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Puzzles with 123456789 in the diagonal

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Re: More Homework 2

Postby marek stefanik » Sat Feb 19, 2022 10:20 pm

2B
Code: Select all
+---------+---------+---------+
| 1  9  8 | 7  6  5 | 3  .  . |
| 7  2  6 | 9  3  . | .  .  . |
| 5  .  3 | .  .  . | .  .  . |
+---------+---------+---------+
| 9  .  . | 4  .  . | 1  .  . |
| .  .  . | .  5  . | .  .  . |
| .  .  . | .  .  6 | .  .  3 |
+---------+---------+---------+
| .  .  . | 1  .  . | 7  .  . |
| .  .  . | .  2  . | .  8  . |
| .  .  . | .  8  . | 5  .  9 |
+---------+---------+---------+
...but surely.

Proof that the first 29 cells are optimal: Show
b1p159 given
r1c23456 highest possible values (below shortened to HPVs)
r1c7 – 4 impossible (any of r1c123 could be filled as a NS, thus would be redundant), therefore 3 is the HPV
r1c89 – would make 9 or 8 in r1 (in that order) a HS, hence redundant as a given
r2c134 HPVs
r2c56 – with PC 4b1\r3 HP 34b2, if 4 were given then r2c2 could be filled with HT 679b3p789, PC 5b3\r2, NS r2c2, hence would be redundant, 3. HPVs
r2c789 – corresponding given in r1 would be redundant (HS)
r3c1 HPV
r3c2 cannot be given (FH b1)
r3c456789 – corresponding given in b1 would be redundant (HS)
r4c1 HPV
r4c2 – corresponding given in b1 would be redundant (HS)

Marek
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Re: More Homework 2

Postby coloin » Sat Feb 19, 2022 10:37 pm

I think the first 15 are optimal ..as this is approaching my best
Code: Select all
+---+---+---+
|198|765|3..|
|726|93.|...|
|5.3|...|...|
+---+---+---+
|9..|427|.1.|
|3..|.5.|...|
|..7|..6|...|
+---+---+---+
|...|..9|7..|
|...|...|.8.|
|2..|...|..9|
+---+---+---+

a space has to be at r4c2 ... r4c3 can be a 7
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Re: More Homework 2

Postby marek stefanik » Sun Feb 20, 2022 12:58 am

This should be the best one:
Code: Select all
+-------+-------+-------+
| 1 9 8 | 7 6 5 | 3 . . |
| 7 2 6 | 9 3 . | . . . |
| 5 . 3 | . . . | . . . |
+-------+-------+-------+
| 9 . 7 | 4 8 . | 6 5 . |
| 8 . . | 3 5 . | . . 7 |
| . . . | . . 6 | . . . |
+-------+-------+-------+
| . . . | . 1 . | 7 . . |
| . . . | . . . | . 8 . |
| . . . | . . . | . 6 9 |
+-------+-------+-------+


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Re: More Homework 2

Postby coloin » Sun Feb 20, 2022 12:05 pm

Yes that is the max , well done for showing that there cant be bigger clues in the first band ..... and the 3 at r5c4 is the largest clue possible
.. then add 3 more clues to give your puzzle.

Relabelling this puzzle to max lex representation presumably we have the answer to the max lex puzzle with the diagonal clues question
[2B1]
Code: Select all
+---+---+---+        +---+---+---+                           
|987|654|3..|        |987|654|3..|                           
|625|83.|...|        |652|73.|...|                           
|4.3|...|...|        |43.|...|...|                           
+---+---+---+        +---+---+---+                           
|8.6|17.|54.|        |8..|34.|..6|                           
|7..|34.|..6|        |76.|18.|54.|                           
|...|..5|...|        |...|..5|...|                           
+---+---+---+        +---+---+---+                           
|...|.9.|6..|        |...|.9.|6..|                           
|...|...|.7.|        |...|...|.8.|                           
|...|...|.58|        |...|...|.57|                           
+---+---+---+        +---+---+---+      edit - larger isomorph 30 clues

