it has two different BUG possibilities. Is that even possible? If so, how can it be exploited? Can they form together a big MUG or something, like two overlapping URs do? Or is it simply a case of no-BUG, as I originally deemed it? Or have I just overlooked something? I'm a bit confused and out of my depth here, so I would appreciate if someone could provide some clarity.

Here's as far as I get without ambiguity (or so I think):

Code: Select all
`.--------------.------------------------.------------.| 2     1   9  | 4        8     5       | 36  7   36 || 8     6   3  | 9        1     7       | 5   2   4  || 7     45  45 | 26       3     26      | 8   9   1  |:--------------+------------------------+------------:| 15    9   6  | 7        25    13+2    | 4   8   23 || 3     45  8  | 1(26)+5  9     4(26)+1 | 12  56  7  || 14+5  2   7  | 35+16    46+5  8       | 13  56  9  |:--------------+------------------------+------------:| 9     8   1  | 3(26)    7     3(26)   | 26  4   5  || 6     7   2  | 15       45    14      | 9   3   8  || 45    3   45 | 8        26    9       | 7   1   26 |'--------------'------------------------'------------'`

Those four (26) combos are the problem. As far as I can see, I could arrange them in two ways and get two different BUG+11s:

BUG+11 (a):

Code: Select all
`.--------------.------------------------.------------.| 2     1   9  | 4        8     5       | 36  7   36 || 8     6   3  | 9        1     7       | 5   2   4  || 7     45  45 | 26       3     26      | 8   9   1  |:--------------+------------------------+------------:| 15    9   6  | 7        25    13+2    | 4   8   23 || 3     45  8  | 12+56    9     46+12   | 12  56  7  || 14+5  2   7  | 35+16    46+5  8       | 13  56  9  |:--------------+------------------------+------------:| 9     8   1  | 36+2     7     23+6    | 26  4   5  || 6     7   2  | 15       45    14      | 9   3   8  || 45    3   45 | 8        26    9       | 7   1   26 |'--------------'------------------------'------------'`

BUG+11 (b):

Code: Select all
`.--------------.------------------------.------------.| 2     1   9  | 4        8     5       | 36  7   36 || 8     6   3  | 9        1     7       | 5   2   4  || 7     45  45 | 26       3     26      | 8   9   1  |:--------------+------------------------+------------:| 15    9   6  | 7        25    13+2    | 4   8   23 || 3     45  8  | 16+25    9     24+16   | 12  56  7  || 14+5  2   7  | 35+16    46+5  8       | 13  56  9  |:--------------+------------------------+------------:| 9     8   1  | 23+6     7     36+2    | 26  4   5  || 6     7   2  | 15       45    14      | 9   3   8  || 45    3   45 | 8        26    9       | 7   1   26 |'--------------'------------------------'------------'`

That doesn't seem to make sense, but does it? Or have I made a rookie mistake somewhere? That's totally possible as I'm doing this manually, plus I don't often dig into other than obvious and useful BUG possibilities. This one is clearly not very useful, even if does have a BUG (or two), so take it as an academic exercise.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Double-BUG???

SpAce wrote:Seems like it has two different BUG possibilities. Is that even possible?

Why not ? Actually i tried to find such one, when i read the other thread, but did not in the samples i looked at. So thanks for this one.
A BUG is just any collection of bivalue cells with strong links in all units. So in a grid with many candidates there should be a number of BUGs hidden.
eleven

Posts: 2469
Joined: 10 February 2008

### Re: Double-BUG???

eleven wrote:
SpAce wrote:Seems like it has two different BUG possibilities. Is that even possible?

Why not ?

I guess you're right... why not indeed? Somehow I've just been fixated on a binary idea that either a puzzle has a single BUG or no BUG at all. I'm still betting that it works for all practical purposes (unless someone shows how to use multi-BUGs), but otherwise it doesn't seem to be correct.

Actually i tried to find such one, when i read the other thread, but did not in the samples i looked at. So thanks for this one.

I looked over all January puzzles and found one more: January 1. It's very similar to the Jan 20 example, having two possible configurations:

Code: Select all
`.--------------.----------------.------------------.| 3   14+5  25 | 18  6   59     | 24    89+4  7    || 6   8     9  | 2   47  47     | 5     1     3    || 12  45+1  7  | 18  59  3      | 6     48+9  29+4 |:--------------+----------------+------------------:| 12  6.15  25 | 7   8   6.15+4 | 3     49    49+1 || 4   6.15  3  | 9   25  6.15   | 8     7     12   || 9   7     8  | 3   24  14     | 12+4  5     6    |:--------------+----------------+------------------:| 5   9     4  | 6   1   2      | 7     3     8    || 7   2     1  | 4   3   8      | 9     6     5    || 8   3     6  | 5   79  79     | 14    2     14   |'--------------'----------------'------------------'`

Candidates preceding a dot are fixed BUG candidates; the indeterminate ones are the four (15)-pairs.

