## The "threat" of using BUG+2 solves a puzzle.

Advanced methods and approaches for solving Sudoku puzzles

### The "threat" of using BUG+2 solves a puzzle.

BUG+1 is an OK concept in my mind. Bug+n feels like a guess.

Here is a puzzle that may take a swordfish and a UR1 to get to a BUG+2 that, like a quantum BUG, solves the puzzle without using the BUG, seeing it is enough.

This is a puzzle that Cluadiarabia almost published at Havard's fine site.

http//www.sudoku.frihost.net/sudokus/03Oct2006_174633_fast_dopel_randl10.sud

There she suggested a variant, which has BUGs, listed below.

Code: Select all
8 . . | . . . | . . 2
. . . | . . . | . . .
. . 4 | 3 . 6 | 5 . .
---------------------
. . 3 | . 1 . | 4 . .
. . . | 9 . 7 | . . .
. . 5 | . 8 . | 3 . .
---------------------
. . 6 | 5 . 4 | 1 . .
. . . | . . . | . . .
2 . . | . . . | . . 7

Various methods and a UR1 get us to this position.
Code: Select all
*--------------------------------------------------*
| 8    5    79   | 17   4    19   | 6    3    2    |
| 3    6    29   | 28   5    89   | 7    1    4    |
| 1    27   4    | 3    27   6    | 5    89   89   |
|----------------+----------------+----------------|
| 79  #28   3    | 6    1    5    | 4    27   89   |
| 4    1    28   | 9    3    7    | 28   6    5    |
| 6    79   5    | 4    8    2    | 3    79   1    |
|----------------+----------------+----------------|
| 79  *789  6    | 5    27   4    | 1    28   3    |
| 5    3   *178  | 27   9    18   | 28   4    6    |
| 2    4    18   | 18   6    3    | 9    5    7    |
*--------------------------------------------------*

BUG+2 suggests that R7C2 is 7 or R8C3 is 8. In either case R7C2 is not 8 which forces R4C2 = 8. Simple puzzle, now!
wapati
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### Re: The "threat" of using BUG+2 solves a puzzle.

wapati wrote:BUG+1 is an OK concept in my mind. Bug+n feels like a guess.

Here is a puzzle that may take a swordfish and a UR1 to get to a BUG+2 that [edit: ...] solves the puzzle without using the BUG, seeing it is enough.
...
BUG+2 suggests that R7C2 is 7 or R8C3 is 8. In either case R7C2 is not 8 which forces R4C2 = 8.

That looks like "using the BUG" to me. Why do you think it's not?
ronk
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### Re: The "threat" of using BUG+2 solves a puzzle.

ronk wrote:That looks like "using the BUG" to me. Why do you think it's not?

Well, a typical BUG+2 would have you fill in one of the BUGs with a number and see if that solved the puzzle.

In this case you use the pattern to spot a value elsewhere, and there is no guess about which of the BUG values is correct.
wapati
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### Re: The "threat" of using BUG+2 solves a puzzle.

wapati wrote:Well, a typical BUG+2 would have you fill in one of the BUGs with a number and see if that solved the puzzle.

For any BUG+n grid, we know only that at least one of the non-BUG candidates must be true.

Therefore, to fill a BUG cell for n>1, the filled cell needs to have only one non-BUG candidate -- ultimately the fill value -- and there needs to be an implication stream for all other non-BUG candidates implying the same fill.

Sorry, I've always only looked for exclusions so I've no example.

[edit: attempted example was incorrect]
Last edited by ronk on Thu Oct 05, 2006 8:36 am, edited 2 times in total.
ronk
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### Re: The "threat" of using BUG+2 solves a puzzle.

ronk wrote:
wapati wrote:Well, a typical BUG+2 would have you fill in one of the BUGs with a number and see if that solved the puzzle.

For any BUG+n grid, we know only that at least one of the non-BUG candidates must be true.

Therefore, to fill a BUG cell for n>1, the filled cell needs to have only one non-BUG candidate -- ultimately the fill value -- and there needs to be an implication stream for all other non-BUG candidates implying the same fill.

Sorry, I've always only looked for exclusions so I've no example.

I better understand BUG+n now. I thought that BUG+3, for example, was a guessing game of "try it".

You are saying that the better idea is to use exclusion, that is more like it.

