How many 1-clue-box and 2-clue-box?

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Re: How many 1-clue-box and 2-clue-box?

Postby coloin » Sat Sep 03, 2022 4:07 am

Difficult !! .... here is a version with 6 clues in box 3

Code: Select all
+---+---+---+
|...|...|.59|
|...|...|.36|
|...|...|7.1|
+---+---+---+
|.2.|..6|...|
|.5.|.73|...|
|.89|...|...|
+---+---+---+
|71.|9..|...|
|...|58.|...|
|6..|4..|...|
+---+---+---+  20C

I think a 19C will be much rarer than the previous 18C quest. [of which I eventually found 75 puzzles]
Though JPFs puzzle wasnt on the list .... so probably significantly more than 75 18C puzzles !

Hidden Text: Show
Code: Select all
........1.......23.....4........54....2..7...173......4........6.183.....3..2....
........1.......23.....4......7.64....9..8....2..5....7.8.........39....14..2....
........1.......23.....4....81..54..2..7.6....3.......6...2......93.....5.4......
........1.......23.....4...5..1.64...1...7.....2......4..38......3.2....96.......
........1.......52.....4...1...874....3..9....5.......819.........23....4..5.....
........3.......21.....4....8..564...231.......7..................238...519......
........3.......21.....4...9...564...231.......7..................238...519......
........1.......23.....4........54...831.7....2.......56..........32....9.4.8....
........1.......23.....4....5...64....9..7....2.8.....7.8.........39....61..2....
........1.......23.....4...5..1.64...1...7.....2......4...8.......32....968......
........1.......23.....4...6..1.54.......7.....2......789........132....4...8....
........1.......27.....4........84...17........31.6...85.......1..27......9.3....
........1.......35.....4....95...7....3..2.....63.....27..98......5.....4....6...
........1.......42.....7.......897..3.26......1.5.....7...........21....946......
........1.......52.....4...1....74....3..9....5.6.....819.........23....4...5....
........3.......21.....4.......564....31......27........8.........238...519......
........3.......21.....4.......564....31......27......2...........238...519......
........5.......23.....4......8.54..1....7....72......5..........632....8.96.....
........5.......23.....4...5..1.84...8...6.....2......198.........32....4...9....
........6.......32.....4........84....26.1.....3......8........7..25....419.3....
........1.......23.....4........9....9.1.54....3......75........6128....2...3....
........1.......23.....4.......564....7.......321.....8...9.......23....6.57.....
........1.......23.....4......7.94....2.......36.1....8..5........32....9.5.6....
........1.......23.....4.....6..84...926.7....3.......8...........29....1.5.3....
........1.......23.....4...17...64....2..8....3.1.....5...........23....4.8.9....
........1.......23.....4...5....64....9..7....2.8.....6.8.........39....17..2....
........1.......23.....4...5....64....9..7....2.8.....8.7.........39....41..2....
........1.......23.....4...5..1.84.......7....31......72..........23....8.6.9....
........1.......32.....4...16...74....5..9....3.1.....8...........23....4.9.5....
........1.......32.....4...6..1.84.......5....21......5...........32....847.9....
........1.......83.....4...7..1.54.......7....8.......5.9......21.36......3.8....
........1.......23.....4.....61.54...1...7...2..........4.........32....7659.....
........1.......23.....4.......654....7.......132.....8...........31....495.8....
........1.......23.....4.......654....7.......312.....8...........31....495.8....
........1.......23.....4.......654....7.......312.....89..........31....4.5.8....
........1.......23.....4.....6..54...7...8...2..9.......5.........32....864.7....
........1.......23.....4.....6..54...7...8....2.9.......5.........32....184.7....
........1.......23.....4.....61.54...7...8...2..........5.........32....8649.....
........1.......23.....4.....61.54.......7...52.........5.........32....874.9....
........1.......23.....4.....67.54.......8...27.........5.........32....864.9....
........1.......23.....4.....61.54......47....2.........5.........32....874.9....
........1.......23.....4.....61.54.......7...42.........5.........32....874.9....
........1.......23.....4.....61.54.......7....2..6......5.........32....874.9....
........1.......23.....4.....18.54.......7...28.........5.........32....794.6....
........1.......23.....4.....68.54.......9...28.........5.........32....694.7....
........1.......23.....4.....18.54.......7...28.........5.........32....749.6....
........1.......23.....4........54...3...6....2.1.....7.5......4...2....81.39....
........1.......23.....4........54..3....6...2..1......75.......8.39....64..2....
........1.......23.....4....6...84....2..7...7.31.....8...........25....9.1.3....
........1.......23.....4........84....3..7....251.....8...........32....946.5....
........1.......23.....4........84....2..6....351.....8...........23....946.5....
........1.......23.....4........84....3..9....251.....8...........32....946.5....
........1.......23.....4........84....3..9....251.....83..........32....9.6.5....
........1.......23.....4........84....2..7....731.....83..........25....9.6.3....
........1.......23.....4........84....3..7....251.....83..........32....9.6.5....
........1.......23.....4........84....3..7....251.....8..........132....9.6.5....
........1.......23.....4........54...1.6.7....38........53.....9..81....6.4......
........1.......23.....4........54...1.9.7....38........53.....9..81....6.4......
........1.......23.....4........54...1.6.7....38........43.....9..81....6.5......
........1.......23.....4........54...1.9.7....38........43.....9..81....6.5......
........1.......23.....4...6....54...1...7....2..1....8.5......4..9.1......23....
........1.......23.....4...6....54...1...7....2..1....8.5..6...4..9........23....
........1.......23.....4......6.54...1.......37..8....2.5.69...8..1.........3....
........1.......32.....4....6...54....3..7....1..2....8.5......7..93....2..1.....
........1.......23.....4...6...154..7....8....3.......4659.....8...........32....
........1.......23.....4...4....56...1...6....2..1....5.49.8...6...........23....
........1.......23.....4.......654....7.......132.....9.6......4..7........318...
........1.......23.....4.......654...7........132.....9.1......46..9.......3.8...
........1.......23.....4.......654....7.......123.....9.6......4..7........218...
........1.......23.....4.......654...7........123.....96.......4..7........218...
........1.......23.....4.......354..6....7...27.........5......1..26....39..1....
........1.......23.....4...7...654...3........1.2.....296........53.........18...
........1.......23.....5...4..1.65.......8....12......5..37......3.2....96.......
........6.......23.....4...9.5..84....21.7....3.......8....1......25....6..3.....
................12.....4..33....54...9...7....1.6.....4.5.1.......29....87.......
Last edited by coloin on Tue Sep 27, 2022 8:54 pm, edited 1 time in total.
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Re: How many 1-clue-box and 2-clue-box?

