Down Under Upside Down - a Sudoku puzzle

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Down Under Upside Down - a Sudoku puzzle

Postby udosuk » Sun Sep 21, 2008 9:03 am

Down Under Upside Down

Image

This looks like a variant puzzle but except for the cell values used there is nothing exotic about the puzzle itself - it has a unique solution under the standard Sudoku rules, i.e. each row/column/box has exactly one each from a set of 9 cell values. Everyone should see why I picked such a set of values if they look at the puzzle pic from multiple angles. In fact the name "Down Under Upside Down" has 3 layers of meanings - kudos to anyone who can figure out all 3.:idea:

The difficulty isn't anything special compared to the festival creatures, the metallic thingies or the new witchy-mirage-illusion crackers. However, if you're smart enough you can solve this one using very elegant simple moves, without any chain/ALS etc. In fact all the required tricks have been discussed in this forum in the past, but it's a matter of whether you guys really want to learn them.

Anyway, I don't recommend it but if you really want to tackle this puzzle the "traditional way", here is a line-format using the values 1-9. But I'd really like to see players using the new set of 9 values just to appreciate the beauty of them.

This is the traditional line format I wrote:006800000090070010300006402100000509000000000602000003507900001030040060000008900

All are welcomed to give it a try!:)
Last edited by udosuk on Tue Sep 23, 2008 2:36 am, edited 1 time in total.
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Postby RW » Sun Sep 21, 2008 1:14 pm

Sorry udosuk, for some reason I can't see your picture.:( But that didn't stop me from solving the puzzle!:D

I shall not post a solution yet, let others try first!

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Postby udosuk » Sun Sep 21, 2008 1:31 pm

The imageshack hosting site must be experiencing some technical problems. Let's wait a day and see if I need to reupload it elsewhere.

So you've solved it without chains/ALS/T&E? I wouldn't think this to be difficult to you, considering you're the other active contributor to that brilliant idea from our South African guru 2 years ago.:D

I have cracked it with the help of a little xy-wing, but I suspect if I look harder using the "special tricks" even that xy-wing could possibly be avoided.:idea:

Would have loved to know the SE rating etc of this puzzle, without using the special tricks.:?: I know JSudoku (my version) struggled with it.
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Postby RW » Sun Sep 21, 2008 1:50 pm

Actually, I didn't spend that much time looking for the "easiest" solution. Spotted a short XY-chain (that made use of the special property) and was satisfied with that solution!:) Perhaps I can look for something easier later.

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Postby Glyn » Sun Sep 21, 2008 2:49 pm

Matt Like RW I can't see the picture, but I've plugged the alternative representation into SE and it rates 8.8.

57 x Hidden Single
3 x Pointing
2 x Turbot Fish
7 x Region Forcing Chains
1 x Dynamic Cell Forcing Chains
3 x Dynamic Region Forcing Chains

Now to look at it properly.
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Postby JPF » Sun Sep 21, 2008 3:04 pm

:idea:
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Postby udosuk » Mon Sep 22, 2008 1:37 am

Thanks Glyn! I was perhaps expecting a higher rating, but this number is perfectly suited to the theme of the puzzle!:D

RW, I guess you haven't completed the task then, because I specifically stated that the puzzle could be solved without chains or ALS. An xy-chain, no matter how short, is still a chain.:) (Although I used to view the xy-wing as marginally a near-chain, but for this one I couldn't find anything easier.)

JPF, the point of this puzzle is while it is a perfectly valid standard Sudoku puzzle (with an SE rating of 8.8), it has a special property (emphasized by my choice of 9 different cell values). If you ignore this special property, you need chains/ALS etc to solve it. But if you make use of this special property, you don't need any move harder than xy-wing to crack the puzzle.

Okay, I'll explain the 3 meanings of the title here:

1. The given clues give an outline of a country with the nickname "Down Under".

2. The whole puzzle pic, if turned upside down, is exactly identical to the original, and again shows an outline of "Down Under".

3. If you divide the whole puzzle by the 5th row, each of the given clues down under is exactly upside down of one of the given clues up above.