Then there was this: 17December18. If it has BUGs, it has many, but I won't even try to enumerate them manually. My detection process got stuck got quite early:

Code: Select all
`.---------------------.-----------------.----------------.| 48+1  5     9.148   | 2     6  9.18   | 7  3     148   || 37    9.18  6.148+9 | 17+9  5  3.18+9 | 2  49+1  6.148 || 37    2     6.18+9  | 79+1  4  3.18+9 | 5  19    6.18  |:---------------------+-----------------+----------------:| 6     18    48+1    | 5     7  14     | 3  2     9     || 9     7     2       | 14    3  6      | 8  5     14    || 14    3     5       | 8     9  2      | 6  14    7     |:---------------------+-----------------+----------------:| 18    9.18  9.18    | 3     2  7      | 4  6     5     || 5     6     3       | 49    8  49     | 1  7     2     || 2     4     7       | 6     1  5      | 9  8     3     |'---------------------'-----------------'----------------'`

How many BUGs (if any) does that have?

A BUG is just any collection of bivalue cells with strong links in all units. So in a grid with many candidates there should be a number of BUGs hidden.

But what exactly do you mean by hidden BUGs? Do you count those BUGs that would become possible after some cells are solved (or candidates eliminated)? Otherwise it seems to me that a fixed PM state either has BUGs (i.e. BUG+Ns) or not, and in most cases it's easy to determine. However, a grid with no BUGs now (i.e. can't form a valid BUG+N with the current PM state) can turn into one with BUGs, so in that sense it has hidden BUGs. For example, I don't think any of the BUG puzzles in my tests were in a BUG+N state before basics were executed. Are some puzzles inherently BUG-free, though? With manual testing this kind of research gets difficult.

Anyway, here's my manual (i.e. error prone) results for the January(+one) puzzles, using the grid state after basics:

No BUGs: 19/29
One BUG: 7/29
Two BUGs: 2/29
Indeterminate (possibly >2 BUGs): 1/29

Individual Results: Show
Jan 28: no
Jan 27: no
Jan 26: no
Jan 25: no
* Jan 24: BUG+22
Jan 23: no
Jan 22: no
Jan 21: no
** Jan 20: two BUG+11s
* Jan 19: BUG+10
* Jan 18: BUG+3
Jan 17: no
Jan 16: no
Jan 15: no
Jan 14: no
Jan 13: no
* Jan 12: BUG+19
Gemstone: no
Jan 10: no
Jan 9: no
Jan 8: no
Jan 7: no
* Jan 6: BUG+2
* Steve Stumble XXIV: BUG+3
* Jan 4: BUG+3
Jan 3: no
Jan 2: no
** Jan 1: two BUG+12s
??? 17December: indeterminate (multi-BUG or no BUG?)

Can anyone's software confirm those results?

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Double-BUG???

SpAce wrote:How many BUGs (if any) does that have?

This one was easy to find, but don't ask me, how many there are.
Code: Select all
`+-------------+-------------+-------------+| 48  5   49  | 2   6   19  | 7   3   18  || 37  19  68  | 17  5   38  | 2   49  46  || 37  2   16  | 79  4   38  | 5   19  68  |+-------------+-------------+-------------+| 6   18  48  | 5   7   14  | 3   2   9   || 9   7   2   | 14  3   6   | 8   5   14  || 14  3   5   | 8   9   2   | 6   14  7   |+-------------+-------------+-------------+| 18  89  19  | 3   2   7   | 4   6   5   || 5   6   3   | 49  8   49  | 1   7   2   || 2   4   7   | 6   1   5   | 9   8   3   |+-------------+-------------+-------------+`
eleven

Posts: 2469
Joined: 10 February 2008

### Re: Double-BUG???

eleven wrote:This one was easy to find, but don't ask me, how many there are.

