The New Sudoku Players' Forum

[Eioru]

Lucky

Code: Select all

..8...3..
...5.4...
4....1..2
.19...85.
.........
.53...62.
1..4.8..7
...9.6...
..7...9..

54 x Hidden Single
4 x Direct Hidden Pair
1 x Pointing
2 x Naked Pair
1 x BUG type 1 (5.6)
1 x BUG type 3 (6.1)

Code: Select all

5     2 8 | (6,7)   (6,9)   (7,9) | 3 4 1
9     3 1 | 5       2       4     | 7 8 6
4     7 6 | 3       8       1     | 5 9 2
---------------------------------------------
(2,7) 1 9 | (2,6,7) (4,6)   (2,3) | 8 5 (3,4)
(2,8) 6 4 | (2,8)   (5,9)   (3,5) | 1 7 (3,9)
(7,8) 5 3 | (1,7,8) (1,4,9) (7,9) | 6 2 (4,9)
---------------------------------------------
1     9 5 | 4       3       8     | 2 6 7
3     8 2 | 9       7       6     | 4 1 5
6     4 7 | (1,2)   (1,5)   (2,5) | 9 3 8

Code: Select all

If the values 2, 7 and 9 were removed from the cells R4C4, R6C5 and R6C4, the Sudoku would exhibit a Bivalue Universal Grave pattern (or BUG).
In a BUG, each value that remains in a row, column or block has exactly two possible positions in that row, column or block; and each empty cell has exactly two possible values. A Sudoku having a BUG has zero, two or more valid solutions.
Because a valid Sudoku has exactly one solution, the BUG cannot be part of it. The only way to avoid the BUG is if at least one of the cells R4C4, R6C5 or R6C4 contains one of the values 2, 7 or 9. It follows that one of R4C4, R6C5 or R6C4 forms a Naked Set (5) with R4C6, R5C5, R5C6 and R6C6 on the values 2, 3, 5, 7 and 9 in the block.
Other potential positions of the values 2, 3, 5, 7 and 9 can therefore be removed from the block.

I didn't see BUG type 3 with 6.0 yet.

[re'born]

Nice find Eioru
An alternative solution is given by using the potential deadly pattern in r456c14:

Code: Select all

.---------------.---------------.---------------.
| 5    2    8   |&67   69   79  | 3    4    1   |
| 9    3    1   | 5    2    4   | 7    8    6   |
| 4    7    6   | 3    8    1   | 5    9    2   |
:---------------+---------------+---------------:
|*27   1    9   |*27+6 46   23  | 8    5    34  |
|*28   6    4   |*28   59   35  | 1    7    39  |
|*78   5    3   |*78+1 149  79  | 6    2    49  |
:---------------+---------------+---------------:
| 1    9    5   | 4    3    8   | 2    6    7   |
| 3    8    2   | 9    7    6   | 4    1    5   |
| 6    4    7   | 12   15   25  | 9    3    8   |
'---------------'---------------'---------------'

The strong link on 7 in row 4 implies that r6c4<>8, and using r1c4=67, we get r6c4<>7 via
[r6c4]=1|6=[r4c4]-6-[r1c4]-7-[r6c4], => r6c4<>7.
Therefore, r6c4=1, solving the puzzle.

[claudiarabia]

Lucky

Code: Select all

..8...3..
...5.4...
4....1..2
.19...85.
.........
.53...62.
1..4.8..7
...9.6...
..7...9..

54 x Hidden Single
4 x Direct Hidden Pair
1 x Pointing
2 x Naked Pair
1 x BUG type 1 (5.6)
1 x BUG type 3 (6.1)

Code: Select all

5     2 8 | (6,7)   (6,9)   (7,9) | 3 4 1
9     3 1 | 5       2       4     | 7 8 6
4     7 6 | 3       8       1     | 5 9 2
---------------------------------------------
(2,7) 1 9 | (2,6,7) (4,6)   (2,3) | 8 5 (3,4)
(2,8) 6 4 | (2,8)   (5,9)   (3,5) | 1 7 (3,9)
(7,8) 5 3 | (1,7,8) (1,4,9) (7,9) | 6 2 (4,9)
---------------------------------------------
1     9 5 | 4       3       8     | 2 6 7
3     8 2 | 9       7       6     | 4 1 5
6     4 7 | (1,2)   (1,5)   (2,5) | 9 3 8

Code: Select all

If the values 2, 7 and 9 were removed from the cells R4C4, R6C5 and R6C4, the Sudoku would exhibit a Bivalue Universal Grave pattern (or BUG).
.....The only way to avoid the BUG is if at least one of the cells R4C4, R6C5 or R6C4 contains one of the values 2, 7 or 9. It follows that one of R4C4, R6C5 or R6C4 forms a Naked Set (5) with R4C6, R5C5, R5C6 and R6C6 on the values 2, 3, 5, 7 and 9 in the block.
Other potential positions of the values 2, 3, 5, 7 and 9 can therefore be removed from the block.

