... by: domP

It seems that when we get BUG, the sudoku can only have one or three solutions. Never two solutions and never more than 3.
Can you confirm ? If not, maybe you have a counter-example ?

So we need to check the number of solutions before using 'BUG'.
As I don't know uniqueness of solution, I never use 'BUG'. It's the same as all the unique rectangle methods.
Is it a correct method to check a new puzzle ?

It seems also that, if we put this BUG test, after XYchains, it will never be usefull. Right ?

Thanks a lot for all explainations.
DomP

... by: NeutrinoAnt

Intreresting 'decisive technique' for hard sudoku. Be careful to check if there's another candidates to be removed by naked pair/triple, otherwise it may not be a BUG.

... by: Kasper D

I don't think this is a good explanation for a bug. When I tried to use it in a puzzle I got the wrong result. I obviously didn't understand the bug method but I still don't, so I think a better explanation is required. Further, when the puzzle is loaded in the solver it doesn't actually find a bug. Yes, 2 is the right answer for D8, but why? Maybe not caused by a bug?

... by: Anonymous

Jonathan, the BUG pattern requires not only bivalue cells, but also every row, column and box having at most two instances of each candidate.

... by: Jonathan Handojo

Alright, this strategy is now proven flawed. I've come across a puzzle where all cells are bi-value cells and can still consist of a unique solution. It's a puzzle that I purchased from the Extreme Pack, so I'm not permitted to sharing it here. Andrew Stuart, I've sent you an email with the puzzle and the step at which I took to make all cells bi-value. I actually played this far myself and wanted to check whether I'm doing the right eliminations. When I thought I saw an XY-Chain that made everything bi-value cells after that, I thought I made a mistake somewhere. So, I used the solver and it happened to also deduced to the same elimination.

... by: Jan

This technique isn't right because in yellow cell (1.2.3) on first pattern it is missing number 4 candidate.

... by: David Filmer

I have found a very simple example of a BUG which has only 13 unsolved cells of which 12 have 2 candidates and one has 3 as follows:-
2..4..5.1..1.38.9..3....7.8.7...2..3.6..9...5.4......9..4....6.62.3..8..81..47...
I entered it into the Brent Knoll News February 2019 edition and called it Valentine, as the clues are in the shape of a heart with a Cupid's Arrow piercing it!

All the other illustrations of a BUG (above) had many more. Can anyone else find a BUG with less than 13 unsolved cells?

... by: Pieter, Newtown, Australia

Happy New Year Andrew!
AS a person reading about BUG for the first time may I make these suggestions to make this brief explanation clearer:
1. As noted by strmckr on 26/10/15, BUG "requires knowledge of unique rectangles and deadly patterns to apply its technique correctly". Since BUG is applied before URs in the solver, I think a reference should be made (in the first paragraph) to UR's strategy explanation for the novice to get an explanation of "deadly patterns".
2. "Removing candidate 1 from the cell ... " OR candidate 3
3. Adding a numbered point 5. something like "Hence the whole of the unsolved part of the puzzle becomes a deadly bi-value pattern". Not obvious to a BUG novice. ;-)

All the best for the new year!

Ciao
Pieter

... by: strmckr

your placing bug strategies way to high in the hierarchy: most bugs are solvable from a

finned/sashimi x-wing { fish pattern's }


out side of that it requires knowledge of unique rectangles and deadly patterns to apply its technique correctly.

Bug
http://forum.enjoysudoku.com/the-bug-bivalue-universal-grave-principle-t2352.html#p14899

bug lite
http://forum.enjoysudoku.com/between-uniqueness-and-bug-bug-lite-t3056.html

for reference to the other type of uniqueness based solving techniques also not covered on this site

http://forum.enjoysudoku.com/collection-of-solving-techniques-t3315.html

look up:
reverse bug,
reverse bug lite
mug

here is another one that is surprising powerful but often missed,
the unique rectangle 1.1

http://forum.enjoysudoku.com/how-do-ars-arise-t31045.html#p226670
{there is early posts this one sums it up the best}
U.R 1.1

Definition: an a/b/b/a pattern in a solution grid is anything isomorphic to that shown below:

Code: Select all
. . . | .
a . . | b
b . . | a
---------+---
. . . | .


Fact: if a solution grid (not necessarily unique) contains an a/b/b/a pattern on four unclued cells, C, then C=b/a/a/b is also a solution.

Theorem: if a puzzle-in-progress (that does not necessarily have a unique solution) has pencilmarks as shown below on four unclued cells then the bottom right value resolves to '3':

Code: Select all
. . . | .
1 . . | 2
2 . . | 13
---------+---
. . . | .