Postby coloin » Sun Sep 04, 2022 9:49 pm

And finally found a version with 5 clues in B3 and 15 clues in B4578

Code: Select all
+---+---+---+
|...|...|..1|
|...|...|.23|
|...|...|45.|
+---+---+---+
|6..|..3|...|
|4.7|..6|...|
|..5|.81|...|
+---+---+---+
|...|74.|...|
|.98|5..|...|
|71.|...|...|
+---+---+---+


So its going to be a rare 19C puzzle which is 5plus14 [or 6 plus13 - ? even less likely]
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Re: How many 1-clue-box and 2-clue-box?

Postby JPF » Mon Sep 05, 2022 2:19 pm

On my side, nothing exciting: two 20C with the same ed pattern:
Code: Select all
+---+---+---+   +---+---+---+
|...|...|..1|   |...|...|..1|
|...|...|.23|   |...|...|.23|
|...|...|456|   |...|...|456|
+---+---+---+   +---+---+---+
|...|..1|...|   |...|..1|...|
|..4|.78|...|   |..5|.78|...|
|36.|...|...|   |36.|...|...|
+---+---+---+   +---+---+---+
|..7|6..|...|   |..8|3..|...|
|.48|...|...|   |.9.|216|...|
|9..|513|...|   |4.7|...|...|
+---+---+---+   +---+---+---+

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Re: How many 1-clue-box and 2-clue-box?

Postby coloin » Tue Sep 06, 2022 6:57 pm

Quite exciting !!
A 7plus13

Code: Select all
+---+---+---+
|...|...|12.|
|...|...|345|
|...|...|.67|
+---+---+---+
|.2.|...|...|
|.64|.7.|...|
|...|.53|...|
+---+---+---+
|38.|...|...|
|6..|2..|...|
|...|461|...|
+---+---+---+    20C


There may well be a 19 ....
What would be good would be a vicinity search which is restricted to B4578 ...
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Re: How many 1-clue-box and 2-clue-box?

