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Unique parallelograms?

 
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Sat Jun 10, 2006 6:12 pm    Post subject: Unique parallelograms? Reply with quote

I have shown only the numbers in one stack which I believe to be relevant to my question.

Do I have to set the upper left cell to "6"? If it is not "6", then it looks like the "deadly pattern." I have seen deadly patterns discussed only within the context of Unique Rectangles; however, should not the same principles apply to any four-cornered figure in two boxes, such as parallelograms and trapezoids?

Code:
--------------
|            |
|368         |
|        38  |
--------------
|            |
|            |
|            |
--------------
|38          |
|            |
|        38  |
--------------
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Ruud



Joined: 18 Jan 2006
Posts: 31

PostPosted: Sat Jun 10, 2006 6:31 pm    Post subject: Reply with quote

Hi Marty,

Unique Rectangles exist because they share exactly 2 rows, 2 columns and 2 boxes.

You parallelogram shares 2 boxes, 4 rows and 2 columns. These 2 extra rows give ample opportunity to avoid 2 solutions.

There is a shape that can be used for uniqueness, which is the Unique Swordfish:

Code:
. . .|. X .|. X .
. X .|. . .|. X .
. X .|. X .|. . .
-----+-----+-----
. . .|. . .|. . .
. . .|. . .|. . .
. . .|. . .|. . .
-----+-----+-----
. . .|. . .|. . .
. . .|. . .|. . .
. . .|. . .|. . .


This shape shares 3 rows, 3 columns and 3 boxes.

Ruud.
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Sat Jun 10, 2006 9:12 pm    Post subject: Reply with quote

Thanks Ruud, you saved me from a heap of frustration, even though I'm not seeing why the parallelogram wouldn't constitute the deadly pattern. Question
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keith



Joined: 19 Sep 2005
Posts: 3174
Location: near Detroit, Michigan, USA

PostPosted: Sat Jun 10, 2006 10:43 pm    Post subject: Parallelograms Reply with quote

Marty,

Let's try this. Assume this is a fragment of a solution:
Code:

----------------
   |        |
   |8       |
   |      3 |
----------------
   |3       |
   |        |
   |      8 |
----------------

We have 3 and 8 in each block, and in each column. Let's add the ones in the rows:
Code:

----------------
   |        |
   |8       |3
  8|      3 |
----------------
   |3       |   8
   |        |
3  |      8 |
----------------

Now, interchange 3 and 8 on the corners of your parallelogram:
Code:

----------------
   |        |
   |3       |3
  8|      8 |
----------------
   |8       |   8
   |        |
3  |      3 |
----------------

Clearly, this is not a fragment of (another) valid solution.

Keith
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Marty R.



Joined: 12 Feb 2006
Posts: 5160
Location: Rochester, NY, USA

PostPosted: Sun Jun 11, 2006 12:15 am    Post subject: Reply with quote

Keith, thank you. I was going to tell you I still didn't understand, but after staring more, I think I get it. I was sure those 38s were interchangeable, which they appear to be, but I was not considering what was outside the stack. So I guess they're not interchangeable and I'm not going to now suggest that the technique name be changed to "Unique Quadrilaterals." Laughing
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