Awesome, thanks! So with the plus-candidates it looks like:

BUG+24:

Code: Select all
`.--------------------.----------------.----------------.| 48+1  5     49+18  | 2     6  19+8  | 7  3     18+4  || 37    19+8  68+149 | 17+9  5  38+19 | 2  49+1  46+18 || 37    2     16+89  | 79+1  4  38+19 | 5  19    68+1  |:--------------------+---------------+-----------------:| 6     18    48+1   | 5     7  14    | 3  2     9     || 9     7     2      | 14    3  6     | 8  5     14    || 14    3     5      | 8     9  2     | 6  14    7     |:--------------------+----------------+----------------:| 18    89+1  19+8   | 3     2  7     | 4  6     5     || 5     6     3      | 49    8  49    | 1  7     2     || 2     4     7      | 6     1  5     | 9  8     3     |'--------------------'----------------'----------------'`

I guess that's indeed solvable normally as a BUG+24, though I'm not going to try. Reduced to the minimum it's easy:

BUG+5:

Code: Select all
`.----------------.-------------.-------------.| 48  5     49+1 | 2     6  19 | 7  3     18 || 37  19    68   | 17    5  38 | 2  49+1  46 || 37  2     16+8 | 79+1  4  38 | 5  19    68 |:----------------+-------------+-------------:| 6   18    48   | 5     7  14 | 3  2     9  || 9   7     2    | 4-1   3  6  | 8  5     14 || 14  3     5    | 8     9  2  | 6  14    7  |:----------------+-------------+-------------:| 18  89+1  19   | 3     2  7  | 4  6     5  || 5   6     3    | 49    8  49 | 1  7     2  || 2   4     7    | 6     1  5  | 9  8     3  |'----------------'-------------'-------------'`

(1)r1c3 - r1c6 = (1)r4c6
(1)r2c8 - r6c8 = (1)r5c9
(1)r3c4
(1)r7c2 - r4c2 = (1)r4c6
(8)r3c3 - (8=4)r4c3 - (4=1)r4c6

=> -1 r5c4; stte

So, can we conclude that in a multi-BUG situation it's enough to find/pick one of them and solve with that? (That is, if one really wants to use a complicated BUG solution -- again, this is more or less academic.) Originally I had a misconception of having to somehow combine all of the BUG variants, but I guess that's not necessary at all (and feels like a really dumb idea right now). A BUG is a BUG, and its derived SIS is valid, even if others are present, right? Seems perfectly logical now but somehow it didn't feel intuitive at first.

PS. I'm still wondering if there was some way to use the multi-BUG as a unit to reduce the list of plus-candidates, so that the combination would actually be simpler to solve than any of the individual BUGs. That'd be kind of cool, but I'm terrible with even regular MUGs.

Added. It should actually work, shouldn't it? At least in the simple case of two BUGs, if you remove all the known plus-candidates shared by both, don't you end up with a situation that can only be one or the other BUG, i.e. impossible? Doesn't it mean that we can simply use those shared plus-candidates as a SIS? If that's true, shouldn't the concept scale to bigger multi-BUGs as well (it's just harder to see if you have one or not)? Again, I'm just thinking aloud and it's totally possible that I'm missing something obvious here...

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Double-BUG???

In other words, I'm asking if this should be an acceptable solution to the January 1 puzzle:

Code: Select all
`.--------------.----------------.------------------.| 3   14+5  25 | 18  6   59     | 24    89+4  7    || 6   8     9  | 2   47  47     | 5     1     3    || 12  45+1  7  | 18  59  3      | 6     48+9  29+4 |:--------------+----------------+------------------:| 12  6.15  25 | 7   8   6.15+4 | 3     49    49+1 || 4   6.15  3  | 9   25  6.15   | 8     7     12   || 9   7     8  | 3   24  14     | 12+4  5     6    |:--------------+----------------+------------------:| 5   9     4  | 6   1   2      | 7     3     8    || 7   2     1  | 4   3   8      | 9     6     5    || 8   3     6  | 5   79  79     | 14    2     14   |'--------------'----------------'------------------'`

BIG-MUG+8

(1)r3c2 - (1=25)b1p73
(1-9)r4c9 = (95)r3c95
(4)r3c9,r6c7 - (4=25)r1c73
(4)r4c6 - r4c89 = r6c7 - (4=25)r1c73
(5)r1c2
(9-8)r1c8 = r3c8 - (8=12)r3c41 - (2=5)r1c3
(9)r3c8 - (9=5)r3c5

=> -5 r1c6; stte

(Would you like fries with that? )