Postby m_b_metcalf » Wed Sep 07, 2022 12:14 pm

coloin wrote:What would be good would be a vicinity search which is restricted to B4578 ...

This puzzle seems to be immutable. It's almost symmetrical about the anti-diagonal when rearranged, and can be made symmetrical by moving a clue position from r6c5 to r5c5 (or r6c4 to r5c4):
Code: Select all
 . . . . . . 1 2 .
 . . . . . . 3 4 5
 . . . . . . . 6 7
 6 . . 2 . . . . .
 3 8 . . 9 . . . .
 . . . 4 . 1 . . .
 . 2 . . . . . . .
 . 6 4 . 7 . . . .
 . . . . 5 3 . . .  20C, 4903 solution(s)

Doesn't help, though!
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Re: How many 1-clue-box and 2-clue-box?

Postby JPF » Wed Sep 07, 2022 7:33 pm

Here are two new twins 20C
Code: Select all
+---+---+---+   +---+---+---+
|...|...|12.|   |...|...|12.|
|...|...|.34|   |...|...|.34|
|...|...|5.6|   |...|...|5.6|
+---+---+---+   +---+---+---+
|72.|...|...|   |72.|...|...|
|3.8|.6.|...|   |3.8|.9.|...|
|...|.94|...|   |...|.64|...|
+---+---+---+   +---+---+---+
|14.|...|...|   |14.|...|...|
|5..|2..|...|   |5..|2..|...|
|...|387|...|   |...|387|...|
+---+---+---+   +---+---+---+

and a 19C - 10 solutions
Code: Select all
+---+---+---+
|...|...|.12|
|...|...|..3|
|...|...|4.5|
+---+---+---+
|.6.|..3|...|
|.1.|.78|...|
|.72|...|...|
+---+---+---+
|54.|2..|...|
|...|71.|...|
|3..|9..|...|
+---+---+---+  19C - 10 sol

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Re: How many 1-clue-box and 2-clue-box?

Postby m_b_metcalf » Thu Sep 08, 2022 7:57 am

JPF wrote:and a 19C - 10 solutions

... which, when tweaked, yields the pretty:
Code: Select all
 . 6 . . . . . . 3
 . 1 . . . . . 6 8
 . 7 2 . . . . . .
 . . . . 2 1 . . .
 . . . . 3 . . . .
 . . . 4 5 . . . .
 . . . . . . 1 7 .
 5 4 . . . . . 2 .
 3 . . . . . . 9 .  19C, 60 solution(s), rotationally symmetric.


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Re: How many 1-clue-box and 2-clue-box?

Postby JPF » Thu Sep 08, 2022 3:03 pm

Nice pattern! but I think that any puzzle with that pattern has at least 33 solutions.
Here is one:
Code: Select all
+---+---+---+
|.1.|...|..2|
|.3.|...|.45|
|.67|...|...|
+---+---+---+
|...|.54|...|
|...|.2.|...|
|...|73.|...|
+---+---+---+
|...|...|36.|
|85.|...|.7.|
|2..|...|.9.|   19C - 33 sol.
+---+---+---+

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Re: How many 1-clue-box and 2-clue-box?

Postby coloin » Thu Sep 08, 2022 11:30 pm

I've put the big guns on it
Not clear if the 19C - [if there is one] will have a 13plus6 or a 14plus5 pattern.
Its strange because I have generated many 20C ... and it hasn't appeared ...
Code: Select all
+---+---+---+
|...|...|123|
|...|...|.56|
|...|...|..9|
+---+---+---+
|.18|...|...|
|...|692|...|
|...|3..|...|
+---+---+---+
|..4|.78|...|
|63.|.5.|...|
|9..|...|...|
+---+---+---+  19C - 2 sol.
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Re: How many 1-clue-box and 2-clue-box?

Postby JPF » Fri Sep 09, 2022 3:26 pm

Great find!
I got some 19C - 2 sol. too.
Not clear if the 19C - [if there is one] will have a 13plus6 or a 14plus5 pattern.

