Manhattan Cocktail

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Manhattan Cocktail

Postby Mathimagics » Sun Aug 01, 2021 10:40 am

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


The Manhattan Cocktail is a puzzle that combines the standard Sudoku rules with extra constraints involving the Manhattan Distance measure. The MD between any two cells is simply the sum of the row and column differences.

The Manhattan constraints are simply stated: if (R, C) = D, then D can not occur in any cell that is (Manhattan) distance D from (R, C).

The set of cells at a fixed MD from a given cell form a diamond around the given cell. For D = 3, 4, 5 in the central square, the potential eliminations for D are shown below (the corners of the diamond are included for clarity, they do not give any extra additional eliminations, of course):

Code: Select all
  . . . . . . . . .        . . . . X . . . .        . . . X . X . . .
  . . . . X . . . .        . . . X . X . . .        . . X . . . X . .
  . . . X . X . . .        . . X . . . X . .        . X . . . . . X .
  . . X . . . X . .        . X . . . . . X .        X . . . . . . . X
  . X . . 3 . . X .        X . . . 4 . . . X        . . . . 5 . . . .
  . . X . . . X . .        . X . . . . . X .        X . . . . . . . X
  . . . X . X . . .        . . X . . . X . .        . X . . . . . X .
  . . . . X . . . .        . . . X . X . . .        . . X . . . X . .
  . . . . . . . . .        . . . . X . . . .        . . . X . X . . .


Some general observations:

  • 1's are unrestricted, since the minimum MD between any cell pair is 2
  • for 2's, the MD constraint is effectively an "anti-King" constraint
  • for 3's, the MD constraint is effectively an "anti-Knight" constraint
  • the sample puzzle given above is singles-only, and there is a hidden single in row 5 for value 4

Solution: Show
Code: Select all
351478296849216375726593841975634128638129457214857639497381562583762914162945783
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Mathimagics
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Manhattan Cocktail #2

Postby Mathimagics » Sun Aug 01, 2021 10:44 am

This one is harder:

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

....6..3..........2....15.7....................79.................7......9.5.....


Solution: Show
Code: Select all
451867239378259164269341587613475892942618753587923641826134975135796428794582316
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Re: Manhattan Cocktail

Postby HATMAN » Thu Aug 05, 2021 8:21 pm

On the first one I'm stuck here:
+-------------------------+-------------------------+-------------------------+
| 38 5 127 | 4 178 238 | 1279 12379 6 |
| 38 4 12679 | 278 1689 2678 | 1237 127 5 |
| 1267 12679 12679 | 5 179 2367 | 8 4 123 |
+-------------------------+-------------------------+-------------------------+
| 1279 1267 5 | 678 3 4 | 1269 1268 1289 |
| 69 3 8 | 1 2 69 | 4 5 7 |
| 1279 1267 4 | 678 5 6789 | 12369 12389 12389 |
+-------------------------+-------------------------+-------------------------+
| 4 26789 2679 | 3 678 1 | 5 26789 289 |
| 5 16789 3 | 2678 68 2678 | 1679 16789 4 |
| 1267 12678 1267 | 9 4 5 | 12367 123678 1238 |
+-------------------------+-------------------------+-------------------------+

please point out what I am missing - or if I have gone wrong
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Location: Nigeria

Re: Manhattan Cocktail

Postby 999_Springs » Thu Aug 05, 2021 8:59 pm

HATMAN wrote:
Code: Select all
+-------------------------+-------------------------+-------------------------+
| 38      5       127     | 4       178     238     | 1279    12379   6       |
| 38      4       12679   | 278     1689    2678    | 1237    127     5       |
| 1267    12679   12679   | 5       179     2367    | 8       4       123     |
+-------------------------+-------------------------+-------------------------+
| 1279    1267    5       | 678     3       4       | 1269    1268    1289    |
| 69      3       8       | 1       2       69      | 4       5       7       |
| 1279    1267    4       | 678     5       6789    | 12369   12389   12389   |
+-------------------------+-------------------------+-------------------------+
| 4       26789   2679    | 3       678     1       | 5       26789   289     |
| 5       16789   3       | 2678    68      2678    | 1679    16789   4       |
| 1267    12678   1267    | 9       4       5       | 12367   123678  1238    |
+-------------------------+-------------------------+-------------------------+

8 in r5c3 means r8c8, r7c9 =/= 8
8 in r3c7 means r1c1, r8c4, r9c9 =/= 8
3r1c1 is a naked single
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Re: Manhattan Cocktail

Postby HATMAN » Fri Aug 06, 2021 9:52 am

Thank you

So on my third attempt at the start, I forgot to clean up the given 8s.
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