Thanks Ronk, I hope this helps someone else, as well!
wapati
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Wapati wrote:Various methods and a UR1 get us to this position.

Before that:

Code: Select all
*---------------------------------------------------*
| 8     5     79  | 17    4     19 | 6     3     2  |
| 3     6     29  | 28    5     89 | 7     1     4  |
| 1     27    4   | 3     27    6  | 5     89    89 |
|-----------------+----------------+----------------|
| 79    28    3   | 6     1     5  | 4     2789  89 |
| 4     1     28  | 9     3     7  | 28    6     5  |
| 6     79    5   | 4     8     2  | 3     79    1  |
|-----------------+----------------+----------------|
| 79    789   6   | 5     27    4  | 1     28    3  |
| 5     3     178 | 27    9     18 | 28    4     6  |
| 2     4     18  | 18    6     3  | 9     5     7  |
*---------------------------------------------------*

[r4c8]=2|8=[r7c2]=9=[r7c1]=7=[r4c1]-7-[r4c8],

and so r4c8=2 which solves the puzzle.

Carcul
Carcul

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Carcul wrote:
Wapati wrote:Various methods and a UR1 get us to this position.

Before that:

Code: Select all
*---------------------------------------------------*
| 8     5     79  | 17    4     19 | 6     3     2  |
| 3     6     29  | 28    5     89 | 7     1     4  |
| 1     27    4   | 3     27    6  | 5     89    89 |
|-----------------+----------------+----------------|
| 79    28    3   | 6     1     5  | 4     2789  89 |
| 4     1     28  | 9     3     7  | 28    6     5  |
| 6     79    5   | 4     8     2  | 3     79    1  |
|-----------------+----------------+----------------|
| 79    789   6   | 5     27    4  | 1     28    3  |
| 5     3     178 | 27    9     18 | 28    4     6  |
| 2     4     18  | 18    6     3  | 9     5     7  |
*---------------------------------------------------*

[r4c8]=2|8=[r7c2]=9=[r7c1]=7=[r4c1]-7-[r4c8],

and so r4c8=2 which solves the puzzle.

Carcul

It isn't that I don't believe you, it is that I have no idea what you did.

What do you call that, where can I learn it?
wapati
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wapati wrote:Various methods and a UR1 get us to this position.
Code: Select all
*--------------------------------------------------*
| 8    5    79   | 17   4    19   | 6    3    2    |
| 3    6    29   | 28   5    89   | 7    1    4    |
| 1    27   4    | 3    27   6    | 5    89   89   |
|----------------+----------------+----------------|
| 79  #28   3    | 6    1    5    | 4    27   89   |
| 4    1    28   | 9    3    7    | 28   6    5    |
| 6    79   5    | 4    8    2    | 3    79   1    |
|----------------+----------------+----------------|
| 79  *789  6    | 5    27   4    | 1    28   3    |
| 5    3   *178  | 27   9    18   | 28   4    6    |
| 2    4    18   | 18   6    3    | 9    5    7    |
*--------------------------------------------------*

BUG+2 suggests that R7C2 is 7 or R8C3 is 8. In either case R7C2 is not 8 which forces R4C2 = 8.

Ah, you make it so complicated, no need to look at any other cells than the ones with extra candidates. As you said, either r7c2=7 or r8c3=8 has to be true. Therefore r7c2<>8 and r8c3<>7, puzzle solved. This is actually the simplest kind of BUG+2 where both cells with extra candidates can see each other and allow direct eliminations.

RW
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Last edited by ronk on Fri Oct 06, 2006 6:27 am, edited 1 time in total.
ronk
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Wapati, the notation is described here.

Carcul
Last edited by Carcul on Fri Oct 06, 2006 7:41 am, edited 1 time in total.
Carcul

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Here is another solution (occuring before or after the UR1) inspired by the early work of Carcul:

(4,2)2 (> (4,8)!2) > (3,2)7 > (6,2)9 > (4,1)7 > (4,8)!7

This leaves a deadly pattern in ([34],[89])<89> (or an empty cell if you did the UR1 first), a contradiction. Therefore, (4,2)8 and this solves the puzzle.
re'born

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Carcul wrote:That loop doesn't imply r4c8=2. In fact, it doesn't imply anything.

Yes, I was brain dead there ... but the wine was great!
ronk
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