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unkx80
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Post by unkx80 »

rep'nA's puzzle continued...

Code: Select all

6712318075115xnj1744948euqc05@23495wr3@86574382qq9c8376684r1me9803k937392uj95190402eae173110156p86#5082m788zpj

.-------------------------------------------.
| 6   7   1   2   3   1   8   0   7   5   1 |
|   +   +---+---+   +   +   +   +   +   +   |
| 1   5 | 3   3 | 9   1   7   4   4   9   4 |
|   +   +---+---+   +   +   +---+   +   +   |
| 8 | 4 | 0   6 | 2   0   5 | 6   2   3   4 |
|   +   +---+---+   +---+   +   +   +   +   |
| 9   5 | 2   7   3 | 6   8   6   5   7   4 |
|   +   +   +---+---+   +   +   +   +   +   |
| 3   8   2   6   6   9 | 2   8   3   7   6 |
|   +   +   +---+   +---+   +   +   +   +   |
| 6   8   4   7   1   2 | 4   9   8   0   3 |
|---+   +   +   +   +   +   +---+   +   +   |
| 0   9   3   7   3   9   2 | 0 | 9   9   5 |
|   +   +   +   +   +   +   +   +   +   +   |
| 1   9   0   4   0   2 | 4 | 0 | 4   1   7 |
|   +   +   +   +   +   +   +---+   +   +---|
| 3   1   1   0   1   5   6   5   8   6 | 7 |
|   +   +   +   +---+   +   +   +---+---+   |
| 5   0   8   2   2   7   8   8 | 5   5 | 9 |
'-------------------------------------------'
Highlight [99] and [09] and we can apply a variant of the hidden pairs technique. On the left side, you will find that [99] straddles across the two [09]s, so the left side can have either [99] or [09], but not both. This means that on the right hand side, we have either [99] or [09]. So we can add two borders on the right hand side.

Code: Select all

6712318075115xnj1744948euqc05@23495wr3@86574382qq9c8376684r1me9803k937392uj9f190402eael73110156p86#5082m788zpj

.-------------------------------------------.
| 6   7   1   2   3   1   8   0   7   5   1 |
|   +   +---+---+   +   +   +   +   +   +   |
| 1   5 | 3   3 | 9   1   7   4   4   9   4 |
|   +   +---+---+   +   +   +---+   +   +   |
| 8 | 4 | 0   6 | 2   0   5 | 6   2   3   4 |
|   +   +---+---+   +---+   +   +   +   +   |
| 9   5 | 2   7   3 | 6   8   6   5   7   4 |
|   +   +   +---+---+   +   +   +   +   +   |
| 3   8   2   6   6   9 | 2   8   3   7   6 |
|   +   +   +---+   +---+   +   +   +   +   |
| 6   8   4   7   1   2 | 4   9   8   0   3 |
|---+   +   +   +   +   +   +---+   +   +   |
| 0   9   3   7   3   9   2 | 0 | 9   9 | 5 |
|   +   +   +   +   +   +   +   +   +---+   |
| 1   9   0   4   0   2 | 4 | 0 | 4   1   7 |
|   +   +   +   +   +   +   +---+   +   +---|
| 3   1   1   0   1   5   6   5   8   6 | 7 |
|   +   +   +   +---+   +   +   +---+---+   |
| 5   0   8   2   2   7   8   8 | 5   5 | 9 |
'-------------------------------------------'
Continue with [09] highlighted, focus on the r7c1 cell. The r7c1 cell can only be either [09] or [01]. If it is [01], we have a border between r8c1 and r9c1. If it is [09], then the [09] at r8c23 is blocked, and then to avoid the non-unique square at r89c12, we will need a border between r8c1 and r9c1. Hence we can add that border across [13].

