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Puzzle 10/09/30: D BBDB XY

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daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Thu Sep 30, 2010 5:07 am Post subject: Puzzle 10/09/30: D BBDB XY

Clearing out the difficult puzzles.

Code:

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

Play this puzzle online at the Daily Sudoku site

This is a test.

Solution wrote:

r17 X-Wing <> 9 r23c4,r34c7

r9 b3 Empty Rectangle <> 6 r3c4
r9c5 2-String Kite <> 6 r6c8

<16+2> XYZ-Wing r9c4/r3c4+r7c5 <> 2 r7c4

r26c23 <89> UR Type 6.2233 r2c3,r6c2<>9
r45c67 <68> UR Type 6.2243 r4c6,r5c7<>6

(6=2)r7c5 - (2=6)r6c5 - (6=9)r6c3 - (9=1)r6c8 - (1=6)r9c8 => r7c7,r9c4<>6
-or-
M-Wing 2B (1=2)r3c4 - r9c4 = (2-1)r9c3 = (1)r7c3 => r7c4<>1
M-Wing 2B (2=1)r3c4 - r7c4 = (1-2)r7c3 = (2)r9c3 => r9c4<>2
M-Wing 3B (2=1)r3c4 - r7c4 = (1-2)r7c3 = (2)r7c5 => r9c4<>2
-or-
W-Wing (1=2)r3c4 - r9c4 = r7c5 - (2=1)r7c3 => r7c4<>1
W-Wing (1=2)r3c4 - r9c4 = r9c3 - (2=1)r7c3 => r7c4<>1
W-Wing (2=1)r3c4 - r7c4 = r7c3 - (1=2)r9c3 => r9c4<>2
-or-
S-Wing (1)r7c3 = r7c4 - (1=2)r3c4 - r9c4 = (2)r7c5 => r7c3<>2
S-Wing (1)r7c3 = r7c4 - (1=2)r3c4 - r9c4 = (2)r9c3 => r9c3<>1, r7c3<>2

peterj

Joined: 26 Mar 2010
Posts: 974
Location: London, UK

Posted: Thu Sep 30, 2010 6:11 pm Post subject:

A one step UR move...

Quote:

(6=9)r7c7 - UR(12)r79c34:[(9)r7c4=(6)r79c4] ; r7c5<>6

Is this just a variant on a type 3?

JC Van Hay

Joined: 13 Jun 2010
Posts: 494
Location: Charleroi, Belgium

Posted: Thu Sep 30, 2010 8:37 pm Post subject:

Quote:

Kite (6)C5R9 : => r6c8<>6
5-SIS AIC : 6C5 (6=89)R6C23 (9=16)R69C8 : (6)r7c5=(6)r9c8 : => r7c7,r9c4<>6

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Thu Sep 30, 2010 8:59 pm Post subject:

peterj wrote:

Is this just a variant on a type 3?

I'm not certain. Mike Barker once produced an extensive list of UR types using his own labelling system. However, that post is now missing from the Players' Forum. I have a text copy of it, but I never could follow his descriptions. He mentions a Type 3b, but I don't think it matches your description.

However, he might have considered adding your elimination using the following logic:

If you'd like to review his list:

Mike Barker wrote:

Keith has written an Introduction to Unique Rectangles. Here's a shot at all of the UR options based on Myth's nomenclature. Because the descriptions of the different types are important, I've added some additional labeling which isn't strictly necessary, for example the "X" in UR2X/1SL to distinguish where the strong link is located. In addition, "Type x" refer to the historical typing definitions.

UR+1 (Type 1): one UR cell with extra candidates => "ab" can be removed from "abX"

Code:

ab ab
ab abX

UR+2: two UR cells with extra candidate(s)

--- UR+2x (Type 2/2b): two cells with the same one extra candidate in a line => "x" can be removed from all cells common to the "abx"

Code:

ab ab
abx abx

--- UR+2d (Type 5): two cells with the extra candidate diagonal to each other => "x" can be removed from all cells common to the "abx" (given the rightmost "abx" and "ab" share a box, then at the "*")

Code:

* * ab | abx
abx | ab * *

--- UR+2X (Type 3/3b): two cells with one or more, not necessarily equivalent, extra candidates => treat "abX" as "X+Y" and "abY" as "abX+Y" and perform naked and hidden set reductions in the unit(s) containing these cells except for these cells.

