The New Sudoku Players' Forum

[Marty R.]

OK, now I've got a question: How would you apply Ted's UAR “externals” approach to show r2c3<>3? I'm still struggling to understand his five External Principles!

That's pretty easy (I don't know offhand his five principles).

For externals, at least in this case, it doesn't matter whether you use the line or box.

R2c2=4-r2c1=r5c1-(4=3)r5c3=>r2c3<>3

And, of course, the 3s in either box 1 or line 2 preclude a 3 in r2c3.

[Sudtyro2]

That's pretty easy ...

Thx, Marty...you're right, that was easy!

I'm also guessing that other possible inferences, especially with the 3s digits, would be unproductive, as well. More study needed on “externals.”

SteveC

[Marty R.]

More study needed on “externals.”

Well worth the time since some URs that can't be solved with internals can be broken with externals.

[daj95376]

There is a <23> UR [r29c12] that overlaps a <34> UR [r25c13]. They translate into the following DP (I believe).

Code: Select all

 +-----------------------------------------------------+
 |  6    7    5    |  4    8    3    |  2    1    9    |
 | *234 *234 *34+8 |  1    7    9    |  5    6    38   |
 |  9    13   138  |  5    6    2    |  8-3  4    7    |
 |-----------------+-----------------+-----------------|
 |  7    8    6    |  3    2    1    |  4    9    5    |
 | *34   5   *34   |  7    9    6    |  18   2    18   |
 |  1    9    2    |  8    5    4    |  7    3    6    |
 |-----------------+-----------------+-----------------|
 |  8    6    19   |  2    3    7    |  19   5    4    |
 |  5    234  349  |  6    1    8    |  39   7    23   |
 | *23  *23+1 7    |  9    4    5    |  6    8    123  |
 +-----------------------------------------------------+
 # 28 eliminations remain

 (1)r9c2 - (1=3)r3c2 - (3)r3c7
 (8)r2c3 - (8=3)r2c9 - (3)r3c7


Verification that r2c3<>8 and r9c2<>1 translates into the DP.

Code: Select all

 r5c1=3
 *-----------------------------------------*
 | 6   7   5   | 4   8   3   | 2   1   9   |
 |=4  =2  =3   | 1   7   9   | 5   6   8   |
 | 9   1   18  | 5   6   2   | 38  4   7   |
 |-------------+-------------+-------------|
 | 7   8   6   | 3   2   1   | 4   9   5   |
 |=3   5  =4   | 7   9   6   | 18  2   18  |
 | 1   9   2   | 8   5   4   | 7   3   6   |
 |-------------+-------------+-------------|
 | 8   6   19  | 2   3   7   | 19  5   4   |
 | 5   4   9   | 6   1   8   | 39  7   23  |
 |=2  =3   7   | 9   4   5   | 6   8   1   |
 *-----------------------------------------*


Code: Select all

 r5c1=4

 r2c12=23 => r3c2<> 3
 r9c12=23 => r8c2<>23
 *--------------------------------------------------*
 | 6    7    5    | 4    8    3    | 2    1    9    |
 |=23  =23  =4    | 1    7    9    | 5    6    8    |
 | 9    1-3  18   | 5    6    2    | 38   4    7    |
 |----------------+----------------+----------------|
 | 7    8    6    | 3    2    1    | 4    9    5    |
 |=4    5   =3    | 7    9    6    | 18   2    18   |
 | 1    9    2    | 8    5    4    | 7    3    6    |
 |----------------+----------------+----------------|
 | 8    6    19   | 2    3    7    | 19   5    4    |
 | 5    4-23 9    | 6    1    8    | 39   7    23   |
 |=23  =23   7    | 9    4    5    | 6    8    1    |
 *--------------------------------------------------*


[Sudtyro2]

There is a <23> UR [r29c12] that overlaps a <34> UR [r25c13]. They translate into the following DP (I believe).

