## Obscured: Unique Rectangle:

Advanced methods and approaches for solving Sudoku puzzles

### Obscured: Unique Rectangle:

The definition in Adrew Stuart's book is (short version):
For an UR to be an UR is has to contain at least two bivalue cells (or one naked pair). If it doesnt, the UR itself is hidden underneath the additional candidates (thus: Hidden UR). If one of the UR candidates occurs only in the UR cells in the row and col opposite to the two value cell we can eliminate the other UR candidate from the UR cell.

Can the above definition of a hidden unique rectangle be upgraded

to also cover situations like the following.

i have a grid where there is three hidden pairs of the same digits linked in a rectangle shape.

with these three corners the 4th corner can be exclued from containing the hidden pairs digits.

Indicated below.

Code: Select all
`.-------------------.------------------.---------------------.| 26    1236   124  | 7     1689@  5    | 2389   249   4-89@ || 2567  9      8    | 1246  16    1236 | 2357   2457   457   || 257   2357   2457 | 24    89@    23   | 6      1     45789@|:-------------------+------------------+---------------------:| 9     2578   6    | 125   157   127  | 12578  2457   3     || 1     2578   257  | 3     567   4    | 25789  25679  56789 || 257   4      3    | 8     1567  9    | 1257   2567   567   |:-------------------+------------------+---------------------:| 8     567    57   | 9     2     67   | 4      3      1     || 3     1567   9    | 156   4     167  | 57     8      2     || 4     12567  1257 | 156   3     8    | 579    5679   5679  |'-------------------'------------------'---------------------'`

R13C5(89) hidden pair + R3C9(89) hidden pair + R1C9(89)

=> R1C9<>89

as well as the normal hidden eliminations

R1C5<>16, R3C9 <>457

is there a better definition for hidden rectangle or avoidable rectangle that can cover this, im looking for links etc.

or any topic in general that can cover this example

- notes: {this new deffintion should also include hidden pairs +naked pairs combinations)
Some do, some teach, the rest look it up.

StrmCkr

Posts: 889
Joined: 05 September 2006

### Re: Obscured: Unique Rectangle:

StrmCkr wrote:
Code: Select all
`.-------------------.------------------.---------------------.| 26    1236   124  | 7     1689@  5    | 2389   249   4-89@ || 2567  9      8    | 1246  16    1236 | 2357   2457   457   || 257   2357   2457 | 24    89@    23   | 6      1     45789@|:-------------------+------------------+---------------------:| 9     2578   6    | 125   157   127  | 12578  2457   3     || 1     2578   257  | 3     567   4    | 25789  25679  56789 || 257   4      3    | 8     1567  9    | 1257   2567   567   |:-------------------+------------------+---------------------:| 8     567    57   | 9     2     67   | 4      3      1     || 3     1567   9    | 156   4     167  | 57     8      2     || 4     12567  1257 | 156   3     8    | 579    5679   5679  |'-------------------'------------------'---------------------'`

R13C5(89) hidden pair + R3C9(89) hidden pair + R1C9(89)

=> R1C9<>89

as well as the normal hidden eliminations

R1C5<>16, R3C9 <>457

Why not just apply the normal hidden pair eliminations ... followed by a Type 1 UR
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Ignoring the fact that this puzzle can be solved with SSTS, I see two UR eliminations. I don't have a name for the UR. It relies on two strong links from a bivalue cell in the UR. The strong links form an "L" pattern of three cells where the vertex is the bivalue cell.