Last edited by coloin on Sun Feb 20, 2022 5:46 pm, edited 1 time in total.
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Re: More Homework 2

Postby marek stefanik » Sun Feb 20, 2022 3:19 pm

2B1, 2A (32 clues)
Code: Select all
+-------+-------+-------+
| 9 8 7 | 6 5 4 | 3 . . |
| 6 5 4 | 3 2 . | . . . |
| 3 . 2 | . . . | . . . |
+-------+-------+-------+
| 8 . 9 | 7 4 5 | 6 . . |
| 7 . 6 | . 8 . | 9 . . |
| . . 5 | . . 6 | . . . |
+-------+-------+-------+
| . . . | . . . | 1 . . |
| . . . | 8 . . | . 4 9 |
| . . . | . . . | . 7 3 |
+-------+-------+-------+

Edit: Given the top band, r6c6 must be 6 (14 impossible, 3 would make 3 in b2 redundant, 8 would make 8 in b1 redundant).
Edit2: It should be the best puzzle possible for 2B1.

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Re: More Homework 2

Postby coloin » Sun Feb 20, 2022 6:00 pm

Excellent
It shows understanding the minimality issue makes for easier getting to the maximum [unlike my crude methods !]
cut to the chase, my best for
2B3
Code: Select all
+---+---+---+     +---+---+---+
|1..|987|63.|     |1..|987|63.|
|.2.|63.|95.|     |.2.|64.|9..|
|..3|5..|8..|     |..3|1..|...|
+---+---+---+     +---+---+---+
|987|4..|56.|     |.6.|4..|...|
|4.6|.5.|...|     |2..|.5.|8..|
|..5|..6|...|     |...|..6|...|
+---+---+---+     +---+---+---+
|..2|3..|7..|     |.4.|...|7..|
|...|...|.8.|     |...|...|.8.|
|...|...|..9|     |..1|8..|..9|
+---+---+---+     +---+---+---+     sigh , edit improved


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Re: More Homework 2

Postby marek stefanik » Wed Feb 23, 2022 8:43 am

Speaking of crude methods...
I was wondering why this one was taking longer than a few minutes... the search got stuck on a DP:
Hidden Text: Show
Code: Select all
+-------+-------+-------+
| 1 . . | 9 8 7 | 6 3 . |
| . 2 . | 6 4 . | 9 5 . |
| . . 3 | 5 . . | . . . |
+-------+-------+-------+
| 9 8 7 | 4 . . | 5 6 . |
| . . . | . 5 . | . . . |
| . . . | . . 6 | . . . |
+-------+-------+-------+
| . . . | . . . | 7 . . |
| . . . | . . . | . 8 . |
| . . . | . . . | . . 9 |
+-------+-------+-------+
3b2, 12b2, 12b3, 12r4, UR12r34c56
And went on to check every minimal subpuzzle from here...


Anyway, having fixed that this should be the best you can get:
Code: Select all
+-------+-------+-------+
| 1 . . | 9 8 7 | 6 3 . |
| . 2 . | 6 4 . | 9 5 . |
| . . 3 | 5 . . | . . . |
+-------+-------+-------+
| 9 8 7 | 4 . . | 5 . . |
| 4 6 . | . 5 . | . 7 . |
| . . . | . . 6 | . . . |
+-------+-------+-------+
| . . . | 1 . . | 7 . . |
| . . . | . . . | . 8 . |
| 2 . . | . . . | . . 9 |
+-------+-------+-------+


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Re: More Homework 2

Postby JPF » Wed Feb 23, 2022 8:05 pm

1A
Code: Select all
+---+---+---+
|1..|.9.|...|
|.2.|.7.|...|
|..3|...|.6.|
+---+---+---+
|...|4..|.3.|
|7..|.5.|1..|
|...|..6|...|
+---+---+---+
|...|.1.|7..|
|..4|...|.8.|
|..6|...|..9|
+---+---+---+    18 clues