I didn't see BUG type 3 with 6.0 yet.

Thank you, Eioru, for this nice example of a BUG Type 3 not in a line but in a box. Until now I only had BUG Type 3 in lines. I always was wondering, if there is an example with such a set in a box and here we have it finally. The BUG Type 3 is happening when all the candidates who are appearing three times in a row, column and box, are forming a triplet, quad or quint etc. together with one or more bi-value-cells in the respective region, here the middle box. In this case the 2 in r4c4, the 7 in r6c4 and the 9 in r6c5 are forming a multiple set with the cells r4c6, r5c5 and r6c6 in which all the three kandidates 2 7 and 9 are showing up again. Because the cells r4c6 and r5c6 are connected with r5c5 (35), the set is now very big - a septuple, eliminating finally the 2 outside of this set in r5c4 which leads in the end to BUG Type 1.

Claudia

[ronk]

Nice find Eioru
An alternative solution is given by using the potential deadly pattern in r456c14:

Code: Select all

.---------------.---------------.---------------.
| 5    2    8   |&67   69   79  | 3    4    1   |
| 9    3    1   | 5    2    4   | 7    8    6   |
| 4    7    6   | 3    8    1   | 5    9    2   |
:---------------+---------------+---------------:
|*27   1    9   |*27+6 46   23  | 8    5    34  |
|*28   6    4   |*28   59   35  | 1    7    39  |
|*78   5    3   |*78+1 149  79  | 6    2    49  |
:---------------+---------------+---------------:
| 1    9    5   | 4    3    8   | 2    6    7   |
| 3    8    2   | 9    7    6   | 4    1    5   |
| 6    4    7   | 12   15   25  | 9    3    8   |
'---------------'---------------'---------------'

The strong link on 7 in row 4 implies that r6c4<>8.

I assume you're referring to ... r6c4-8-r6c1-7-r4c1=7=r4c4=6|1=r6c4, implies r6c4<>8

There's also an xy-chain ... r5c5-9-r1c5-6-r4c5-4-r4c9-3-r5c9-9-r5c5, implies r5c5 ... which solves the puzzle.

Loading the puzzle into Sudoku Explainer, I was surprised to find that "Get All Hints" gives only the "BUG type 3" hint. Is there an option somewhere to tell it to consider chains too?

[edit: thanks to re'born, corrected typo in xy-chain]

[re'born]

I assume you're referring to ... r6c4-8-r6c1-7-r4c1=7=r4c4=6|1=r6c4, implies r6c4<>8

yep.

There's also an xy-chain ... r5c5-9-r1c5-6-r4c5-4-r4c9-3-r5c9-8-r5c5, implies r5c5 ... which solves the puzzle.

I guess the last link in your chain should be r5c9-9-r5c5.

[RW]

There's also an xy-chain ... r5c5-9-r1c5-6-r4c5-4-r4c9-3-r5c9-9-r5c5, implies r5c5 ... which solves the puzzle.

Loading the puzzle into Sudoku Explainer, I was surprised to find that "Get All Hints" gives only the "BUG type 3" hint. Is there an option somewhere to tell it to consider chains too?

I don't think that you can tell it to include chains with the "get all hints" tool if there are easier moves available. But, you can find the available chains with the "Get next hint" tool. At the point of the BUG there is 13 different forcing chains with ER 7.2, one of them makes the same elimination as yours, but with a different chain:

[r5c5]-9-[r5c9]=9=[r6c9]=4=[r6c5]=1=[r9c5]=5=[r5c5]

I believe Explainer finds this chain before your XY-chain because the links in the chain are hidden singles, XY-chains use naked singles. As we know, Explainer rates hidden singles a lot easier than naked. SE only looks for one chain to eliminate each candidate, so it will not find for your XY-chain.

RW

[ronk]

I don't think that you can tell it to include chains with the "get all hints" tool if there are easier moves available. But, you can find the available chains with the "Get next hint" tool.

Thanks, I didn't know one could repeatedly click "Get next hint" to get additional hints for the same pencilmarks.