-----------------------------------------------

Code: Select all
`.--------------.----------------------.------------.| 2     1   9  | 4       8     5      | 36  7   36 || 8     6   3  | 9       1     7      | 5   2   4  || 7     45  45 | 26      3     26     | 8   9   1  |:--------------+----------------------+------------:| 15    9   6  | 7       25    13+2   | 4   8   23 || 3     45  8  | 1.26+5  9     4.26+1 | 12  56  7  || 14+5  2   7  | 35+16   46+5  8      | 13  56  9  |:--------------+----------------------+------------:| 9     8   1  | 3.26     7     3.26  | 26  4   5  || 6     7   2  | 15       45    14    | 9   3   8  || 45    3   45 | 8        26    9     | 7   1   26 |'--------------'----------------------'------------'`

BIG-MUG+7

(1)r5c6 - r5c7 = (1)r6c7
(1)r6c4
(2)r4c6 - (2=31)b6p47
(5)r5c4,r6c5 - (5=2)r4c5 - (2=31)b6p47
(5-4)r6c1 = (452)r684c5 - (2=31)b6p47
(6)r6c4 - (6=54)r6c85 - (4=52)r84c5 - (2=31)b6p47

=> -1 r6c1; stte

-----------------------------------------------

It would really simplify the 17December (+24 >> +9), but I have even less idea if this is valid logic or not:

Code: Select all
`.---------------------.-----------------.----------------.| 48+1  5     9.148   | 2     6  9.18   | 7  3     148   || 37    9.18  6.148+9 | 17+9  5  3.18+9 | 2  49+1  6.148 || 37    2     6.18+9  | 79+1  4  3.18+9 | 5  19    6.18  |:---------------------+-----------------+----------------:| 6     18    48+1    | 5     7  14     | 3  2     9     || 9     7     2       | 14    3  6      | 8  5     14    || 14    3     5       | 8     9  2      | 6  14    7     |:---------------------+-----------------+----------------:| 18    9.18  9.18    | 3     2  7      | 4  6     5     || 5     6     3       | 49    8  49     | 1  7     2     || 2     4     7       | 6     1  5      | 9  8     3     |'---------------------'-----------------'----------------'`

BIG-MUG+9

(1)r1c1,r4c3 - (1=4*)r6c1 - b6p(8=6) - r1c9*1 = (4-9)r1c3 = (9)r1c6
(1)r2c8 - (1=4)r6c8 - r5c9 = (49)r58c4
(1)r3c4 - (1=49)r58c4
(9)r23c3 - r1c3 = (9)r1c6
(9)r2c4 - (9=4)r8c4 - r5c(4=9*) - r6c(8=1) - r1c1*9 = (4-9)r1c3 = (9)r1c6
(9)r23c6

=> -9 r8c6; stte

What do you think, eleven, are those valid SIS or not? In these examples they all did contain at least one true candidate, but is that guaranteed? You're the MUG expert. I'm flying blind here. (Anyone else is welcome to chime in as well, of course.)

Edit: added a missing chain (1r3c4) to the last example.
Last edited by SpAce on Wed Jan 30, 2019 9:39 pm, edited 1 time in total.

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Double-BUG???

Good question. We have to be careful.

If a mixed (undetermined) extra candidate always kills the alternative one in the other BUG, a non mixed candidate must be true.
But if you look at these BUG's (from the above sample), a 1r2c3 would kill both BUG's, or e.g. 1r1c3 would kill the first one, and 8r2c3 the second.
Code: Select all
`    .---------------------.-----------------.----------------.    | 48+1  5     49+18   | 2     6  19+8   | 7  3     18+4  |    | 37    19+8  68+149  | 17+9  5  38+19  | 2  49+1  46+18 |    | 37    2     16+89   | 79+1  4  38+19  | 5  19    68+1  |    :---------------------+-----------------+----------------:    | 6     18    48+1    | 5     7  14     | 3  2     9     |    | 9     7     2       | 14    3  6      | 8  5     14    |    | 14    3     5       | 8     9  2      | 6  14    7     |    :---------------------+-----------------+----------------:    | 18    89+1  19+8    | 3     2  7      | 4  6     5     |    | 5     6     3       | 49    8  49     | 1  7     2     |    | 2     4     7       | 6     1  5      | 9  8     3     |    '---------------------'-----------------'----------------'    .---------------------.-----------------.----------------.    | 48+1  5     19+48   | 2     6  89+1   | 7  3     14+8  |    | 37    19+8  46+189  | 17+9  5  38+19  | 2  49+1  68+14 |    | 37    2     68+19   | 79+1  4  13+89  | 5  19    68+1  |    :---------------------+-----------------+----------------:    | 6     18    48+1    | 5     7  14     | 3  2     9     |    | 9     7     2       | 14    3  6      | 8  5     14    |    | 14    3     5       | 8     9  2      | 6  14    7     |    :---------------------+-----------------+----------------:    | 18    89+1  19+8    | 3     2  7      | 4  6     5     |    | 5     6     3       | 49    8  49     | 1  7     2     |    | 2     4     7       | 6     1  5      | 9  8     3     |    '---------------------'-----------------'----------------'`

