The New Sudoku Players' Forum

[EnderGT]

So I'm solving away, and everything's going well. Then I see what looks like a non-unique rectangle pattern, so I fill in the remaining candidate - and my solver says it's wrong! Huh? The solver tells me my candidate lists are all up to date, so it's not like I forgot to remove a candidate or something... I'm hoping someone can show me why this isn't a non-unique rectangle, so I can avoid making a mistake on future puzzles.

Original puzzle:

Code: Select all

.1.|7..|5..
.35|..4|..7
8..|.3.|..6
---+---+---
..4|.71|6..
..3|...|7..
..7|89.|4..
---+---+---
5..|.1.|..8
3..|2..|17.
..1|..8|.5.


And the "stuck" state, or rather, the state where I see the non-unique rectangle pattern (R3C3,R3C7,R7C3,R7C7)

Code: Select all

4     1     6     |  7     8     29    |  5     39    239
29    3     5     |  69    26    4     |  8     1     7
8     7     29    |  1     3     5     |  29    4     6
------------------+--------------------+--------------------
29    28    4     |  5     7     1     |  6     38    39
1     89    3     |  4     26    26    |  7     89    5
6     5     7     |  8     9     3     |  4     2     1
------------------+--------------------+--------------------
5     4     29    |  39    1     7     |  239   6     8
3     69    8     |  2     5     69    |  1     7     4
7     269   1     |  369   4     8     |  39    5     29


[Pat]

So I'm solving away, and everything's going well. Then I see what looks like a non-unique rectangle pattern, so I fill in the remaining candidate - and my solver says it's wrong! Huh? The solver tells me my candidate lists are all up to date, so it's not like I forgot to remove a candidate or something... I'm hoping someone can show me why this isn't a non-unique rectangle, so I can avoid making a mistake on future puzzles.

Original puzzle:

Code: Select all

.1.|7..|5..
.35|..4|..7
8..|.3.|..6
---+---+---
..4|.71|6..
..3|...|7..
..7|89.|4..
---+---+---
5..|.1.|..8
3..|2..|17.
..1|..8|.5.


And the "stuck" state, or rather, the state where I see the non-unique rectangle pattern (R3C3,R3C7,R7C3,R7C7)

Code: Select all

4     1     6     |  7     8     29    |  5     39    239
29    3     5     |  69    26    4     |  8     1     7
8     7     29    |  1     3     5     |  29    4     6
------------------+--------------------+--------------------
29    28    4     |  5     7     1     |  6     38    39
1     89    3     |  4     26    26    |  7     89    5
6     5     7     |  8     9     3     |  4     2     1
------------------+--------------------+--------------------
5     4     29    |  39    1     7     |  239   6     8
3     69    8     |  2     5     69    |  1     7     4
7     269   1     |  369   4     8     |  39    5     29


your rectangle is in 4 boxes

only works if it's 2 boxes

[mike_bike_kite]

I was trying out the puzzles in this forum with my new web program and it gave me this advice to your problem.

Pair found at R5C2 R5C8 for 9 and 8 which eliminates 1 option
X-Wing on 2 at R7C3 R7C7 R3C7 R3C3 eliminates 1 option
X-Wing on 3 at R4C8 R4C9 R1C9 R1C8 eliminates 1 option
R1C6 forced chain at R1C6 shows it cannot hold 9 so it must hold 2

Hope it helps

Mike

http://www.checkmypages.com/sudoku/index.php

[Luke]

Pat has already answered yr question, so since you're into unique rectangles, here's a way to solve the puzzle.

Code: Select all

4     1     6     |  7     8     29    |  5     39    239
29    3     5     |  69    26    4     |  8     1     7
8     7     29    |  1     3     5     |  29    4     6
------------------+--------------------+--------------------
29    28    4     |  5     7     1     |  6     38    39
1     89    3     |  4     26    26    |  7     89    5
6     5     7     |  8     9     3     |  4     2     1
------------------+--------------------+--------------------
5     4     29    | *3-9  1     7      | *239   6     8
3     69    8     |  2    5     69     |  1     7     4
7     269   1     | *369  4     8      | *3-9   5     29

Yet again: X-wing overlay on a UR with diagonal bivalues.
"The diagonal pair must have the x-wing component." ~ Keith