:idea:
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Postby JPF » Mon Sep 22, 2008 1:53 am

udosuk wrote:JPF, the point of this puzzle is while it is a perfectly valid standard Sudoku puzzle (with an SE rating of 8.8), it has a special property (emphasized by my choice of 9 different cell values). If you ignore this special property, you need chains/ALS etc to solve it. But if you make use of this special property, you don't need any move harder than xy-wing to crack the puzzle.

In my previous post, the:idea: was clickable:)

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Postby Smythe Dakota » Mon Sep 22, 2008 4:48 am

I notice you have no 69's, 88's, or 96's -- precisely the three which are their own upside-downs! If you throw in these as well, you could have a true variant with 12 possible values, still only 9 cells per row/column/box, and some special rules.

Or a 12x12 puzzle with 3x4 or 4x3 boxes (or both!).

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Postby eleven » Mon Sep 22, 2008 6:01 am

I understood, that from the symmetry the center cell must be 8, but cant find any solution without chains.
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Postby udosuk » Mon Sep 22, 2008 9:08 am

Smythe Dakota wrote:I notice you have no 69's, 88's, or 96's -- precisely the three which are their own upside-downs! If you throw in these as well, you could have a true variant with 12 possible values, still only 9 cells per row/column/box, and some special rules.

Or a 12x12 puzzle with 3x4 or 4x3 boxes (or both!).

Just to note that this is exactly the reason I didn't use 9 double-digit values as my set, since we can have at most one value which is its own upside-down (8 in my current set), and we have three such values in the set {66,68,69,86,88,89,96,98,99}.

But for 12x12 this will work, because there is no central row or column. If you like you can explore the possibility.:)

eleven I will reveal my solving path this weekend, in case nobody else has posted one by then.

BTW nice trick JPF!:)
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Postby RW » Mon Sep 22, 2008 11:13 am

Ok, ok... I'll have another look at it before the weekend...

:D

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Postby eleven » Mon Sep 22, 2008 11:43 am

udosuk wrote:eleven I will reveal my solving path this weekend, in case nobody else has posted one by then.
Ok, for the time this is, how i did it after the x-wing 8:
r8c3=1 -> r2c7=3 -> r1c7=7
r8c3=9 -> r5c1=9 -> r1c1=7
Then r1c9=5 and r9c1=2

Added:
This one has 2 shorter chains.
r1c9=7 -> r9c1=4 -> r1c1=2
r1c9=5 -> r9c1=2
So r28c1<>2 (and r28c5<>5)

Then
r8c3=1 -> r9c3=4
r8c3=9 -> r8c1=8 -> r2c1=4
So r2c3=5, r9c1=2, ...
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Postby susume » Mon Sep 22, 2008 10:12 pm

Not the simple method you were looking for, but it can be solved with one Nice Loop after the 8 X-Wing:

Code: Select all
[r8c1]=8=[r2c1]-8-[r3c3]=8=[r4c3]=66=[r5c3]=9=[r8c3]-9-[r8c1] => r8c1<>9
Singles to end.


A lovely emerald!!
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Postby Pat » Tue Sep 23, 2008 4:30 am

hey udosuk,

on earlier visits, i had no trouble seeing the image at
http://img207.imageshack.us/img207/2769/duudib0.png

but today,
it's unavailable

this creates great difficulty in following the discussion,
as your posted text-version uses different symbols --

Code: Select all
 . . 6 | 8 . . | . . .
 . 9 . | . 7 . | . 1 .
 3 . . | . . 6 | 4 . 2
-------+-------+------
 1 . . | . . . | 5 . 9
 . . . | . . . | . . .
 6 . 2 | . . . | . . 3
-------+-------+------
 5 . 7 | 9 . . | . . 1
 . 3 . | . 4 . | . 6 .
 . . . | . . 8 | 9 . .


-- where i cannot guess, for example, how the symbol '66' (used in the image) was translated---
Last edited by Pat on Tue Sep 23, 2008 12:44 am, edited 1 time in total.
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