The New Sudoku Players' Forum

[kurbads]

Hi, could someone explain, why the "+1" is 3 in this "BUG+1"?

[Leren]

If the 3 was removed from that cell, then all unsolved cells would have 2 candidates, and all candidates would appear exactly twice in there row, column and box.

In that case it would look like the puzzle could have two solutions, but since almost all sites only publish puzzles with one solution, both halves of the pattern must be invalid (check it and see).

So the unique solution must contain the 3 in that cell.

Leren

[kurbads]

Dear Leren, thank you for taking time and explaining.

But I did read about only two solutions in box, row and column in the help and guidance of the Jason's app.

What I am asking is for you to explain me – dummy, how is that wrong?

What is wrong with 2 candidates? If there is one candidate in one cell then other fits in the other.

I placed 1 and I placed 2 in the cell in question, but it did not cause immediate conflict.

It did arise later but I failed to see the connection.

Could you elaborate further?

Thank you!

[Leren]

It's no surprise that the BUG situation eventually caused a conflict, because the puzzle designer made the puzzle with one solution.

In theory a fully exposed BUG pattern could either have 0 or 2 solutions (ie not 1 solution), but the 2 solution case is not compatible with a single solution, and so is never used by puzzle designers these days, only the 0 solution case is used.

Think of the way we use traffic lights. There is no logical reason why a red traffic light could not mean "Go" and a green traffic light could not mean "Stop", but I'm pretty sure that the Red/Stop - Green/Go convention is the one that is used in every country (it is in Australia, where I come from, amazingly in every state and territory .) Following that convention world wide ensures that we minimise the number of traffic accidents.

When Sudoku first became a world wide craze, there may have been puzzles with multiple solutions, but it quickly became the norm for puzzles to only have one solution, because that was what puzzle addicts wanted.

If you want to read further about the so-called Uniqueness Controversy, try, for example, here.

Leren

[marek stefanik]

Hi kurbads,

I think that the best way to see how BUG works is to have a look at a puzzle with two solutions. So I created this puzzle:
8.5.....696.1.7.58.........5.14863..4..391..2..972518.78.2..6.519..63..7.5..7.9..

After basics and an X-Wing on 3s, one arrives at this BUG:

Code: Select all

+--------------+--------------+--------------+
| 8   14  5    | 9   43  2    | 7   31  6    |
| 9   6   23   | 1   34  7    | 42  5   8    |
| 32  41  7    | 6   5   8    | 24  9   13   |
+--------------+--------------+--------------+
| 5   2   1    | 4   8   6    | 3   7   9    |
| 4   7   8    | 3   9   1    | 5   6   2    |
| 6   3   9    | 7   2   5    | 1   8   4    |
+--------------+--------------+--------------+
| 7   8   34   | 2   1   9    | 6   43  5    |
| 1   9   42   | 5   6   3    | 8   24  7    |
| 23  5   6    | 8   7   4    | 9   12  31   |
+--------------+--------------+--------------+

As for the BUG, the only difference is in box 1.
You can see that the puzzle has two solutions, one uses the first candidate in every unsolved cell, the other uses the second.

As Leren wrote, a BUG either has two solutions or none. If it has none, there should be a contradiction common to both options.
Coming back to the original puzzle, we can find exactly that:

Code: Select all

   +---------------+---------------+---------------+
   | 8    14   5   | 9    34   2   | 7    13   6   |
   | 23b  6    7   | 1    34   8   | 24   5    9   |
   | 9    14   23a | 6    5    7   | 24   8    13b |
   +---------------+---------------+---------------+
   | 5    2    1   | 7    8    6   | 3    9    4   |
   | 4    7    8   | 3    9    1   | 5    6    2   |
   | 6    3    9   | 4    2    5   | 1    7    8   |
   +---------------+---------------+---------------+
   | 7    8    34  | 2    1    9   | 6    34   5   |
   | 1    9    24  | 5    6    3   | 8    24   7   |
   | 23a  5    6   | 8    7    4   | 9    123  13a |
   +---------------+---------------+---------------+

As you can see, the 3s in r9c19 are both false, since they cannot both be true. That forces 3r9c8 to be true.

Alternatively, we can use a technique called Broken Wing.
It states that the five marked cells would create an oddagon (with no solution), therefore there has to be a 3 (so-called guardian) preventing it. The only guardian is 3r9c8.
This approach is mostly used when there is more than one guardian (and thus we cannot use the chain directly).

Hopefully that explains why the BUG options are equivalent.

Marek

[Leren]

Another way of solving the puzzle without a BUG, or other Uniqueness move is to use a Skyscraper.

Code: Select all

*-----------------------------------*
| 8  14  5  | 9 34 2 | 7   1-3  6   |
| 23 6   7  | 1 34 8 | 24  5    9   |
| 9  14 b23 | 6 5  7 | 24  8   a13  |
|-----------+--------+--------------|
| 5  2   1  | 7 8  6 | 3   9    4   |
| 4  7   8  | 3 9  1 | 5   6    2   |
| 6  3   9  | 4 2  5 | 1   7    8   |
|-----------+--------+--------------|
| 7  8  c34 | 2 1  9 | 6  d34   5   |
| 1  9   24 | 5 6  3 | 8   24   7   |
| 23 5   6  | 8 7  4 | 9   123  1-3 |
*-----------------------------------*

If you look at the marked cells a-b-c-d it's easy to show that one of cells a or d must be 3, and they remove the two 3's as marked. You can read about Skyscrapers here.

The Oddagon also does not depend on uniqueness. The best writeup on that technique that I can find is here.

Leren

[kurbads]

Thank you, thank you, I got it. It actually took me to spot one in another game and use it as a solution. Indeed if there are two unique pairs un a rectangle or parallelogram and one of the cells has an extra candidate, then to avoid two solutions the extra has to be the one as otherwise there would nothing else to affect the cells in question.

I have a new problem with guidance. I will start a new topic about it.