[hobiwan]

Yet again: X-wing overlay on a UR with diagonal bivalues.
"The diagonal pair must have the x-wing component." ~ Keith

What you have here can also be described as a combintion of two hidden rectangles:

Hidden Rectangle: 3/9 in r7c47,r9c47 => r7c4<>9
Hidden Rectangle: 3/9 in r7c47,r9c47 => r9c7<>9

(Only one of them needs to be performed)

[daj95376]

From my notes:

Code: Select all

Unique Rectangle Type 6   (UR + X-Wing in <1>)
(diagonal variant of Type 4)

+---------------+
|   -   -   -   |
|  1-2  -  23-1 |
|   -   -   -   |
+---------------+
| 24-1  -  1-2  |
|   -   -   -   |
|   -   -   -   |
+---------------+


[EnderGT]

only works if it's 2 boxes

Thank you very much, that is a distinction I was not aware of until now.

Luke451, hobiwan, and daj95376, thanks for the additional info about the more advanced technique.

[hobiwan]

From my notes:...

Thank's, I should have seen that

[Luke]

I was trying out the puzzles in this forum with my new web program and it gave me this advice to your problem.

X-Wing on 2 at R7C3 R7C7 R3C7 R3C3 eliminates 1 option
X-Wing on 3 at R4C8 R4C9 R1C9 R1C8 eliminates 1 option

Hi, Mike,
Looks like EnderGT had already cleaned up his x-wings quite nicely. Your "advice" pertains only to the original grid and not the PM under discussion. Maybe you only intended to plug your site?

Moving on: Have I got this right? [r4c8]<>3

Code: Select all

4     1     6     |  7     8     29    |  5    *39   *239
29    3     5     |  69    26    4     |  8     1     7
8     7     29    |  1     3     5     |  29    4     6
------------------+--------------------+--------------------
29    28    4     |  5     7     1     |  6    *-38  *39
1     89    3     |  4     26    26    |  7     89    5
6     5     7     |  8     9     3     |  4     2     1
------------------+--------------------+--------------------
5     4     29    |  39    1     7     |  239   6     8
3     69    8     |  2     5     69    |  1     7     4
7     269   1     |  369   4     8     |  39    5     29


This looks like one of them there "avoidable/forbidden/unresolvable rectangles" under much discussion hereabouts lately. [r4c8]<>[3] lest we end up with a deadly pattern.

[ronk]

Have I got this right? [r4c8]<>3
[...]
This looks like one of them there "avoidable/forbidden/unresolvable rectangles" under much discussion hereabouts lately. [r4c8]<>[3] lest we end up with a deadly pattern.

You've got it right. Because none of the four cells r14c89 contain a given, you may "freely reinvent" the missing '9' in r4c8.

AUR(39)r14c89:(r4c8 =8|2= r1c9) -2- r9c9 -9- r4c9 -3- r4c8 ==> r4c8<>3

Although the "reinvented pattern" is an AUR, the deduction does not depend upon an assumption of uniqueness.

[daj95376]

... you may "freely reinvent" the missing '9' in r4c8.

I'm more interested in how EnderGT reached the elimination [r4c8]<>9 in the first place. Another good reason to provide the original puzzle.

[udosuk]

I'm more interested in how EnderGT reached the elimination [r4c8]<>9 in the first place. Another good reason to provide the original puzzle.

He probably used the UR of {89} @ r45c28 to eliminate 9 from r4c28.

[eleven]

Although the "reinvented pattern" is an AUR, the deduction does not depend upon an assumption of uniqueness.

Yes, but then you must be able to get rid of the 9 in r4c8 without using uniqueness

[ronk]

Although the "reinvented pattern" is an AUR, the deduction does not depend upon an assumption of uniqueness.

Yes, but then you must be able to get rid of the 9 in r4c8 without using uniqueness

I carefully did not make a claim as to "overall" uniqueness.

[daj95376]

I'm more interested in how EnderGT reached the elimination [r4c8]<>9 in the first place. Another good reason to provide the original puzzle.

He probably used the UR of {89} @ r45c28 to eliminate 9 from r4c28.

Thanks udosuk! I should have spotted it myself.

Another example of the old claim that you should apply other URs before a UR Type 4.