The New Sudoku Players' Forum

[ronk]

Code: Select all

ALS: A=(r5c13459:v145689), B=(r8c4+r9c5:v246), X=6, Z=4

.---------------.---------------.---------------.
| 2789 3    4   | 259  289  58  | 278  1    6   |
| 1    6    289 | 7    2489 348 | 5    249  38  |
| 2789 5    289 | 6    1    348 | 2478 249  378 |
:---------------+---------------+---------------:
| 589  4    3   | 159  6789 5678| 278  26   178 |
|A589  7   A1589|A1459A4689 2   | 3    46  A18  |
| 6    2    18  | 1-4  3    478 | 478  5    9   |
:---------------+---------------+---------------:
| 4    1    7   | 8    5    9   | 6    3    2   |
| 3    9    26  |B24   2467 467 | 1    8    5   |
| 25   8    256 | 3   B26   1   | 9    7    4   |
'---------------'---------------'---------------'

Although another exclusion is not required to solve the puzzle, those ALS sets provide others. The values for X and Z may be interchanged ... for r4c5<>6 and r8c5<>6 too.

And since sets A and B are doubly-linked, some values are locked within the sets. vB\xz = {2} may be excluded from cells that see all the 2s in B ... for r8c5<>2. Similarly vA\xz = {1589} could be excluded from row 5 ... if there were any.

[edit: But I see Mike has found a simpler ALS.]

[RW]

I've added Ruud's puzzles to the list, thank you for the submissions.

RW

[wapati]

Here is an easy xyz-wing. I hope it fits?

Code: Select all

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


[wapati]

Here is a BUG+1 puzzle that may belong?

Code: Select all

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


This one is just barely easier and also BUG+1.

Code: Select all

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


[Carcul]

Here is an easy xyz-wing.

The Almost Unique Pattern in cells r13c268 is also very easy to use.

Carcul

[wapati]

Here is an easy xyz-wing.

The Almost Unique Pattern in cells r13c268 is also very easy to use.

Carcul

I see the pattern, I think. What do I do with it?
I am guessing that it means I can eleminate 7 from R1C68.

Is that correct?

[wapati]

BUG+2, I think.

Code: Select all

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


[RW]

Sorry for the slow reply, but the puzzles seem to be good, I'll add them to the list.

The Almost Unique Pattern in cells r13c268 is also very easy to use.

Easy to use, but it doesn't seem to solve the puzzle, or maybe I'm missing something. I get stuck with a BUG+3 that I can use to eliminate '1' fro r1c5, but I think the XYZ-wing is easier to spot in this case. Actually you could also immediately use the BUG+5 to eliminate '7' from r1c9, but I suppose there's not many people around here who consider that an easy move...

RW

[Del]

I apologize in advance if I am not conforming to the requirements of this thread but I would like to offer the solutions by the Forcing Chain (or should it be Forcing Net) method.

Grid of 3-10-2006 3.53p.m
After the preliminary clearances:
If r7c5=5, then r9c4=1, r9c7=4, r4c7=1, r4c8=9, r7c8=5.

Grids of 3-10-2006 4.02p.m.
No. 1
Last part:
If r4c3=4, then r5c9=4, r9c9=1, r3c7=1, r3c3=3, r9c3=7, r5c3=4.
No. 2
Last part:
If r8c5=2, then r8c3=9, r3c3=8, r2c5=8, r6c5=2.

Regards,
Del.

Grid of 4-10-2006 1.12a.m.
Last part:
If r4c4=4, then r4c9=9, r6c9=3, r6c4=8, r1c4=4, r1c6=7, r6c6=9, r5c6=4.

They are then solved with singles.

[wapati]

Here is a nice and easy Bug+1, full symmetry.

(I have no idea how minimal it is. How can I find out?)

Code: Select all

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

[ronk]

Here is a nice and easy Bug+1, full symmetry.

I really like that BUG+1 because it's the first one I've seen with no placements in the box containing the BUG+1 cell. It's not something I've been watching for, but it may actually be the first I've seen with "no placements in the unit (box/row/co)l containing the BUG+1 cell".

Code: Select all

 9    7    8    | 16   12   26   | 3    4    5
 5    1    2    | 8    3    4    | 6    9    7
 3    4    6    | 9    7    5    | 8    1    2
----------------+----------------+--------------
 78   6    9    | 17+4 14   38   | 5    2    34
 4    2    1    | 56   59   36   | 7    8    39
 78   5    3    | 47   29   28   | 1    6    49
----------------+----------------+--------------
 1    3    4    | 2    8    7    | 9    5    6
 2    8    5    | 3    6    9    | 4    7    1
 6    9    7    | 45   45   1    | 2    3    8

RW, puzzle #3 in the BUG+1 list looks like a BUG+2, so you might consider moving it and adding wapati's.

Code: Select all

 2    5    9    | 36   8    1    | 7    46    34+6
 3    8    7    | 56   4    9    | 12   15+26 26
 4    1    6    | 35   2    7    | 38   58    9
----------------+----------------+----------------
 7    2    4    | 1    6    3    | 5    9     8
 1    6    3    | 9    5    8    | 4    27    27
 5    9    8    | 2    7    4    | 13   16    36
----------------+----------------+----------------
 6    3    2    | 8    1    5    | 9    47    47
 8    4    1    | 7    9    2    | 6    3     5
 9    7    5    | 4    3    6    | 28   28    1

Take my M+N split of r2c8 with a grain of NaCl.

[RW]

(I have no idea how minimal it is. How can I find out?)

Under full symmetry it is symmetrically minimal. Under vertical, diagonal or rotational symmetry you can at least get it down to 26 clues and maintain the BUG+1:

Code: Select all

.......45...834..7...9..8...69...52..2.....8..53...16...4..7...2..369...69.......
.7.......5..834......9.58...69...5...2.....8..53...16...42.79......69..1.......38
.7.....4.5..834..7..69.58....9...5...2.....8............42.79..2...6...169.....38

You could also make a 24 with diagonal symmetry

Code: Select all

........55..8.4..7..69.58...69...52..2........53...16...42.79..2..3.9..1........8

but unfortunately it seems to require both a BUG-lite+1 and the BUG.

There's an applet here that shows redundant clues in grids, bit slow to use though (hold down shift and click in the grid to cycle through the values).

RW, puzzle #3 in the BUG+1 list looks like a BUG+2, so you might consider moving it and adding wapati's.

You're right, I'll move it. Your diagram is correct, then just pair up the extra candidates (26) with the bivalue cell in r2c9 and you may eliminate all other candidates '2' and '6' in the box.

RW

[wapati]

Here is an xyz, full symmetry, easy as pie!

Code: Select all

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


[RW]

Here is an xyz, full symmetry, easy as pie!

Sorry, it's a BUG+1. Another XYZ-wing already failed for the same reason here.

RW

[wapati]

And this one, submitted earlier?

Here is a nice and easy Bug+1, full symmetry.

(I have no idea how minimal it is. How can I find out?)

Code: Select all

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