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# BUG

BUG stands for Bi-Value Universal Grave

As of July 2015 this strategy has been re-instated in the solver..

The principle behind BUG is the observation that any Sudoku where all remaining cells contain just two candidates is fatally flawed. There would have been a last remaining cell with three candidates. The odd number that couldn't be paired with another cell would have to be the solution for that cell in order to prevent the bi-value 'Graveyard'.

Update July 2015

Thanks to Peter Hopkins for re-engaging me with BUG. He has found the original discussion which goes back to November 2005. Here is the link. From my testing of large data sets I believe that every instance of BUG can be solved by an XY-Chain. Hence it is positioned just before that strategy in the solver - it is an easy solution if you can recognise the pattern. Other simpler strategies may also do the same job but not as completely as XY-Chains.

Here is an example written up by Peter

The BUG cell is D8.

Removing candidate 1 from the cell does not create a deadly pattern, since candidate 1 would appear in Row D, Column 8 and Box 6 just once. Removing candidate 2 results in:
1. Row D containing candidates 1, 2, 3, 4 and 8 all exactly twice.
2. Column 8 containing candidates 1, 2, 3 and 4 all exactly twice.
3. Box 6 containing candidates 1, 2, 3 and 4 all exactly twice.
4. Every other unit containing unsolved cells in which all candidates appear exactly twice.

Thus, in order to kill the BUG, D8 must be 2.

It is possible for the BUG to exist in a sea of bi-value cells, such as this one discovered by Klaus Brenner. It is also notable for have two whole boxes with only bi-value cells.

## BUG Exemplars

These puzzles require the Bi-Value Universal Grave strategy at some point.
Only the first is somewhat trivial. They make good practice puzzles.

# Comments

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## ... 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: 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
Andrew Stuart writes:

Interesting question, I'd have to test it to be sure. There exists in Str8ts the idea of deadly rectangles - double solutions based on rectangles, but if this spans two compartments then the deadly pattern might not occur. A positive example would be nice, lots of negative ones donâ€™t really prove it

## ... 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

Andrew Stuart writes:

Requires that Simple Colouring, Y-Chains and X-Cycles are turned off to find this example - just because of the ordering of the strategies in the solver.

## ... 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.
Andrew Stuart writes:

Don't know BUG+1, do share a link to someone's explanation if you can.

## ... 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 |
+--------------+--------------+--------------+
Article created on 11-April-2008. Views: 102924
This page was last modified on 20-February-2019.
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Copyright Andrew Stuart @ Syndicated Puzzles Inc, 2019