Code:

ab ab
abX abY

--- UR+2D: two cells with extra candidates diagonal to each other such that "X+Y"="xy" and a naked "xy" common the "abX" and "abY" => eliminate "xy" from the cell common to all three (given "abX" and the rightmost "ab" share a box then at the "*")

Code:

ab | abX
abY | ab xy *

UR+2/1SL: two UR cells with extra candidates, strong link between two cells

--- UR+2X/1SL (Type 4): link between both cells with extra candidates, both cells with extra candidates in a line which forms an X-wing => X-wing eliminations if not previously performed (a strong link on "a" removes "a" in cells common to the rightmost "ab" and "abX" and "a" in cells comon to the leftmost "ab" and "abY"), and "b" from "abX" and "abY"

Code:

ab ab

a
abX-----abY

--- UR+2B/1SL: link between one cell with extra candidates and one bivalue cell, both cells with extra candidates in a line => a strong link on "a" removes "b" from "abY" - repeat for each strong link

Code:

ab ab
|
|a
|
abX abY

--- UR+2D/1SL: cells with extra candidates diagonal to each other => strong link on "a" removes "a" from "abY" - repeat for each strong link

Code:

ab abY
|
|a
|
abX ab

UR+3: three UR cells with extra candidate(s)

--- UR+3x: three cells with the same one extra candidate => "x" can be removed from all cells common to the "abx" (given the rightmost "abx" share a box, then at the "*")

Code:

ab | abx
abx | abx * *

--- UR+3X: three cells with extra candidates diagonal to each other such that "X+Y+Z"="xy" and a naked "xy" common the "abX", "abY", and "abZ" => eliminate "xy" from the cell common to all four (given "abX" and "abZ" share a box then at the "*")

Code:

ab | abX
abY | abZ xy *

UR+3/1SL: two or three UR cells with extra candidates (Z is optional), plus one strong link and at least one extra cell

--- UR+3x/1SL: "Y" is a single candidate "y", the extra cell "(ab)y" can include "a", and/or can include "b" if it shares a house with "abX" => "b" can be removed from "abX". Similarly, the extra cell "(ab)y" can include "b", and/or can include "a" if it shares a house with "abX" => "b" can be removed from "ab(Z)".

Code:

ab abX
|
|a
|
aby ab(Z) (ab)y

--- UR+3X/1SL: includes the extra cell "(ab)U..." such that "U" is a locked set which includes "Y", "abY" is seen by all of the cells of "(ab)U..." which contain elements of "Y", "(ab)U..." can contain "a", and "(ab)U..." can contain "b" if all of its cells which contain "b" are seen by "abX" => "b" can be removed from "abX". Similarly, "(ab)U..." can contain "b", and "(ab)U..." can contain "a" if all of its cells which contain "b" are seen by "abX" => "b" can be removed from "ab(Z)".

Code:

ab abX
|
|a
|
abY ab(Z) (ab)U...

UR+3/2SL: three UR cells with extra candidates, plus two strong links, at most one of which includes the bivalue cell

--- UR+3X/2SL: both strong links share a node, do not include the bivalue cell and have different labels which forms a continuous nice loop => strong links as shown remove "a" in cells common to "ab" and "abY", "b" in cells comon to "ab" and "abX", and "Z" in "abZ" which reduces the problem to UR+2D/1SL so "b" can be removed from "abY" and "a" can be removed from "abX"

Code:

ab abX
|
b|
a |
abY-----abZ

--- UR+3C/2SL: both strong links share a node, do not include the bivalue cell and have equal labels => "b" can be removed from "abZ"

Code:

ab abX
|
a|
a |
abY-----abZ

--- UR+3N/2SL: both strong links share a node, have different labels and one link includes the bivalue cell => "a" can be removed from "abY", and treat "abY" as "Y+Z" and "abZ" as "abY+Z" and perform naked and hidden set reductions in the unit(s) containing these cells except for these cells.

