David's broken rule pattern

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David's broken rule pattern

Postby eleven » Tue Jan 17, 2017 8:40 pm

When i looked at David's (temporary) post in the JExocet Compendium, i manually tried to find a unique puzzle for the "One Rule Broken" pattern (X=5-9).
1.......3.X.X..2X...2...41....X...X.....X.....X...X.....3...1..2X...X.X.41......2

This is, what i got.
Code: Select all
 1 . . . . . . . 3
 . 5 . 6 1 . 2 9 .
 8 . 2 . . . 4 1 .
 . . . 8 . . . 7 .
 . . . . 6 7 . . .
 . 8 . . . 9 . 2 .
 . . 3 . 8 . 1 . .
 2 9 . . . 6 . 8 .
 4 1 . . . . . . 2
eleven
 
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Re: David's broken rule pattern

Postby Leren » Tue Jan 17, 2017 10:28 pm

Code: Select all
*-----------------------------------------------------------------------*
| 1      4      9       | 257    257    8       |b567    56B    3       |
| 3      5      7       | 6      1      4       | 2      9      8       |
| 8      6      2       | 3579   3579   35b     | 4      1     a7-5aA   |
|-----------------------+-----------------------+-----------------------|
| 59     23     46      | 8      235    1       | 359    7      46      |
| 59     23     14      | 235    6      7       | 8      345    1459    |
| 7      8      16      | 345    345    9       | 35     2      16      |
|-----------------------+-----------------------+-----------------------|
| 6      7      3       | 459    8      2       | 1      45     459     |
| 2      9      5       | 1      347    6       |c37     8      47      |
| 4      1      8       | 3579   3579   35c     | 35679 d356dC  2       |
*-----------------------------------------------------------------------*

Kraken Cell r9c8:

5 r3c9 - 7 r3c9 = r1c7 - (7=3) r8c7 - 3 r9c8;

5 r3c9 - r3c6 = r9c6                - 5 r9c8;

5 r3c9 - (5=6) r1c8                 - 6 r9c8; => - 5 r3c9; stte

Leren
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Re: David's broken rule pattern

Postby David P Bird » Tue Jan 17, 2017 11:30 pm

Well done eleven, but to make the puzzle unique you are up to 28 givens which makes it a lot easier than the puzzles I've been trying to tackle.

To make these puzzles hard the coverage of the unavoidable sets must be very economical. They seem to set separate sub-puzzles for digit sets (1-4) and (5-9). The equivalencies I wanted to prove simplifies the coverage needed for the (1-4) set and always seem to be present. On sleeping on it though I can't see a revised experimental design that could be used to explore this sort of issue.

DPB
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Re: David's broken rule pattern

Postby eleven » Wed Jan 18, 2017 8:29 pm

Code: Select all
 *---------------------------------------------------*
 | 1   4   9   | 257   257   8   | 56-7  #56   3     |
 | 3   5   7   | 6     1     4   | 2      9    8     |
 | 8   6   2   | 3579  3579 #35  | 4      1   b57    |
 |-------------+-----------------+-------------------|
 | 59  23  46  | 8     235   1   | 359    7    46    |
 | 59  23  14  | 235   6     7   | 8      345  1459  |
 | 7   8   16  | 345   345   9   | 35     2    16    |
 |-------------+-----------------+-------------------|
 | 6   7   3   | 459   8     2   | 1      45   459   |
 | 2   9   5   | 1     347   6   |a37     8    4-7   |
 | 4   1   8   | 3579  3579 #35  | 35679 #356  2     |
 *---------------------------------------------------*

Almost skyscraper for 5: r9c8=3 or r3c9 (and r1c45) <> 5
(7=3)r8c7-3r9c8=(skyscraper 5r39c6r19c8)-(5=7)r3c9 => -7r1c6,r8c9; stte
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