Code: Select all
` (89) UR in r13c59: bivalue [r3c5]=8 + "L" on <9> => [r1c5],[r3c9]=9 => [r1c9]<>8 (89) UR in r13c59: bivalue [r3c5]=9 + "L" on <8> => [r1c5],[r3c9]=8 => [r1c9]<>9 +-----------------------------------------------------------------------+ |  26     1236   124    |  7     L1689   5      |  2389   249    4-(89) | |  2567   9      8      |  1246   16     1236   |  2357   2457   457    | |  257    2357   2457   |  24    L89     23     |  6      1     L45789  | |-----------------------+-----------------------+-----------------------| |  9      2578   6      |  125    157    127    |  12578  2457   3      | |  1      2578   257    |  3      567    4      |  25789  25679  56789  | |  257    4      3      |  8      1567   9      |  1257   2567   567    | |-----------------------+-----------------------+-----------------------| |  8      567    57     |  9      2      67     |  4      3      1      | |  3      1567   9      |  156    4      167    |  57     8      2      | |  4      12567  1257   |  156    3      8      |  579    5679   5679   | +-----------------------------------------------------------------------+ # 126 eliminations remain_________________________________________________________________________________`
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

Code: Select all
`Why not just apply the normal hidden pair eliminations ... followed by a Type 1 UR `

that was not the point here.

the point is why doesnt hidden ur peramaters detect these types when they clearly exsits.

this is correct daj

there is a significant diffrence between standard ssts and what this single step accomplishes.

2 locked digits(pointing)
and the rest is all naked/hidden singles

over intial ssts:
12 locked digits (poiting)
1 hidden pair.
and the rest is naked/hidden singles.

Ignoring the fact that this puzzle can be solved with SSTS, I see two UR eliminations. I don't have a name for the UR. It relies on two strong links from a bivalue cell in the UR. The strong links form an "L" pattern of three cells where the vertex is the bivalue cell.

Code:
(89) UR in r13c59: bivalue [r3c5]=8 + "L" on <9> => [r1c5],[r3c9]=9 => [r1c9]<>8
(89) UR in r13c59: bivalue [r3c5]=9 + "L" on <8> => [r1c5],[r3c9]=8 => [r1c9]<>9
Code: Select all
` +-----------------------------------------------------------------------+  |  26     1236   124    |  7     L1689   5      |  2389   249    4-(89) |  |  2567   9      8      |  1246   16     1236   |  2357   2457   457    |  |  257    2357   2457   |  24    L89     23     |  6      1     L45789  |  |-----------------------+-----------------------+-----------------------|  |  9      2578   6      |  125    157    127    |  12578  2457   3      |  |  1      2578   257    |  3      567    4      |  25789  25679  56789  |  |  257    4      3      |  8      1567   9      |  1257   2567   567    |  |-----------------------+-----------------------+-----------------------|  |  8      567    57     |  9      2      67     |  4      3      1      |  |  3      1567   9      |  156    4      167    |  57     8      2      |  |  4      12567  1257   |  156    3      8      |  579    5679   5679   |  +-----------------------------------------------------------------------+ `

it is a type 1.
but falls into the hidden catagory as well.

to find it you would first need to make the deductions of the hidden pair.
then you find it.

im asking if there should be a change to the hidden class to cover these types:

and have 1 step.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 889
Joined: 05 September 2006

StrmCkr wrote:
Code: Select all
`Why not just apply the normal hidden pair eliminations ... followed by a Type 1 UR `

that was not the point here.

the point is why doesnt hidden ur peramaters detect these types when they clearly exsits.

[...]

it is a type 1.
but falls into the hidden catagory as well.

to find it you would first need to make the deductions of the hidden pair.
then you find it.

im asking if there should be a change to the hidden class to cover these types:

and have 1 step.

IMO 1) the "hidden UR" term is a bad term and 2) three simple steps are better than one complex step.

Perhaps this pursuit requires a better example.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

im not sure how its more complex its a random occurance.

all your looking for is naked and/or hidden pairs that form a L pattern.

its only when they 3 cells line up as a L shape in the same band or stack.

make reductions in the 4th cell thats complets the rectangle.

you make extra reductions from the same group
rather then looking again for the same shape and calling it a URtype 1.

perhaps a better example is required.
a puzzle that is not just singles?

a technique should work regardles of state.

its more or less a bonus reduction nothing more complex.

its the bonus part the makes it a Hidden Unique rectangle...