However this is no proof, that all of the fixed common extra candidates can be false.
We would need a counter-example - and probably a program to find it.
eleven

Posts: 2469
Joined: 10 February 2008

### Re: Double-BUG???

Or we try this:
If we can show, that each mixed candidate is actually part of a BUG (and it seems so), then it should be proven (?), that one of the fixed extra candidates must be true.

Too short of time now ...
eleven

Posts: 2469
Joined: 10 February 2008

### Re: Double-BUG???

eleven wrote:If we can show, that each mixed candidate is actually part of a BUG (and it seems so), then it should be proven (?), that one of the fixed extra candidates must be true.

I guess that's sort of my hypothesis, but I have no idea of its validity. The more I think about it the more my head wants to explode. I think you're right that a program is probably needed. Finding a positive proof seems difficult anyway, but a single counter-example would quickly disprove it, as you said. That shouldn't be too hard if someone has the infrastructure ready and easily modifiable for such testing.

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Double-BUG???

The December puzzles seem like a more fruitful set to find both normal and potential multi-BUGs:

Code: Select all
`No BUG     : 16Single BUG : 10Multi-BUG? : 6---------------Total      : 32`

Individual results: Show
Code: Select all
`1  December 31, 2018:     no2  December 30, 2018:     no3  Steve Stumble XXIII:   no4  December 28, 2018:     no5  27 December 2018:      no6  Steve Stumble XXII:    BUG+317  December 25, 2018:     Multi-BUG?8  New puzzle from Hell:  no9  December 23, 2018:     BUG+510 December 22, 2018:     no11 December 21, 2018:     BUG+1312 December 20, 2018:     BUG+513 December 19, 2018:     no14 December 18, 2018:     no15 December 17, 2018:     no16 December 16, 2018:     BUG+1317 December 15, 2018:     BUG+1118 December 14, 2018:     Multi-BUG?19 December 13, 2018:     no20 December 12, 2018:     no21 December 11, 2018:     Multi-BUG?22 October 20, 2018:      BUG+323 2018-12-10:            no24 December 9, 2018:      Multi-BUG?25 December 8, 2018:      BUG+2426 December 7, 2018:      BUG+327 December 6, 2018:      no28 December 5, 2018:      Multi-BUG?29 December 4, 2018:      no30 December 3, 2018:      no31 December 2, 2018:      BUG+332 17November18:          Multi-BUG?`

They're still manually checked, so errors are quite possible, but it seems that at least these might include some more test cases for multi-BUGs:

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Double-BUG???

SpAce wrote:you're right that a program is probably needed. Finding a positive proof seems difficult anyway, but a single counter-example would quickly disprove it, as you said.

Here are two puzzles showing counterexamples:

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`.86.75...3.......47...........2891.3...5..2...6...1.....21...97..3...4..67..4....186475932395628714724913685457289163931564278268731549842156397513897426679342851.......4.6.38...1...1...5........8.3..7..5......2.8.5.7.23....4.34....258....4.6.978513642653842719241967538526491873487635291319278456762359184134786925895124367`

For the first one: After basics, there are two BUG+31's with 25 shared +N candidates.
The *'s in the PMs, designate +N candidates that are true in the solution.
None of the shared (+N) candidates are true in the solution.