Code: Select all

 +-----------------------------------------------------+
 |  6    7    5    |  4    8    3    |  2    1    9    |
 | *234 *234 *34+8 |  1    7    9    |  5    6    38   |
 |  9    13   138  |  5    6    2    |  8-3  4    7    |
 |-----------------+-----------------+-----------------|
 |  7    8    6    |  3    2    1    |  4    9    5    |
 | *34   5   *34   |  7    9    6    |  18   2    18   |
 |  1    9    2    |  8    5    4    |  7    3    6    |
 |-----------------+-----------------+-----------------|
 |  8    6    19   |  2    3    7    |  19   5    4    |
 |  5    234  349  |  6    1    8    |  39   7    23   |
 | *23  *23+1 7    |  9    4    5    |  6    8    123  |
 +-----------------------------------------------------+
 # 28 eliminations remain

 (1)r9c2 - (1=3)r3c2 - (3)r3c7
 (8)r2c3 - (8=3)r2c9 - (3)r3c7


Interesting find, Danny! Looks almost like one of Myth's MUG patterns.
Just one (stupid) question...(4)r2c2 is not a digit of either UR, so why isn't it treated as an extra candidate (like the 8 and 1)?

SteveC

[daj95376]

There is a <23> UR [r29c12] that overlaps a <34> UR [r25c13]. They translate into the following DP (I believe).

Code: Select all

 +-----------------------------------------------------+
 |  6    7    5    |  4    8    3    |  2    1    9    |
 | *234 *234 *34+8 |  1    7    9    |  5    6    38   |
 |  9    13   138  |  5    6    2    |  8-3  4    7    |
 |-----------------+-----------------+-----------------|
 |  7    8    6    |  3    2    1    |  4    9    5    |
 | *34   5   *34   |  7    9    6    |  18   2    18   |
 |  1    9    2    |  8    5    4    |  7    3    6    |
 |-----------------+-----------------+-----------------|
 |  8    6    19   |  2    3    7    |  19   5    4    |
 |  5    234  349  |  6    1    8    |  39   7    23   |
 | *23  *23+1 7    |  9    4    5    |  6    8    123  |
 +-----------------------------------------------------+
 # 28 eliminations remain

 (1)r9c2 - (1=3)r3c2 - (3)r3c7
 (8)r2c3 - (8=3)r2c9 - (3)r3c7


Interesting find, Danny! Looks almost like one of Myth's MUG patterns.
Just one (stupid) question...(4)r2c2 is not a digit of either UR, so why isn't it treated as an extra candidate (like the 8 and 1)?

I get in trouble when I try to identify DP patterns. However, I had expected that Luke or blue would comment and call it a BUG-Lite.

I used all of the UR cells to form the DP. Candidate 4r2c2 dropped out when I tested the DP through selecting alternate candidates in r5c1. Specifically:

Code: Select all

 r5c1=3 reduction after r2c3<>8 and r9c2<>1
 *-----------------------------------------*
 | 6   7   5   | 4   8   3   | 2   1   9   |
 |=4  =2  =3   | 1   7   9   | 5   6   8   |
 | 9   1   18  | 5   6   2   | 38  4   7   |
 |-------------+-------------+-------------|
 | 7   8   6   | 3   2   1   | 4   9   5   |
 |=3   5  =4   | 7   9   6   | 18  2   18  |
 | 1   9   2   | 8   5   4   | 7   3   6   |
 |-------------+-------------+-------------|
 | 8   6   19  | 2   3   7   | 19  5   4   |
 | 5   4   9   | 6   1   8   | 39  7   23  |
 |=2  =3   7   | 9   4   5   | 6   8   1   |
 *-----------------------------------------*


Code: Select all

 r5c1=4 reduction after r2c3<>8 and r9c2<>1

 r3c2<> 3 from <23> in r2c12
 r8c2<>23 from <23> in r9c12
 r9c9<>23 from <23> in r9c12
 *--------------------------------------------------*
 | 6    7    5    | 4    8    3    | 2    1    9    |
 |=23  =23  =4    | 1    7    9    | 5    6    38   |
 | 9    1    18   | 5    6    2    | 38   4    7    |
 |----------------+----------------+----------------|
 | 7    8    6    | 3    2    1    | 4    9    5    |
 |=4    5   =3    | 7    9    6    | 18   2    18   |
 | 1    9    2    | 8    5    4    | 7    3    6    |
 |----------------+----------------+----------------|
 | 8    6    19   | 2    3    7    | 19   5    4    |
 | 5    4    9    | 6    1    8    | 39   7    23   |
 |=23  =23   7    | 9    4    5    | 6    8    1    |
 *--------------------------------------------------*


So, I never considered 4r2c2 a hindrance to forming the DP. It does raise the question as to whether or not every (unblocked) candidate in every DP cell must lead to the DP.

_

[Sudtyro2]

So, I never considered 4r2c2 a hindrance to forming the DP. It does raise the question as to whether or not every (unblocked) candidate in every DP cell must lead to the DP.