.......obsucred..... fits better.

and the sited above rules deffintion misses this complety.
if im doing a search for moves 1 type at a time apply no reductions.
nothing catches it even though it is there.

a debth based application of hidden pairs first
followed by + ur finds it.

that is not needed at all.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 889
Joined: 05 September 2006

StrmCkr wrote:its more or less a bonus reduction nothing more complex.

its the bonus part the makes it a Hidden Unique rectangle...

.......obsucred..... fits better.

I was referring to the fact that this forum has used the AUR term, rather than the hidden UR term, for quite some time.

StrmCkr wrote:and the sited above rules deffintion misses this complety.

How did your "rules" miss the use of the two hidden pair steps? I only see that they were incorporated into a more complex step.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

I am not sure whether a new technique is necessary or not, but I would drop the "Hidden UR" name for it too. The HUR (according to Andrew Stuart - and I have no idea who originally coined the term or described the technique) needs only two strong links on one of the UR digits.

What StrmCkr has described is a UR Type 1 with hidden instead of naked pairs (as has already been stated above). AUR doesnt fit either. In my understanding an AUR doesnt work until one or more candidates are removed that turn it into a real UR. StrmCkr's UR works without removing anything.
hobiwan
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Posts: 321
Joined: 16 January 2008
Location: Klagenfurt

StrmCkr wrote:
and the sited above rules deffintion misses this complety.

How did your "rules" miss the use of the two hidden pair steps? I only see that they were incorporated into a more complex step.

this was in regards to the deffinition of a HUR in my first post.

my rules dont miss the hidden pairs, i find them just the same.

but when i turn them off:

i don't find this as a HUR either.

which is why i raised this question.

aur doesnt quite fit the situation either.
its not an almost setup either.

ive only seen naked UR's posted here.

isnt there anything on hidden/naked combinations that can comprise a UR
.
rather then only haveing it arive after some other techniques make them naked.

hows this for a name?

"obscured unique rectangle" OUR

(these can be any of the known types(I-VI) as well)
.....if it actually needs one...
Some do, some teach, the rest look it up.

StrmCkr

Posts: 889
Joined: 05 September 2006

hobiwan wrote:What StrmCkr has described is a UR Type 1 with hidden instead of naked pairs (as has already been stated above). AUR doesnt fit either. In my understanding an AUR doesnt work until one or more candidates are removed that turn it into a real UR. StrmCkr's UR works without removing anything.

My definition for an AUR is quite broad. An AUR is any uniqueness pattern for four cells in two rows, two columns, and two boxes that doesn't fit one of the standard definitions for UR Types 1 thru 6.

[edit: minor rewording improvements]
Last edited by ronk on Mon Mar 16, 2009 7:42 pm, edited 1 time in total.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

that explains the diffrence in points of views.

thanks for clarity ron.

my deffinition of a almost unique rectangle - was a connecting chain that implicates a UR state.

(from my point of view this case didnt have that type of affect)
2 hidden pairs + 1 naked (nothing almost with this)
Some do, some teach, the rest look it up.

StrmCkr

Posts: 889
Joined: 05 September 2006

I have a a very limited range for identifying URs. If there are two identical, adjacent/diagonal bivalue cells in a chute, then I look for a UR Type 1-6. If not, then I look for one bivalue cell and two strong links in an "L" pattern for at least one of the candidates. This is necessary for the two remaining UR patterns that I'm able to identify.

Now, since all URs should be found before any eliminations are performed, I consider my two URs above to be one step. Since StrmCkr is so hung up on having one step instead of several, maybe this will make him happy. Sheezzz!
daj95376
2014 Supporter

Posts: 2624
Joined: 15 May 2006

sheez
im not hung up on having one step.

i read yours as one step daj.
only broken notation to show it whole.

im hung up on the rest of the term HUR. (not used here)

the defintion i know doesnt include hidden/naked combinations.

as a few diffrent programs

i have ran it through do not pic this elimination up either
and it is using the defintion above.

im asking if the definition should be refined or have these placed in a class by them selfevs.

or links to similar topics would be greatly appreciated, as i cant find anything that covers these types.
Some do, some teach, the rest look it up.

StrmCkr

Posts: 889
Joined: 05 September 2006