17-clue symmetric puzzles

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17-clue symmetric puzzles

Postby m_b_metcalf » Fri May 06, 2022 8:36 am

Using the program I mentioned elsewhere, I found a handful of 17-clue puzzles that can be transformed to be symmetric. Here are two as examples:
Code: Select all
 . . . . . . . . .
 . . . 3 . 4 . . .
 . 7 . . . . 9 . .
 9 . . . . . . 5 .
 . 2 . 8 . . . . .
 . . . 6 7 . . 4 .
 4 . . . . . . . .
 . . . . 8 . 2 . .
 5 . 3 . . 9 . . .   ED=2.6/1.2/1.2, anti-diagonal

 . . . 3 . . . 8 .
 . 6 . . . . . 9 .
 . . 3 1 . . . . .
 1 . 2 . . . 5 . .
 . . . . 4 . . . .
 . . . . . 6 . . .
 . . . 2 . . 1 . 7
 8 4 . . . . . . .
 . . . . . . 3 . .   ED=4.5/1.2/1.2, diagonal


Mike
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Re: 17-clue symmetric puzzles

Postby JPF » Fri May 06, 2022 9:29 am

Hi Mike,

yeah, that's an old idea. See here.
gsf's program finds it very quickly.

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Re: 17-clue symmetric puzzles

Postby m_b_metcalf » Fri May 06, 2022 10:08 am

JPF wrote:yeah, that's an old idea. See here.
gsf's program finds it very quickly.


Ah, your memory's better than mine. FWIW, my program can also, optionally, find puzzles that are 'off-by-n' symmetrical. One of the patterns that I've submitted to the Patterns Game is such a pattern with the required 'correction'.

Here's an 'off-by-1' rotationally symmetric 17-clue puzzle (an asterisk marks the offending cell):

Code: Select all
 4 . . . . . . 3 .
 . 5 . 2 . . . . .
 . . . 1 . . . * .
 . . . . . . 2 . 1
 3 . . . . . . . 5
 6 . 8 . . . . . .
 . 1 . . . 8 . . .
 . . . . . 3 . 6 .
 . 7 . . . . . . 2


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Re: 17-clue symmetric puzzles

Postby JPF » Sun May 08, 2022 9:51 pm

you wrote:Ah, your memory's better than mine.

You might also be interested in this old thread...

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Re: 17-clue symmetric puzzles

Postby m_b_metcalf » Mon May 09, 2022 2:48 pm

JPF wrote:
you wrote:Ah, your memory's better than mine.

You might also be interested in this old thread...

Indeed. It's of note that there are no puzzles with rotational, or up/down or left/right, symmetry. It turns out that there are many with 'off-by-1' rotational symmetry, here an example:
Code: Select all
 4 . . . . . . 3 .
 . 5 . 2 . . . . .
 . . . 1 . . . * .
 . . . . . . 2 . 1
 3 . . . . . . . 5
 6 . 8 . . . . . .
 . 1 . . . 8 . . .
 . . . . . 3 . 6 .
 . 7 . . . . . . 2   ED=1.5/1.2/1.2, rotational, 1 missing


but none for u/d, l/r. For these, I found just four that are 'off-by-2', for instance:
Code: Select all
 2 5 . . 1 . . . .
 . . . 8 . . 6 . .
 * . . . . . . . .
 . . . . . . . 1 5
 . 7 3 2 . . . . .
 . . . . . . . 4 *
 1 . . . . . . . .
 . . . 6 . . 3 . .
 5 4 . . 9 . . . .   ED=4.5/1.2/1.2, up/down, 2 missing

 . . . 8 . 1 . . .
 3 . . . . . . . 5
 5 . . . . . . . 4
 . . . 3 4 * . . .
 . 8 . . . . . 1 .
 . 9 . . . . . 2 .
 . 2 . . . . . 8 .
 4 . . . 3 . . . *
 . . . . 6 . . . .   ED=7.6/1.2/1.2, left/right, 2 missing   


I'll stop there.

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