FWIW, I treated (4)r2c2 as an extra candidate and got:
(4)r2c2-(4)r9c2=(4-9)r9c3=(9-3)r9c7 => no (3) in c7; contradiction.
So, there's clearly a loose end in my thinking!

SteveC

[JC Van Hay]

Code: Select all

+-----------------------+---------+------------+
| 6      7      5       | 4  8  3 | 2   1  9   |
| (234)  (234)  (+8-34) | 1  7  9 | 5   6  3-8 |
| 9      (13)   13-8    | 5  6  2 | 38  4  7   |
+-----------------------+---------+------------+
| 7      8      6       | 3  2  1 | 4   9  5   |
| (34)   5      (34)    | 7  9  6 | 18  2  18  |
| 1      9      2       | 8  5  4 | 7   3  6   |
+-----------------------+---------+------------+
| 8      6      19      | 2  3  7 | 19  5  4   |
| 5      234    349     | 6  1  8 | 39  7  23  |
| (23)   (123)  7       | 9  4  5 | 6   8  123 |
+-----------------------+---------+------------+


UR(34)r25c13=*[8r2c3=*2r2c1-(2=3)r9c1-3r5c1=3r5c3] :=> -3r2c3
UR(23)r29c12=*[4r2c12=*1r9c2-(1=234)r3c2,r2c12] :=> -4r2c3
or
MUG(234)r2c123,r5c13,r9c12=*[8r2c3=*1r9c2-(1=234)r3c2,r2c12] :=> -34r2c3(=8)

[blue]

There is a <23> UR [r29c12] that overlaps a <34> UR [r25c13]. They translate into the following DP (I believe).

Code: Select all

 +-----------------------------------------------------+
 |  6    7    5    |  4    8    3    |  2    1    9    |
 | *234 *234 *34+8 |  1    7    9    |  5    6    38   |
 |  9    13   138  |  5    6    2    |  8-3  4    7    |
 |-----------------+-----------------+-----------------|
 |  7    8    6    |  3    2    1    |  4    9    5    |
 | *34   5   *34   |  7    9    6    |  18   2    18   |
 |  1    9    2    |  8    5    4    |  7    3    6    |
 |-----------------+-----------------+-----------------|
 |  8    6    19   |  2    3    7    |  19   5    4    |
 |  5    234  349  |  6    1    8    |  39   7    23   |
 | *23  *23+1 7    |  9    4    5    |  6    8    123  |
 +-----------------------------------------------------+
 # 28 eliminations remain

 (1)r9c2 - (1=3)r3c2 - (3)r3c7
 (8)r2c3 - (8=3)r2c9 - (3)r3c7


Interesting find, Danny! Looks almost like one of Myth's MUG patterns.
Just one (stupid) question...(4)r2c2 is not a digit of either UR, so why isn't it treated as an extra candidate (like the 8 and 1)?

I get in trouble when I try to identify DP patterns. However, I had expected that Luke or blue would comment and call it a BUG-Lite.

I mostly avoid them like the plague. [ Don't count me among the "DP pros". ]
I do appreciate the elegance in the logic, however.

For what it's worth, there is a (BUG-Lite)+4 pattern using those cells.
The chains for the extra "+n" candidates are rather long, though.
[ Maybe someone can come up with something shorter ? ]

Code: Select all

+-------------------+-----------------+-----------------+
|  6     7     5    |  4    8    3    |  2    1    9    |
| *24+3 *23+4 *34+8 |  1    7    9    |  5    6    38   |
|  9     13    138  |  5    6    2    |  8-3  4    7    |
+-------------------+-----------------+-----------------+
|  7     8     6    |  3    2    1    |  4    9    5    |
| *34    5    *34   |  7    9    6    |  18   2    18   |
|  1     9     2    |  8    5    4    |  7    3    6    |
+-------------------+-----------------+-----------------+
|  8     6     19   |  2    3    7    |  19   5    4    |
|  5     234   349  |  6    1    8    |  39   7    23   |
| *23   *23+1  7    |  9    4    5    |  6    8    123  |
+-------------------+-----------------+-----------------+

(BUG-Lite)+4 => -3r3c7 :

Code: Select all

(BUG-Lite)
    ||
  3r2c1 - (3=1)r3c2 - r9c2 = r9c9 - (1=9)r7c7 - (9=3)r8c7 - 3r3c7
    ||
  4r2c2 - r8c2 = (4-9)r8c3 = (9-1)r7c3 = r3c3 - (1=3)r3c2 - 3r3c7
    ||
  8r2c3 - (8=3)r2c9 --------------------------------------- 3r3c7
    ||
  1r9c2 - (1=3)r3c2 --------------------------------------- 3r3c7


Best Regards,
Blue.