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Re: More Homework 2

Postby coloin » Wed Feb 23, 2022 9:37 pm

Well done in finding the 18 ..... there are only half a dozen more I believe !
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Re: More Homework 2

Postby JPF » Thu Feb 24, 2022 6:06 pm

coloin wrote:there are only half a dozen more I believe !
maybe.
It takes time to find them.
Here is an other one:
Code: Select all
+---+---+---+
|1..|.8.|...|
|.2.|...|..6|
|..3|...|..4|
+---+---+---+
|...|4..|...|
|78.|.5.|1..|
|...|..6|...|
+---+---+---+
|...|.1.|7..|
|...|...|.8.|
|..6|..2|..9|
+---+---+---+    18 clues

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Re: More Homework 2

Postby JPF » Sun Feb 27, 2022 7:11 pm

Last proposal:

3B
Code: Select all
based on Pattern game 438
+---+---+---+
|1..|...|..5|
|.2.|9..|8..|
|..3|.8.|.7.|
+---+---+---+
|.6.|4..|...|
|..2|.5.|3..|
|5..|..6|.1.|
+---+---+---+
|.4.|.2.|7..|
|..6|..7|.8.|
|...|3..|..9|
+---+---+---+  ED=10.6/10.6/10.6

1A
Code: Select all
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|1..|.9.|...|   |1..|.8.|...|   |1..|...|...|   |1..|.2.|...|   |1..|...|4..|
|.2.|.7.|...|   |.2.|...|..6|   |.2.|.7.|...|   |.2.|.7.|...|   |52.|...|...|
|..3|...|.6.|   |..3|...|..4|   |..3|8..|.6.|   |..3|...|.6.|   |..3|..9|..6|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|...|4..|.3.|   |...|4..|...|   |..8|4..|...|   |...|4..|.3.|   |...|4..|...|
|7..|.5.|1..|   |78.|.5.|1..|   |...|.5.|1.2|   |7..|.5.|2..|   |7..|.5.|1..|
|...|..6|...|   |...|..6|...|   |...|..6|...|   |...|..6|...|   |...|..6|...|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+
|...|.1.|7..|   |...|.1.|7..|   |...|.1.|7..|   |...|...|7.5|   |...|.1.|7..|
|..4|...|.8.|   |...|...|.8.|   |..4|...|.8.|   |..4|3..|.8.|   |...|.7.|.8.|
|..6|...|..9|   |..6|..2|..9|   |..6|...|..9|   |...|...|..9|   |..6|...|..9|
+---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+   +---+---+---+    18 clues

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Answers

Postby coloin » Thu Mar 10, 2022 11:43 pm

1A
Code: Select all
1.....3...2..8......3...4.....4.7....9..5...2.....6...4..3..7.........8.....2...9
1.....6...2..8......3...4.....4......98.5...2.....6...4..3..7.........8.....2...9
1.....6...2..8......3...4.....4......98.5...2.....6...6..1..7.........8.....2...9
1.....6...2..8......3.9.......4..1...9..5...2.....6...4.....7..6......8.....2...9
1.....3...2..9......3...4....84......9..5...2...7.6.....43..7.........8.........9

2 more ... giving 7 in total found ...
Code: Select all
1.........25........37..4.....4......9..5...2...1.6...4.....7....7....8.....2...9
1...9.4...2...5.....3.........4......9..5...2.....6.....43.17.........86........9


1B
two minimal 36s
Code: Select all
1....342.42.71.3....32.....6.142.95..4.15.........6...51.8..73.3.4.7..8.27..315.9
1....342.42.71.3....32.....6.142.95..4.15.........6...51.8..73.3.4.7..8.27..3.549


1C
That 10.6 diamond is plenty good enough !

Filtered from the hardest database however were these two
Code: Select all
1....8....2...5.3...3.2.1.....4.....3...5..2..7...64...9....7..5...1..8...6.....9 ED=11.4/1.2/1.2
1..26..7..2.8..1....3..1......4...5...4.5...78....63..6....27...92....8...7.....9 ED=11.2/11.2/11.0
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