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`+----------------+------------------+-----------------------+| 19  8     6    | 4     7     5    | 39     23+1    12+9   || 3   29+1  5    | 68+9  19+2* 26+8*| 7      18      4      || 7   12+9  4    | 39+8  12+9  38+2 | 69+58  58+1    56+189 |+----------------+------------------+-----------------------+| 4   5     7    | 2     8     9    | 1      6       3      || 19  3     18+9 | 5     6     4    | 2      7       89     || 2   6     89   | 7     3     1    | 58+9   4       59+8   |+----------------+------------------+-----------------------+| 8   4     2    | 1     5     36   | 36     9       7      || 5   19    3    | 68+9  29    7    | 4      12+8    68+12  || 6   7     19   | 39+8  4     28+3 | 58+3   35+128  12+58  |+----------------+------------------+-----------------------++----------------+------------------+-----------------------+| 19  8     6    | 4     7     5    | 39     23+1    12+9   || 3   29+1  5    | 69+8  12+9  68+2 | 7      18      4      || 7   12+9  4    | 38+9* 19+2  23+8 | 69+58  58+1    56+189 |+----------------+------------------+-----------------------+| 4   5     7    | 2     8     9    | 1      6       3      || 19  3     18+9 | 5     6     4    | 2      7       89     || 2   6     89   | 7     3     1    | 58+9   4       59+8   |+----------------+------------------+-----------------------+| 8   4     2    | 1     5     36   | 36     9       7      || 5   19    3    | 68+9  29    7    | 4      12+8    68+12  || 6   7     19   | 39+8  4     28+3 | 58+3   35+128  12+58  |+----------------+------------------+-----------------------+`

For the second one: After basics, there are two BUG+4's that don't share any +N candidates.

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`+-----------+-----------+---------------+| 29  79  8 | 5   1  3  | 26+7  4  67+2*|| 6   5   3 | 8   4  27 | 79+2  1  29+7 || 24  47  1 | 9   6  27 | 5     3  8    |+-----------+-----------+---------------+| 5   2   6 | 4   9  1  | 8     7  3    || 14  8   7 | 6   3  5  | 24    9  12   || 3   14  9 | 2   7  8  | 46    5  16   |+-----------+-----------+---------------+| 7   6   2 | 3   5  9  | 1     8  4    || 19  3   4 | 17  8  6  | 79    2  5    || 8   19  5 | 17  2  4  | 3     6  79   |+-----------+-----------+---------------++-----------+-----------+---------------+| 29  79  8 | 5   1  3  | 67+2  4  26+7 || 6   5   3 | 8   4  27 | 29+7* 1  79+2 || 24  47  1 | 9   6  27 | 5     3  8    |+-----------+-----------+---------------+| 5   2   6 | 4   9  1  | 8     7  3    || 14  8   7 | 6   3  5  | 24    9  12   || 3   14  9 | 2   7  8  | 46    5  16   |+-----------+-----------+---------------+| 7   6   2 | 3   5  9  | 1     8  4    || 19  3   4 | 17  8  6  | 79    2  5    || 8   19  5 | 17  2  4  | 3     6  79   |+-----------+-----------+---------------+`
blue

Posts: 894
Joined: 11 March 2013

### Re: Double-BUG???

Great, thanks ! Easy to see now, what i have missed.
Could you also tell us, how many BUG's the 17December puzzle has, please ?
eleven

Posts: 2469
Joined: 10 February 2008

### Re: Double-BUG???

eleven wrote:Could you also tell us, how many BUG's the 17December puzzle has, please ?

Seven BUG+24's (according to the code).
I can list them if you're interested.
blue

Posts: 894
Joined: 11 March 2013

### Re: Double-BUG???

blue wrote:Here are two puzzles showing counterexamples:

Thanks, blue! Awesome work!! Fortunately there's not much to be disappointed about, because it probably wouldn't have had much practical value as a solving technique anyway. It's good to be sure, though, so we can close the ticket.

blue wrote:
eleven wrote:Could you also tell us, how many BUG's the 17December puzzle has, please ?

Seven BUG+24's (according to the code).
I can list them if you're interested.

Yes, please! That'd be nice. What about December 9 and December 14? With those I also got stuck with quite a few indeterminate candidates left so I suspected they might have > 2 BUGs as well.

SpAce

Posts: 2674
Joined: 22 May 2017

### Re: Double-BUG???

SpAce wrote:What about December 9 and December 14?

For December 9: 8 BUG+35's
For December 14: 8 42 BUG+58's

I checked your full result lists for the January and December puzzles -- good job !
Hidden Text: Show
SpAce 1
ok Jan 28: no
ok Jan 27: no
ok Jan 26: no
ok Jan 25: no
ok * Jan 24: BUG+22
ok Jan 23: no
ok Jan 22: no
ok Jan 21: no
ok ** Jan 20: two BUG+11s
ok * Jan 19: BUG+10
ok * Jan 18: BUG+3
ok Jan 17: no
ok Jan 16: no
ok Jan 15: no
ok Jan 14: no
ok Jan 13: no
ok * Jan 12: BUG+19
ok Gemstone: no
ok Jan 10: no
ok Jan 9: no
ok Jan 8: no
ok Jan 7: no
ok * Jan 6: BUG+2
ok * Steve Stumble XXIV: BUG+3
ok * Jan 4: BUG+3
ok Jan 3: no
ok Jan 2: no
ok ** Jan 1: two BUG+12s
??? 17December: indeterminate (multi-BUG or no BUG?) 7 BUG+24