Code:

ab-----abX
a |
b|
|
abY abZ

--- UR+3U/2SL: the strong links are disjoint with different labels => "a" can be removed from "abY"

Code:

ab-----abX
a

b
abY-----abZ

--- UR+3E/2SL: the strong links are disjoint with the same labels which forms an X-wing => X-wing eliminations if not previously performed (strong links as shown remove "a" from cells common to "ab" and "abY" and "a" in cells common to "abX" and "abZ"), and "b" from "abZ"

Code:

ab-----abX
a

a
abY-----abZ

UR+4/1SL: four UR cells with extra candidates, plus one strong link and at least two extra cells

--- UR+4x/1SL: "Y" and "Z" are single candidates "y" and "z", the extra cell "(ab)y" can contain "a" if it shares a house with "abW" and/or "b" if it shares a house with "abX", similarly the extra cell "(ab)z" can contain "a" if it shares a house with "abW" and/or "b" if it shares a house with "abX" => "b" can be removed from "abX".

Code:

abW-----abX
a
aby abz (ab)y (ab)z

--- UR+4X/1SL: includes the extra cell(s) "(ab)U..." such that "U" is a locked set which includes "Y", "abY" is seen by all of the cells of "(ab)U..." which contain elements of "Y", and "(ab)U..." can contain "a" if all of its cells which contain "a" are seen by "abW" and/or can contain "b" if all of its cells which contain "b" are seen by "abX" and similarly for "(ab)V..." where "V" is a locked set which includes "Z" => "b" can be removed from "abX".

Code:

abW-----abX
a
abY abZ (ab)U... (ab)V...

UR+4/2SL: three or four UR cells with extra candidates (Z is optional), plus two strong link and at least one extra cell

--- UR+4x/2SL: "Y" is a single candidate "y", the extra cell "(ab)y" can include "a", and/or can include "b" if it shares a house with "abX" => "b" can be removed from "abX".

Code:

abW-----abX
a |
|a
|
aby ab(Z) (ab)y

--- UR+4X/2SL: includes the extra cell "(ab)U..." such that "U" is a locked set which includes "Y", "abY" is seen by all of the cells of "(ab)U..." which contain elements of "Y", "(ab)U..." can contain "a", and "(ab)U..." can contain "b" if all of its cells which contain "b" are seen by "abX" => "b" can be removed from "abX".

Code:

abW-----abX
a |
|a
|
abY ab(Z) (ab)U...

UR+4/3SL: all four UR cells with extra candidates, plus three strong links

--- UR+4X/3SL: the links with equal labels are disjoint which forms a continuous nice loop => X-wing eliminations if not previously performed ("a" can be removed from cells common to "abX" and "abY" and cells common to "abZ" and "abW"), "Z" can be removed from "abZ", "W" can be removed from "abW" which reduces the problem to UR+2B/1SL so "b" can be removed from "abX" and "abY"

Code:

abX-----abZ
a |
b|
a |
abY-----abW

--- UR+4C/3SL: the links with equal labels share a node => "b" can be removed from "abZ"

Code:

abX-----abZ
a |
a|
b |
abY-----abW

peterj

Joined: 26 Mar 2010
Posts: 974
Location: London, UK

Posted: Fri Oct 01, 2010 8:03 am Post subject:

Danny, thanks! A comprehensive and daunting list. I guess it's just a useful strong link then...

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Fri Oct 01, 2010 7:05 pm Post subject:

I initially found two Type 6 URs, then I also found a variation of Peter's move. AUR(12)r79c34 Internal SIS => pseudocell (69)r79c4 ALS[(6)r79c4=(5)r1c4]r179c4-(5=9)r1c7-(9=6)r7c7; r7c5<>6 Ted

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sun Oct 03, 2010 12:05 am Post subject:

Heh heh, I'm the only one for whom it was actually a BBDB, with my seven moves. Among the moves were the two Type 6s, which are never a help, but they sound good.

storm_norm

Joined: 18 Oct 2007
Posts: 1741

Posted: Sun Oct 03, 2010 2:23 am Post subject:

peterj wrote:

Danny, thanks! A comprehensive and daunting list.
I guess it's just a useful strong link then...

a useful/powerful strong link it is.

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