Code: Select all

6712318075115xnj1744948euqc05@23495wr3@86574382qq9c8376684r1me9803k937392uj9f190402eael7n110156p86#5082m788zpj

.-------------------------------------------.
| 6   7   1   2   3   1   8   0   7   5   1 |
|   +   +---+---+   +   +   +   +   +   +   |
| 1   5 | 3   3 | 9   1   7   4   4   9   4 |
|   +   +---+---+   +   +   +---+   +   +   |
| 8 | 4 | 0   6 | 2   0   5 | 6   2   3   4 |
|   +   +---+---+   +---+   +   +   +   +   |
| 9   5 | 2   7   3 | 6   8   6   5   7   4 |
|   +   +   +---+---+   +   +   +   +   +   |
| 3   8   2   6   6   9 | 2   8   3   7   6 |
|   +   +   +---+   +---+   +   +   +   +   |
| 6   8   4   7   1   2 | 4   9   8   0   3 |
|---+   +   +   +   +   +   +---+   +   +   |
| 0   9   3   7   3   9   2 | 0 | 9   9 | 5 |
|   +   +   +   +   +   +   +   +   +---+   |
| 1   9   0   4   0   2 | 4 | 0 | 4   1   7 |
|---+   +   +   +   +   +   +---+   +   +---|
| 3   1   1   0   1   5   6   5   8   6 | 7 |
|   +   +   +   +---+   +   +   +---+---+   |
| 5   0   8   2   2   7   8   8 | 5   5 | 9 |
'-------------------------------------------'
What's next?
rep'nA
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Post by rep'nA »

unkx80 wrote:rep'nA's puzzle continued...

What's next?
I'm not sure yet, but very nice work on getting the last few steps. I especially like your improvisation with the [09],[99] psedo-hidden pair and your almost non-unique square.
"Obviousness is always the enemy to correctness."-Bertrand Russell
unkx80
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Post by unkx80 »

Thanks rep'nA. In a way, I am using your puzzle to try to discover new techniques.

Here is the remainder of the puzzle walkthrough.

Code: Select all

6712318075115xnj1744948euqc05@23495wr3@86574382qq9c8376684r1me9803k937392uj9f190402eael7n110156p86#5082m788zpj

.-------------------------------------------.
| 6   7   1   2   3   1   8   0   7   5   1 |
|   +   +---+---+   +   +   +   +   +   +   |
| 1   5 | 3   3 | 9   1   7   4   4   9   4 |
|   +   +---+---+   +   +   +---+   +   +   |
| 8 | 4 | 0   6 | 2   0   5 | 6   2   3   4 |
|   +   +---+---+   +---+   +   +   +   +   |
| 9   5 | 2   7   3 | 6   8   6   5   7   4 |
|   +   +   +---+---+   +   +   +   +   +   |
| 3   8   2   6   6   9 | 2   8   3   7   6 |
|   +   +   +---+   +---+   +   +   +   +   |
| 6   8   4   7   1   2 | 4   9   8   0   3 |
|---+   +   +   +   +   +   +---+   +   +   |
| 0   9   3   7   3   9   2 | 0 | 9   9 | 5 |
|   +   +   +   +   +   +   +   +   +---+   |
| 1   9   0   4   0   2 | 4 | 0 | 4   1   7 |
|---+   +   +   +   +   +   +---+   +   +---|
| 3   1   1   0   1   5   6   5   8   6 | 7 |
|   +   +   +   +---+   +   +   +---+---+   |
| 5   0   8   2   2   7   8   8 | 5   5 | 9 |
'-------------------------------------------'
Now look at the interplay between [19], [11] and the non-unique square r89c12. If r2c56=[91], then we force r9c23=[11], which adds a border across r9c12. If r8c12=[19], then we cannot have r9c12=[13] else we get a non-unique square. If r89c2=[91], we also have a border across r9c12. In any case, we have a border across r9c12.

Then we can clean up some singles and apply a square isolation.