SpAce 2
ok 1 December 31, 2018: no
ok 2 December 30, 2018: no
ok 3 Steve Stumble XXIII: no
ok 4 December 28, 2018: no
ok 5 27 December 2018: no
ok 6 Steve Stumble XXII: BUG+31
7 December 25, 2018: Multi-BUG? 4 BUG+23
ok 8 New puzzle from Hell: no
ok 9 December 23, 2018: BUG+5
ok 10 December 22, 2018: no
ok 11 December 21, 2018: BUG+13
ok 12 December 20, 2018: BUG+5
ok 13 December 19, 2018: no
ok 14 December 18, 2018: no
ok 15 December 17, 2018: no
16 December 16, 2018: BUG+13 (BUG+14)
ok 17 December 15, 2018: BUG+11
18 December 14, 2018: Multi-BUG? 42 BUG+58
ok 19 December 13, 2018: no
ok 20 December 12, 2018: no
21 December 11, 2018: Multi-BUG? no BUG
ok 22 October 20, 2018: BUG+3
ok 23 2018-12-10: no
24 December 9, 2018: Multi-BUG? 8 BUG+35
ok 25 December 8, 2018: BUG+24
ok 26 December 7, 2018: BUG+3
ok 27 December 6, 2018: no
28 December 5, 2018: Multi-BUG? no BUG
ok 29 December 4, 2018: no
ok 30 December 3, 2018: no
ok 31 December 2, 2018: BUG+3
32 17November18: Multi-BUG? 1 BUG+26

The BUG+24's for the "17December18" puzzle:
Hidden Text: Show
Code: Select all
`+--------------------+----------------+----------------+| 48+1  5     19+48  | 2     6  19+8  | 7  3     48+1  || 37    19+8  46+189 | 17+9  5  38+19 | 2  49+1  68+14 || 37    2     68+19  | 79+1  4  38+19 | 5  19    16+8  |+--------------------+----------------+----------------+| 6     18    48+1   | 5     7  14    | 3  2     9     || 9     7     2      | 14    3  6     | 8  5     14    || 14    3     5      | 8     9  2     | 6  14    7     |+--------------------+----------------+----------------+| 18    89+1  19+8   | 3     2  7     | 4  6     5     || 5     6     3      | 49    8  49    | 1  7     2     || 2     4     7      | 6     1  5     | 9  8     3     |+--------------------+----------------+----------------++--------------------+----------------+----------------+| 48+1  5     89+14  | 2     6  19+8  | 7  3     14+8  || 37    19+8  46+189 | 17+9  5  38+19 | 2  49+1  68+14 || 37    2     16+89  | 79+1  4  38+19 | 5  19    68+1  |+--------------------+----------------+----------------+| 6     18    48+1   | 5     7  14    | 3  2     9     || 9     7     2      | 14    3  6     | 8  5     14    || 14    3     5      | 8     9  2     | 6  14    7     |+--------------------+----------------+----------------+| 18    89+1  19+8   | 3     2  7     | 4  6     5     || 5     6     3      | 49    8  49    | 1  7     2     || 2     4     7      | 6     1  5     | 9  8     3     |+--------------------+----------------+----------------++--------------------+----------------+----------------+| 48+1  5     49+18  | 2     6  19+8  | 7  3     18+4  || 37    19+8  68+149 | 17+9  5  38+19 | 2  49+1  46+18 || 37    2     16+89  | 79+1  4  38+19 | 5  19    68+1  |+--------------------+----------------+----------------+| 6     18    48+1   | 5     7  14    | 3  2     9     || 9     7     2      | 14    3  6     | 8  5     14    || 14    3     5      | 8     9  2     | 6  14    7     |+--------------------+----------------+----------------+| 18    89+1  19+8   | 3     2  7     | 4  6     5     || 5     6     3      | 49    8  49    | 1  7     2     || 2     4     7      | 6     1  5     | 9  8     3     |+--------------------+----------------+----------------++--------------------+----------------+----------------+| 48+1  5     19+48  | 2     6  19+8  | 7  3     48+1  || 37    89+1  46+189 | 17+9  5  38+19 | 2  49+1  16+48 || 37    2     16+89  | 79+1  4  38+19 | 5  19    68+1  |+--------------------+----------------+----------------+| 6     18    48+1   | 5     7  14    | 3  2     9     || 9     7     2      | 14    3  6     | 8  5     14    || 14    3     5      | 8     9  2     | 6  14    7     |+--------------------+----------------+----------------+| 18    19+8  89+1   | 3     2  7     | 4  6     5     || 5     6     3      | 49    8  49    | 1  7     2     || 2     4     7      | 6     1  5     | 9  8     3     |+--------------------+----------------+----------------++--------------------+----------------+----------------+| 48+1  5     49+18  | 2     6  19+8  | 7  3     18+4  || 37    89+1  16+489 | 17+9  5  38+19 | 2  49+1  46+18 || 37    2     16+89  | 79+1  4  38+19 | 5  19    68+1  |+--------------------+----------------+----------------+| 6     18    48+1   | 5     7  14    | 3  2     9     || 9     7     2      | 14    3  6     | 8  5     14    || 14    3     5      | 8     9  2     | 6  14    7     |+--------------------+----------------+----------------+| 18    19+8  89+1   | 3     2  7     | 4  6     5     || 5     6     3      | 49    8  49    | 1  7     2     || 2     4     7      | 6     1  5     | 9  8     3     |+--------------------+----------------+----------------++--------------------+----------------+----------------+| 48+1  5     19+48  | 2     6  89+1  | 7  3     14+8  || 37    19+8  46+189 | 17+9  5  38+19 | 2  49+1  68+14 || 37    2     68+19  | 79+1  4  13+89 | 5  19    68+1  |+--------------------+----------------+----------------+| 6     18    48+1   | 5     7  14    | 3  2     9     || 9     7     2      | 14    3  6     | 8  5     14    || 14    3     5      | 8     9  2     | 6  14    7     |+--------------------+----------------+----------------+| 18    89+1  19+8   | 3     2  7     | 4  6     5     || 5     6     3      | 49    8  49    | 1  7     2     || 2     4     7      | 6     1  5     | 9  8     3     |+--------------------+----------------+----------------++--------------------+----------------+----------------+| 48+1  5     19+48  | 2     6  89+1  | 7  3     14+8  || 37    89+1  46+189 | 17+9  5  13+89 | 2  49+1  68+14 || 37    2     16+89  | 79+1  4  38+19 | 5  19    68+1  |+--------------------+----------------+----------------+| 6     18    48+1   | 5     7  14    | 3  2     9     || 9     7     2      | 14    3  6     | 8  5     14    || 14    3     5      | 8     9  2     | 6  14    7     |+--------------------+----------------+----------------+| 18    19+8  89+1   | 3     2  7     | 4  6     5     || 5     6     3      | 49    8  49    | 1  7     2     || 2     4     7      | 6     1  5     | 9  8     3     |+--------------------+----------------+----------------+`

