The New Sudoku Players' Forum

[rjamil]

Hi,

While I was checking today's puzzle in HoDoKu, out of so many other next moves, found four XY-Chain moves containing exactly four bi-value cells as follows:

Code: Select all

.........6..7..5.9.8954..7.2....1.57...374...76.2....3.7..9823.8.6..2..4.........
 +------------------+---------+---------------+
 | 135   1235  7    | 8  12 9 | 1346 146 16   |
 | 6     124   124  | 7  12 3 | 5    8   9    |
 | 13    8     9    | 5  4  6 | 13   7   2    |
 +------------------+---------+---------------+
 | 2    (34)   348  | 9  6  1 | 48   5   7    |
 | 159   159   158  | 3  7  4 | 168  2   168  |
 | 7     6    (14)  | 2  8  5 | 9    14  3    |
 +------------------+---------+---------------+
 | 145   7    (15)  | 46 9  8 | 2    3   156  |
 | 8    (35)   6    | 1  35 2 | 7    9   4    |
 | 13459 12359 1235 | 46 35 7 | 168  16  1568 |
 +------------------+---------+---------------+

1) XY-Chain: 5 5- r7c3 -1- r6c3 -4- r4c2 -3- r8c2 -5 => r79c1,r9c23<>5
2) XY-Chain: 1 1- r6c3 -4- r4c2 -3- r8c2 -5- r7c3 -1 => r259c3<>1
3) XY-Chain: 3 3- r4c2 -4- r6c3 -1- r7c3 -5- r8c2 -3 => r19c2<>3
4) XY-Chain: 4 4- r4c2 -3- r8c2 -5- r7c3 -1- r6c3 -4 => r4c3<>4

Where as following ALS-XZ rule eliminates combined above four XY-Chains:
Almost Locked Set XZ-Rule: A=r4c2,r6c3 {134}, B=r7c3,r8c2 {135}, X=1,3 => r19c2<>3, r259c3<>1, r4c3<>4, r79c1,r9c23<>5

I think BarnS=4 (WXYZ-Wings) will also cover the same. Am I right?

R. Jamil

[SpAce]

1) XY-Chain: 5 5- r7c3 -1- r6c3 -4- r4c2 -3- r8c2 -5 => r79c1,r9c23<>5
2) XY-Chain: 1 1- r6c3 -4- r4c2 -3- r8c2 -5- r7c3 -1 => r259c3<>1
3) XY-Chain: 3 3- r4c2 -4- r6c3 -1- r7c3 -5- r8c2 -3 => r19c2<>3
4) XY-Chain: 4 4- r4c2 -3- r8c2 -5- r7c3 -1- r6c3 -4 => r4c3<>4

Where as following ALS-XZ rule eliminates combined above four XY-Chains:
Almost Locked Set XZ-Rule: A=r4c2,r6c3 {134}, B=r7c3,r8c2 {135}, X=1,3 => r19c2<>3, r259c3<>1, r4c3<>4, r79c1,r9c23<>5

I think BarnS=4 (WXYZ-Wings) will also cover the same. Am I right?

I think you might get different answers from different people, as definitions seem to vary. To me it's easiest to see as:

XY-Loop: (3=4)r4c2 - (4=1)r6c3 - (1=5)r7c3 - (5=3)r8c2 - loop => -4 r4c3, -1 r259c3, -5 b7p1789, -3 r19c2

Your doubly-linked ALS XZ works too, although I hate the name. As an ALS move, I'd rather call it:

ALS-Loop: (3={4}1)b4p29 - (1{5}=3)b7p35 - loop => same eliminations

Of course that's just one way to express it, as the ALSs can be seen either in the boxes or the columns. These work just the same:

(4={1}5)r67c3 - (5={3}4)r84c2 - loop

(1={5}3)b7p35 - (3={4}1)b4p29 - loop

(5={1}4)r76c3 - (4={3}5)r48c2 - loop

By StrmCkr's definitions it's a Barn, I think, but not by John Welch's (his BARN doesn't cover fully restricted cases, as far as I understand). By StrmCkr's definitions it's probably a WXYZ-Wing as well, but not by Andrew Stuart's (loops not covered) or John Welch's (only the most classic case covered). So, I guess it's up to you. (I don't see it as either kind, but my opinion doesn't count.)

I think it's definitely a DDS, though: 4 cells, 4 digits, 4 sectors, each digit restricted to 1 sector.

[ArkieTech]

I think you might get different answers from different people

Makes life interesting I like it.

[SpAce]

I think you might get different answers from different people

Makes life interesting I like it.

Yeah, it does Too bad it sometimes makes communication rather "interesting" as well, when people use different definitions without realizing it

[rjamil]

Hi all,

Many thanks for your valuable comments.

I will definitely go with WXYZ-Wings move as now, after analysing all aspacts in this post, it supersedes most of the techniques and easy to merge under one label.

I am still analysing all aspacts of the same and under finalizing paper work.

R. Jamil

[StrmCkr]

Barn size 4, aka Wxyz wing(my version) , or als xz double linked.. Sue du coq aka Dds (size 2)
Either way all the same elims s in the end, many techniques and names overlap personal preference for deffintion and eliminations are all over the place.

Others can find it, but takes 2 versions of Andrews /John's wxyz wings plus box line reduction afterwards to hit all the same eliminations. But each their own.

Cheers.