Code: Select all

671231807f11pxnj1744948euqcup@md495wr3@sg5h4382qq9csn76684r1me9803k937392uj9z190402eaelhnb10156p86#5a82mr88zpj

.-------------------------------------------.
| 6   7   1   2   3   1   8   0   7 | 5   1 |
|   +---+---+---+   +   +   +   +   +   +   |
| 1   5 | 3   3 | 9   1   7   4   4   9   4 |
|   +   +---+---+   +---+---+---+---+   +   |
| 8 | 4 | 0   6 | 2 | 0   5 | 6   2 | 3   4 |
|   +   +---+---+   +---+---+   +   +   +   |
| 9   5 | 2   7   3 | 6   8 | 6   5 | 7   4 |
|   +   +   +---+---+   +   +---+---+   +   |
| 3   8   2   6   6   9 | 2   8   3   7   6 |
|   +   +   +---+   +---+   +   +   +   +   |
| 6   8   4   7   1   2 | 4   9   8   0   3 |
|---+   +   +   +   +   +   +---+   +   +---|
| 0   9   3   7   3   9   2 | 0 | 9   9 | 5 |
|   +   +   +   +   +   +   +   +   +---+   |
| 1   9   0   4   0   2 | 4 | 0 | 4   1 | 7 |
|---+   +   +   +   +   +   +---+   +   +---|
| 3 | 1   1   0   1   5   6   5   8   6 | 7 |
|   +   +   +   +---+---+   +   +---+---+   |
| 5 | 0   8   2   2   7   8   8 | 5   5 | 9 |
'-------------------------------------------'
Next, look at [12] and [13]. At the lower side, we can have either [12] or [13], but not both. Hence, there must be a [12] or [13] on the upper side. As both [12] and [13] share a common border, add that border across r1c45.

Code: Select all

6712d1807f11pxnj1744948euqcup@md495wr3@sg5h4382qq9csn76684r1me9803k937392uj9z190402eaelhnb10156p86#5a82mr88zpj

.-------------------------------------------.
| 6   7   1   2 | 3   1   8   0   7 | 5   1 |
|   +---+---+---+   +   +   +   +   +   +   |
| 1   5 | 3   3 | 9   1   7   4   4   9   4 |
|   +   +---+---+   +---+---+---+---+   +   |
| 8 | 4 | 0   6 | 2 | 0   5 | 6   2 | 3   4 |
|   +   +---+---+   +---+---+   +   +   +   |
| 9   5 | 2   7   3 | 6   8 | 6   5 | 7   4 |
|   +   +   +---+---+   +   +---+---+   +   |
| 3   8   2   6   6   9 | 2   8   3   7   6 |
|   +   +   +---+   +---+   +   +   +   +   |
| 6   8   4   7   1   2 | 4   9   8   0   3 |
|---+   +   +   +   +   +   +---+   +   +---|
| 0   9   3   7   3   9   2 | 0 | 9   9 | 5 |
|   +   +   +   +   +   +   +   +   +---+   |
| 1   9   0   4   0   2 | 4 | 0 | 4   1 | 7 |
|---+   +   +   +   +   +   +---+   +   +---|
| 3 | 1   1   0   1   5   6   5   8   6 | 7 |
|   +   +   +   +---+---+   +   +---+---+   |
| 5 | 0   8   2   2   7   8   8 | 5   5 | 9 |
'-------------------------------------------'
The rest is all singles.

--------------------------------------------------------------------------------

Admittedly, I didn't see the [12], [13] interplay the first time round, leading to a very long and ugly solving path involving contradictions and large isolations. But I think one thing that deserves mentioning.

Large clusters of candidate placements for a particular tile makes good candidates for short contradiction chains. Because if one of them is assumed to be the true tile placement then we can add a lot of borders. For example, take the first or second diagram in this post. There is a huge cluster of [01] candidates at the bottom left. Together with the r89c12 non-unique square, we can quickly derive a contradiction if either r89c3=[01] or r9c34=[10]. This allows us to add two borders and hence isolate a six-pack (or square if we start from the second diagram). This step is what I initially found.
rep'nA
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Post by rep'nA »

Awesome ending! And really excellent explanations.
unkx80 wrote:Thanks rep'nA. In a way, I am using your puzzle to try to discover new techniques.
Cool, I'm a muse! In that case, can you see anything nice on this one?

