## problem with uniqueness test 6

Post the puzzle or solving technique that's causing you trouble and someone will help

### problem with uniqueness test 6

I've got a problem with the following puzzle:

Code: Select all
`.---------------.---------------.---------------.|*34   37   1   | 6    8    2   | 5    79  *349 ||*349  5    8   | 7    39   1   | 6    2   *34  || 6    2    379 | 4    39   5   | 37   1    8   |:---------------+---------------+---------------:| 8    37   37  | 1    4    9   | 2    5    6   || 1    4    6   | 5    2    8   | 9    3    7   || 5    9    2   | 3    7    6   | 8    4    1   |:---------------+---------------+---------------:| 2    1    39  | 8    6    4   | 37   79   5   || 7    8    4   | 9    5    3   | 1    6    2   || 39   6    5   | 2    1    7   | 4    8    39  |'---------------'---------------'---------------'`

There is a unique rectangle for digits 34 in r12c1/r12c9. Two of the corners do have an additional digit, none of the rows or columns contains any more candidates for 4, so this looks like a uniqueness test 6 to me. Candidates 3 in r2c1 and r1c9 can be deleted.

Unfortunately 3 has to be placed in r1c9 to solve the puzzle (checked with SudoCue), so something is wrong here. The only thing different from other type 6 tests I have seen is, that the additional candidates in the rectangle are equal. Is this forbidden in a test type 6?
hobiwan
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Location: Klagenfurt

### Re: problem with uniqueness test 6

[Withdrawn: I've decided that a UR Type 6 can be interpreted in three different ways ... leading to three different conclusions ... all of which are correct.]
Last edited by daj95376 on Fri Jan 25, 2008 5:54 am, edited 2 times in total.
daj95376
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I am no expert by any means but I have a different approach.

I used an AIC on (4's) as follows: r1c1>r1c9>r9c9>r9c1 therefore the (4) in r2c1 can be eliminated.. That leaves r1c1=4 and r2c9=4

If this is in error, I am sure I will here about it, as I should.
Jasper32

Posts: 60
Joined: 04 January 2008

WHOOPS!!!!! I goofed...the AIC is with (3's). removes (3) from r2c1. Don't have time to work on puzzle...think there may be a nice loop but will have to look later... Sorry for my error.
Jasper32

Posts: 60
Joined: 04 January 2008

ok - this comes from posting at night without sleeping over it...

I got it wrong of course, the elimination is for Candidate 4 not 3, which leads to a BUG+1 and solves the puzzle. The same error was in sudopedia, I even recognized it there.
hobiwan
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Location: Klagenfurt

### Re: problem with uniqueness test 6

daj95376 wrote:[Withdrawn: I've decided that a UR Type 6 can be interpreted in three different ways ... leading to three different conclusions ... all of which are correct.]

Which three different ways did you have in mind?
hobiwan
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Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

### Re: problem with uniqueness test 6

hobiwan wrote:Which three different ways did you have in mind?

Code: Select all
` +-----------------------------------+ | 34  .  .  |  .  .  .  |  .  . 349 | | 349 .  .  |  .  .  .  |  .  . 34  | |  .  .  .  |  .  .  .  |  .  .  .  | +-----------------------------------+`

Going back to basics for a Unique Rectangle, you have the following constraint to prevent the UR deadly pattern.

Code: Select all
`[r1c9]=9 -or- [r2c1]=9 must be true`

Combine this with the X-Wing constraint on 4, and the results can be viewed as ...

Code: Select all
`1) [r1c1],[r2c9]= 4   -- forced assignment viewpoint2) [r1c1],[r2c9]<>3   -- or my original viewpoint as eliminations3) [r1c9],[r2c1]<>4   -- or your viewpoint as eliminations`

I've seen a UR Type 6 described as a diagonal version of a UR Type 4. In a UR Type 4, the non- X-Wing digit is eliminated in all of the descriptions I've read. Scenario (2) would be the equivalent for a UR Type 6.
daj95376
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Posts: 2624
Joined: 15 May 2006

### Re: problem with uniqueness test 6

daj95376 wrote:
Code: Select all
` +-----------------------------------+ | 34  .  .  |  .  .  .  |  .  . 349 | | 349 .  .  |  .  .  .  |  .  . 34  | |  .  .  .  |  .  .  .  |  .  .  .  | +-----------------------------------+`

Going back to basics for a Unique Rectangle, you have the following constraint to prevent the UR deadly pattern.

Code: Select all
`[r1c9]=9 -or- [r2c1]=9 must be true`

Combine this with the X-Wing constraint on 4, and the results can be viewed as ...

Code: Select all
`1) [r1c1],[r2c9]= 4   -- forced assignment viewpoint2) [r1c1],[r2c9]<>3   -- or my original viewpoint as eliminations3) [r1c9],[r2c1]<>4   -- or your viewpoint as eliminations`

I've seen a UR Type 6 described as a diagonal version of a UR Type 4. In a UR Type 4, the non- X-Wing digit is eliminated in all of the descriptions I've read. Scenario (2) would be the equivalent for a UR Type 6.

Thanks for your explanation. I missed the X-Wing angle because the X-Wing does no eliminations on it's own. Learned something again...
hobiwan
2012 Supporter

Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

Ruud: After reading hobiwan's reference to Sudopedia, I reviewed its description of a UR Type 4 and a UR Type 6.

For the UR Type 4, I agree with Sudopedia that V can be eliminated in the ceiling cells.

For the UR Type 6, I don't agree with Sudopedia that V can be eliminated in the ceiling cells. Would you please review the description and see if U should be eliminated in the ceiling cells. Thanks!!!
daj95376
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Joined: 15 May 2006