Proof: suppose to the contrary the bottom right value resolves to '1'. Then (vacuously) the solution grid contains the 1/2/2/1 pattern on four unclued cells, C. So, by the Fact above, C=2/1/1/2 is also a solution. But wait! - the pencilmarks do not allow that other solution - contradiction.


denis_berthier wrote:
Thanks, RedEd, for this very smart proof.

Before it, UR1.1 was only a conjecture, a matter of belief or disbelief. It is now a valid theorem (we'll see later under what implicit conditions). It shows that a short and clean proof can do what pages of repeated but unsustained claims can't.

... by: mike

can the bug method also be used to solve str8ts puzzles thank you

... by: Strmckr

Technically most bugs contain a finned or sashimi X- wing (skyscraper) on a single digit.
Which are easier to spot then xy wings and even this.
Not to mention bugs and bug lite patterns only function based on uniqueness assumed.

... by: Brett Yarberry

I have found a good example of a solution easily solved by the BUG.

  4-6-7 | 18-9-3 | 18-2-5 
  9- 2-8 | 17-5-4 | 3-6-17
  1- 3-5 | 2-6-78 | 4-78-9
 -------------------------------
  3- 1-4 | 78-78-5 | 2-9-6
  2- 5-6 | 3-4-9 | 17-17-8
 78-78-9 | 6-1-2 | 5-4-3
 -------------------------------
 78- 9-3 | 4-78-1 | 6-5-2
  6- 4-2 | 5-3-78 | 9-178-17
  5-78-1 | 9-2-6 | 78-3-4

The initial position of the board (loaded in solver) is: LOAD HERE

... by: Arthur Lurvey

When you write up this technique, consider using the following example

I got it from http://homepages.cwi.nl/~aeb/games/sudoku/solving18.html. It can be solved using other methods, but they are of the diabolical class. So this makes for a good application of this technique.

Art

... by: Peru Boro

Does Bug+1 system always work? Usually it does work but twice it failed me so I want to be sure.Thank you.

... by: Sean Forbes

Andrew, While I agree that a more astute player will more than likely identify and utilize some other solving technique before resorting to this one, I find this method very handy in real-time online competitions, especially if I've overlooked one of the more effective solving techniques up to the point when I can recognize the BUG pattern.

Thanks. Sean

... by: Harmen Dijkstra

i have a sudoku with this strategy:

+--------------+--------------+--------------+
|    4   2   1 |    5   8   6 |    9   3   7 |
|    5   9  38 |    1  34   7 |    2  48   6 |
|    6   7  38 |    2  34   9 |   14 148   5 |
+--------------+--------------+--------------+
|    7   1   9 |    8   2   3 |    5   6   4 |
|    2   5   6 |    4   7   1 |    8   9   3 |
|    8   3   4 |    9   6   5 |   17  17   2 |
+--------------+--------------+--------------+
|    1   6   5 |    3   9   2 |   47  47   8 |
|    3   4   2 |    7   1   8 |    6   5   9 |
|    9   8   7 |    6   5   4 |    3   2   1 |
+--------------+--------------+--------------+

with this strategy, we will get this solution:

+--------------+--------------+--------------+
|    4   2   1 |    5   8   6 |    9   3   7 |
|    5   9   3 |    1   4   7 |    2   8   6 |
|    6   7   8 |    2   3   9 |    1   4   5 |
+--------------+--------------+--------------+
|    7   1   9 |    8   2   3 |    5   6   4 |
|    2   5   6 |    4   7   1 |    8   9   3 |
|    8   3   4 |    9   6   5 |    7   1   2 |
+--------------+--------------+--------------+
|    1   6   5 |    3   9   2 |    4   7   8 |
|    3   4   2 |    7   1   8 |    6   5   9 |
|    9   8   7 |    6   5   4 |    3   2   1 |
+--------------+--------------+--------------+

However, there are other solutions, for example:

+--------------+--------------+--------------+
|    4   2   1 |    5   8   6 |    9   3   7 |
|    5   9   8 |    1   3   7 |    2   4   6 |
|    6   7   3 |    2   4   9 |    1   8   5 |
+--------------+--------------+--------------+
|    7   1   9 |    8   2   3 |    5   6   4 |
|    2   5   6 |    4   7   1 |    8   9   3 |
|    8   3   4 |    9   6   5 |    7   1   2 |
+--------------+--------------+--------------+
|    1   6   5 |    3   9   2 |    4   7   8 |
|    3   4   2 |    7   1   8 |    6   5   9 |
|    9   8   7 |    6   5   4 |    3   2   1 |
+--------------+--------------+--------------+