[daj95376]

FWIW, I treated (4)r2c2 as an extra candidate and got:
(4)r2c2-(4)r9c2=(4-9)r9c3=(9-3)r9c7 => no (3) in c7; contradiction.
So, there's clearly a loose end in my thinking!

Well, since you and blue both want to consider 4r2c2 as an extra candidate in the DP, then:

Code: Select all

 (4)r2c2 - (423=231)r8c2,r9c12  =>  4r2c2 true results in 1r9c2 true as well.


As far as I'm concerned, forcing r2c3<>8 and r9c2<>1 has the following results based on the candidates in r5c1.

Code: Select all

 r5c1=3  =>  <34> UA in r25c13

 r5c1=4  =>  <23> DP in r29c12


Thus, at least one of r2c3=8 or r9c2=1 must be true.

_

[blue]

Hi Danny,

Well, since you and blue both want to consider 4r2c2 as an extra candidate in the DP, then:
(...)

I found your DP quite acceptible -- no problems with it at all.
My post was a sort of an "FYI", and "FWIW"/"'not much at all''" post.

It was also a [slight] challenge for someone/anyone to come up with a shorter chain for either (3r2c1 => -3r3c7) or (4r2c2 => ~3r3c7). [ Whether shorter chains exist, I can't say. ]

[ This isn't important, and I haven't looked in the earlier posts, and maybe this was already covered ... but there's akso a "discontinuous loop" AIC elimination for 3r3c7, that's shorter than either of the chains that I used for the "extra +n candidates" in my (overblown) BUG-Lite:

(3=1)r3c2 - r9c2 = r9c9 - (1=9)r7c7 - (9=3)r8c7 => r3c7<>3. ]

Again, Best Regards,
Blue.

[daj95376]

Hello blue,

For your BUG-Lite, you could have use:

Code: Select all

 3r2c1 -<34>UR- (34=8)r2c3
   ||
 4r2c2 - (423=231)r8c2,r9c12


You'll notice that 3r2c1 forces r2c3=8, and that 4r2c2 forces r9c2=1. At this point, these two cases degenerate to the results from the remaining cases in your BUG-Lite.

_

[blue]

I'm so bad at this stuff ...

It took be a while to digest this bit: "3r2c1 -<34>UR- (34=8)r2c3"
I probably would have written "(3-2)r2c1 =(UR: (34)r25c13)= 8r2c3"

[Luke]

There is a <23> UR [r29c12] that overlaps a <34> UR [r25c13]. They translate into the following DP (I believe).

Code: Select all

 +-----------------------------------------------------+
 |  6    7    5    |  4    8    3    |  2    1    9    |
 | *234 *234 *34+8 |  1    7    9    |  5    6    38   |
 |  9    13   138  |  5    6    2    |  8-3  4    7    |
 |-----------------+-----------------+-----------------|
 |  7    8    6    |  3    2    1    |  4    9    5    |
 | *34   5   *34   |  7    9    6    |  18   2    18   |
 |  1    9    2    |  8    5    4    |  7    3    6    |
 |-----------------+-----------------+-----------------|
 |  8    6    19   |  2    3    7    |  19   5    4    |
 |  5    234  349  |  6    1    8    |  39   7    23   |
 | *23  *23+1 7    |  9    4    5    |  6    8    123  |
 +-----------------------------------------------------+


Ah, to plumb the murky depths of MUG uncertainty and poke its soft spots with a stick!

Daj, although your approach works wonders for this particular puzzle, I side with Sudtyro2 that (4)r2c2 is not part your overlapping URs and must be accounted for.

I have no problem with URs overlapping in one cell being called a MUG, BTW. I can show you where smart people say it isn't, but that's still my opinion. I would not call it a BUG-Lite under any circumstances.

Sidebar:

Three other (234) DPs can be woven into this.
1) There's another (34)UR, boxes 1 and 7.
2) There's a (34)BUG-Lite in boxes 1, 4, and 7.
3) There's a (23)BUG-Lite in boxes 1, 7, and 9.

I'm out there enuf to try to find something else, but not today. You guys got this one pretty damn well covered.