Here is a 12plus7...
Code: Select all
+---+---+---+
|...|...|.12|
|...|...|3.4|
|...|...|567|
+---+---+---+
|.16|...|...|
|...|248|...|
|...|7..|...|
+---+---+---+
|...|.36|...|
|48.|.5.|...|
|2..|...|...|
+---+---+---+  19C - 2 sol.

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Re: How many 1-clue-box and 2-clue-box?

Postby blue » Fri Sep 16, 2022 1:06 pm

coloin wrote:I've put the big guns on it
Not clear if the 19C - [if there is one] will have a 13plus6 or a 14plus5 pattern.

Big guns ?

Are 7plus12 and 8plus11 already ruled out ... by Serg, perhaps ?
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Re: How many 1-clue-box and 2-clue-box?

Postby JPF » Fri Sep 16, 2022 2:41 pm

About 7plus13, here are two 20C:
Code: Select all
+---+---+---+   +---+---+---+
|...|...|123|   |...|...|12.|
|...|...|456|   |...|...|345|
|...|...|..7|   |...|...|.67|
+---+---+---+   +---+---+---+
|.18|...|...|   |4..|...|...|
|...|362|...|   |53.|8.7|...|
|...|7..|...|   |2..|6..|...|
+---+---+---+   +---+---+---+
|..4|.98|...|   |..6|19.|...|
|37.|.5.|...|   |...|.4.|...|
|6..|...|...|   |.87|...|...|
+---+---+---+   +---+---+---+


and, just in case, a 8plus13 = 21C minimal:
Code: Select all
+---+---+---+
|...|...|123|
|...|...|.45|
|...|...|678|
+---+---+---+
|4..|...|...|
|59.|3.8|...|
|2..|7..|...|
+---+---+---+
|..7|16.|...|
|...|.4.|...|
|.38|...|...|
+---+---+---+

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Re: How many 1-clue-box and 2-clue-box?

Postby JPF » Fri Sep 16, 2022 4:42 pm

Hi blue,
Are 7plus12 and 8plus11 already ruled out ... by Serg, perhaps ?

do you mean you know a proof based on Serg's invalid patterns or is this an open question?

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Re: How many 1-clue-box and 2-clue-box?

Postby blue » Fri Sep 16, 2022 5:14 pm

Hi JPF,

do you mean you know a proof based on Serg's invalid patterns or is this an open question?

Using his invalid ("magic 40") patterns, I know how to prove that at least 5 clues are required in the long box ... but that's it.

I know he has done some work with patterns with empty boxes, and (some large, some small) clue counts for the other boxes, but I'm too lazy to try to find it.
I wondered if maybe some of it covered cases like this:

Code: Select all
9 |  0 |  0
--+----+---
0 | n6 | n7
--+----+---
0 | n8 | n9

... and if so, whether it was enough to show that 12 clues in b5689 was impossible.
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Re: How many 1-clue-box and 2-clue-box?

Postby blue » Fri Sep 16, 2022 5:39 pm

Related: Here's a puzzle showing that 5 clues in band 2 is possible

Code: Select all
+-------+-------+-------+
| . . . | . . . | . 5 6 |
| . . . | . . . | 2 9 1 |
| . . . | . . . | 8 7 3 |
+-------+-------+-------+
| . . 1 | . . . | . . . |
| . 2 3 | . . . | . . . |
| . . . | . 4 5 | . . . |
+-------+-------+-------+
| . . . | 2 . 1 | . . . |
| 4 . . | 3 6 . | . . . |
| 8 9 . | 7 . . | . . . |  21C : 8+13
+-------+-------+-------+

Here's one with 5 clues in band 2, and a box with only one clue:

Code: Select all
+-------+-------+-------+
| . . . | . . . | . 1 3 |
| . . . | . . . | 8 9 4 |
| . . . | . . . | 7 5 . |
+-------+-------+-------+
| . . . | . . 1 | . . . |
| . . . | . 2 3 | . . . |
| . . 4 | 5 . . | . . . |
+-------+-------+-------+
| . 6 . | 7 . . | . . . |
| 3 2 . | 4 . . | . . . |
| 5 1 . | 8 9 . | . . . |  21C : 7+14
+-------+-------+-------+
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