---

For kicks ...

For anyone to verify/refute: this puzzle has 5643 BUG+66's (after basics).
It was the largest count in a ~30 min search, using randomly generated puzzles.

Code: Select all
`.85.......4.9...17.9.4...5.4.7.....3....5.....1....64.9..2.837....6...8..........+-------------------+-----------------+-----------------+| 1267  8     5     | 17  1267   1267 | 49    3   49    || 236   4     236   | 9   2368   5    | 28    1   7     || 1237  9     123   | 4   12378  1237 | 28    5   6     |+-------------------+-----------------+-----------------+| 4     25    7     | 8   1269   1269 | 15    29  3     || 2368  236   23689 | 13  5      4    | 7     29  18    || 2358  1     2389  | 37  279    279  | 6     4   58    |+-------------------+-----------------+-----------------+| 9     56    146   | 2   14     8    | 3     7   145   || 1235  2357  1234  | 6   13479  1379 | 1459  8   12459 || 1238  237   12348 | 5   13479  1379 | 149   6   1249  |+-------------------+-----------------+-----------------+`

Added: Supressing the console ouptut, I got some larger counts in a 10 min run ...
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`..62.....2.......3.35.8..9..5.....3.6.7.....4...4.2....8.6..9.....1.......3..964. : 7785x BUG+87......4...6.4.85.........964....68.....7.3.2.......65..526.......3..9...74..3...8 : 9492x BUG+86.8.1..5.9....5..78..6..7.4.1....2....65..8..1..25..4...3...5........4....9.....3. : 15482x BUG+106.1.....37...4.1.854.........47.3...2.5.1................2..7....8..6.5..9..84..6. : 60968x BUG+99`
blue

Posts: 894
Joined: 11 March 2013

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