## Weird Hidden Rectangle

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### Weird Hidden Rectangle

I have a couple of questions about this newspaper puzzle (non-basic):

Code: Select all
`+--------------+---------------+--------------+| 3   8   1    | 4567 467 57   | 9   56  2    || 7   4   9    | 256  26  8    | 3   56  1    || 5   6   2    | 9    3   1    | 8   7   4    |+--------------+---------------+--------------+| 8   9   3    | 27   1   27   | 5   4   6    || 46  1   46   | 8    5   9    | 7   2   3    || 2   5   7    | 346  46  36   | 1   9   8    |+--------------+---------------+--------------+| 1   2   58   | 57   78  4    | 6   3   9    || 69  3   56   | 1    29  25   | 4   8   7    || 49  7   48   | 36   89  36   | 2   1   5    |+--------------+---------------+--------------+`

First, a little polling question: which solving pattern(s) do you see first? There are a few simple non-basic moves to choose from, and I'm interested in how people would rate their relative difficulty. Personally I saw one pattern without even looking, then another almost as easily, and guessed correctly the existence of a third simple pattern (but didn't bother to look for those very hard, because I don't like them). That order is also how I would personally rate their relative difficulty in general:

Hidden Text: Show
1. UR Type 1
2. W-Wing
3. XY-Wing

I think UR Type 1 is probably the easiest non-basic pattern to spot, and it's often easy to find even without pencil marks. It's also easier than some basic patterns like quads and even triples (and often makes it possible to bypass those, which is useful if solving harder basic puzzles without pencil marks). W-Wings are also easy to look for because of a recognizable end-point signature. XY-Wings (and XY-Chains in general) are much harder for my eyes.

After solving the puzzle I ran it in SudokuWiki to see other possibilities. That's what prompted my main question: what the heck is the structure below?

Screen Shot 2018-06-20 at 23.40.36.png (135.12 KiB) Viewed 422 times

SudokuWiki calls it a Hidden Unique Rectangle, but isn't that actually two of those intermingled? Or is it somehow a single structure (like an Extended UR)?

Original puzzle: 301000000700008000002900070093000046000859000250000190020004600000100007000000205
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2579
Joined: 22 May 2017

### Re: Weird Hidden Rectangle

As I see it you don't need 2 overlapping URs, as the type 1 UR of 36 at r69c46 => -36 r6c4; stte. There is a hidden UR at r16c45 and a type 4 at r12c48, but these both only allow -6 r1c4. I would be interested to know if such overlapping URs allow any further eliminations.

Phil
pjb
2014 Supporter

Posts: 2232
Joined: 11 September 2011
Location: Sydney, Australia

### Re: Weird Hidden Rectangle

pjb wrote:As I see it you don't need 2 overlapping URs, as the type 1 UR of 36 at r69c46 => -36 r6c4; stte.

That's definitely enough (and the first pattern I saw), but this weirdo was what SudokuWiki offered as a Hidden UR once normal URs and other earlier techniques had been switched off. The accompanying text was:

"Hidden Unique Rectangle
Type 1: removing 6 at A4 because of AF45 and two strong links on 4 Type 1: removing 6 at F4 because of FJ46 and two strong links on 3"

I guess it's seeing the r69c46 as a Hidden UR (instead of normal type 1) when normal URs are turned off, even though there's nothing "hidden" about it except for the strong links. Maybe? Nevertheless I think it's confusing to show two separate but overlapping URs at once, unless that overlap actually adds new properties to the whole.

There is a hidden UR at r16c45 and a type 4 at r12c48, but these both only allow -6 r1c4. I would be interested to know if such overlapping URs allow any further eliminations.

I would be interested also, but I kind of doubt that possibility. If we agree that this is just SudokuWiki's habit of showing multiple samples of a pattern at once, instead of some more interesting superstructure, then I guess there's no functional benefit of putting them together.
-SpAce-: Show
Code: Select all
`   *             |    |               |    |    *        *        |=()=|    /  _  \    |=()=|               *            *    |    |   |-=( )=-|   |    |      *     *                     \  ¯  /                   *    `

"If one is to understand the great mystery, one must study all its aspects, not just the dogmatic narrow view of the Jedi."

SpAce

Posts: 2579
Joined: 22 May 2017

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