The New Sudoku Players' Forum

[coloin]

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.......

[coloin]

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]

[JPF]

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|...|...|
+---+---+---+   +---+---+---+


JPF

[coloin]

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 ...

[m_b_metcalf]

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!

[JPF]

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


JPF

[m_b_metcalf]

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.

Mike

[JPF]

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.
+---+---+---+


JPF

[coloin]

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.


[JPF]

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.


JPF

[blue]

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 ?

[JPF]

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|...|...|
+---+---+---+


JPF

[JPF]

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?

JPF

[blue]

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.

[blue]

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
+-------+-------+-------+