Lozenge tiling 8.3

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Lozenge tiling 8.3

Postby denis_berthier » Tue Dec 01, 2020 8:05 am

This puzzle belongs to the general LOZENGE family of perfectly symmetric puzzles: http://forum.enjoysudoku.com/perfectly-symmetric-patterns-t38444.html, more precisely to the lozenge-tiling pattern (that allows a semi-regular tiling of the plane).

Code: Select all
X———X———X
—X—X—X—X—
——X———X——
—X—————X—
X———————X
—X—————X—
——X———X——
—X—X—X—X—
X———X———X


Contrary to the lozenges 8.3 puzzle I proposed before, it doesn't have an inner small lozenge.

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

6...8...1.4.7.1.9...3...8...8.....5.7.......4.2.....7...9...3...1.4.3.8.3...5...9 # 95318 FNBHXYK C24.M/S8.f
SER 8.3


If you like oddagons, you can find some here also.
denis_berthier
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Re: Lozenge tiling 8.3

Postby Leren » Tue Dec 01, 2020 8:28 am

If you like Uniqueness moves, you'll find these:

Code: Select all
*---------------------------------------------------*
| 6   579 257  | 259   8     2459  | 457  3    1    |
| 258 4   258  | 7     3     1     |*6-5  9   *25-6 |
| 1   579 3    | 2569  246   24569 | 8    24   257  |
|--------------+-------------------+----------------|
| 49  8   146  | 1269  12467 24679 | 129  5    3    |
| 7   3   15   | 12589 12    2589  | 129  6    4    |
| 459 2   1456 | 3     146   4569  | 19   7    8    |
|--------------+-------------------+----------------|
| 48  567 9    | 1268  1267  2678  | 3    124  257  |
| 25  1   257  | 4     9     3     |*57-6 8   *6-5  |
| 3   67  48   | 1268  5     2678  | 47   124  9    |
*---------------------------------------------------*

Unique Rectangle Type 6 {56} r2c79, r8c79 => - 5 r3c7, - 6 r3c9, r8c7, -5 r8c9

Code: Select all
*------------------------------------------------*
| 6   79 25   | 259   8     2459  | 47  3    1   |
| 58  4  258  | 7     3     1     |*6   9   *2-5 |
| 1   79 3    | 2569  246   24569 | 8   24   257 |
|-------------+-------------------+--------------|
| 49  8  146  | 1269  12467 24679 | 129 5    3   |
| 7   3  15   | 12589 12    2589  | 129 6    4   |
| 459 2  1456 | 3     146   4569  | 19  7    8   |
|-------------+-------------------+--------------|
| 48  5  9    | 1268  1267  2678  | 3   124  27  |
| 2   1  7    | 4     9     3     |*5   8   *6   |
| 3   6  48   | 128   5     278   | 47  124  9   |
*------------------------------------------------*

Avoidable Rectangle (56) r28c79 => - 5 r7c9; stte

How did I know that the solution was unique ? Divine inspiration :D Leren
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Joined: 03 June 2012

Re: Lozenge tiling 8.3

Postby denis_berthier » Tue Dec 01, 2020 9:12 am

Leren wrote:How did I know that the solution was unique ? Divine inspiration :D Leren

I have nothing about divine inspiration or uniqueness (though uniqueness...) but I can hardly admit the pata-logic of the AR (copied from Hodoku):

Hodoku wrote:Avoidable Rectangles differ from Unique Rectangles in that some cells of the UR have already been placed. If placing the remaining cell(s) would cause an UR, the sudoku maker would have had to supply one of the four cells as a given to avoid a possible second solution (hence the name)...

Nothing divine, just guessing what could have been in the puzzle creator's brain ;)
denis_berthier
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Location: Paris


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