Code: Select all

12124852309338698705074148936462771915771767030662506598623921435244101916898366249307054957458085048813792253
where DominoCue (and I) get stuck here:

Code: Select all

12bc4852309nnig9870507ovo893646277b9l5771767k3066250659862392b435244l01916898366249307054957ypi0850488bnr92253

Code: Select all

.-------------------------------------------.
| 1   2 | 1 | 2   4   8   5   2   3   0   9 |
|---+---+   +   +   +   +   +   +   +   +   |
| 3   3 | 8 | 6   9   8   7   0   5   0   7 |
|---+---+---+   +   +   +   +   +   +   +   |
| 4 | 1   4   8   9   3   6   4   6   2   7 |
|   +   +   +---+   +   +   +   +   +   +   |
| 7 | 1   9   1   5   7   7   1   7   6   7 |
|---+   +   +   +   +   +   +   +   +   +   |
| 0   3   0   6   6   2   5   0   6   5   9 |
|   +   +   +   +   +   +   +   +   +   +   |
| 8   6   2   3   9   2 | 1   4   3   5   2 |
|   +   +---+   +   +   +   +   +   +   +   |
| 4   4   1   0   1   9   1   6   8   9   8 |
|   +   +   +   +   +   +   +   +   +   +   |
| 3   6   6   2   4   9   3   0   7   0   5 |
|   +   +   +   +---+---+   +   +   +   +   |
| 4   9   5   7 | 4   5 | 8   0   8   5   0 |
|   +   +   +   +---+---+   +   +   +   +   |
| 4   8   8 | 1   3   7   9   2   2   5   3 |
'-------------------------------------------'
"Obviousness is always the enemy to correctness."-Bertrand Russell
unkx80
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Post by unkx80 »

Didn't figure this one out yet, but one possible move: by making use of [28], the 0, 5, 0, 5 non-unique square and a possible isolation on the bottom right, you can derive a border across the [05] at r89c{10}.
unkx80
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Post by unkx80 »

Para wrote:What about the size of this isolation block in R1234C123456789.

Code: Select all

.-------------------------------------------.
| 0   0   3   9   5   5   6   8   4 | 2   9 |
|   +   +   +   +   +   +---+---+   +---+---|
| 5   6   3   7   2   6 | 8 | 1   5   3   0 |
|   +   +   +---+   +   +   +   +   +   +   |
| 0   2   6 | 0 | 4 | 7 | 8 | 4   5 | 3   4 |
|   +   +   +   +   +   +---+---+   +   +---|
| 5   8   9 | 1 | 1   5   7   7   7   1   1 |
|---+---+---+---+---+---+   +---+   +   +   |
| 1   7 | 0   2 | 9   9 | 1   6   2   8   9 |
|   +   +   +   +---+---+   +   +   +   +   |
| 1   9 | 4   2   8   1   6   5   7   3   6 |
|---+---+   +   +   +   +   +   +   +   +   |
| 4   7 | 8   0   7   3   6   8   1   3   8 |
|---+---+   +   +   +   +   +   +   +---+---|
| 4   5 | 2   3   6   9 | 2   2   7 | 4   6 |
|   +   +---+   +   +---+   +   +   +---+---|
| 9 | 9   3 | 0   6   0   0   8   3 | 1 | 4 |
|   +---+   +   +   +   +   +   +   +   +   |
| 0   9   4 | 7   8   3   2   5   5 | 2 | 4 |
'-------------------------------------------'
greetings

Para
Here is my guess. If we place borders across both [57]s at r4c67 and r34c9, then we are going to obtain an isolation of an odd number of cells. Therefore one of these [57]s must be true. This allows us to isolate all of r1234c123456789 (and eliminate all other [57] possibilities). Is this what you are looking for?
Para
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Post by Para »

It doesn't matter what digits are there. The area is always isolated. The three holes all can't be innies as you would lock off an uneven number of cells otherwise.
unkx80
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Post by unkx80 »

Para wrote:It doesn't matter what digits are there. The area is always isolated. The three holes all can't be innies as you would lock off an uneven number of cells otherwise.
Got it, thanks! :)
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