The New Sudoku Players' Forum

[jbeck2862]

Hello,

I am new to killer sudoku puzzles and to setting puzzles but I would like a review of my second puzzle. maybe some tips on what I cam improve upon. what I am doing wrong. My first puzzle I did not think had a good solve path but the second puzzle solved and looked better.

[tarek]

Hi jbeck,

We had an active group of killer sudoku players here but the numbers dwindled over the years. Try also the SudokuSover forum as there is a bastion of killer sudoku solvers still active there!!!

As a puzzle setter, you would need to work on how you can post your puzzle so that it would be easy for people to paste into a solver. Have a look around to check what is popular!!!

All the best,

Tarek

[HATMAN]

More White Space - 34

jbeck posted a killer on the assassin site that was unique with 32 empty calls. I took this as a challenge, so in order to minimize cages I started with an easy 17 givens vanilla. I then made each given into a doublet. not surprisingly a lot of solutions, after playing around a bit I got to a unique solution with 34 spaces and it is assassin level, SS gives it 1.55 and JS uses 8 big fishes.

I'm sure it can be increased quite a bit but I have no idea of the maximum.

tarek do you have any ideas about this?

Note I believe the minimum number of cages is 14, see
www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=3&t=804
{ URL corrected }



JS Code:
3x3::k:13:2049:4098:14:2068:15:2308:2308:17:24:2049:4098:2068:25:3851:1541:26:1541:27:2579:2579:2068:3095:28:3851:1541:29:30:31:2579:3095:2310:1287:32:6166:33:3593:3593:34:35:2310:1287:36:6166:6166:3602:3602:3602:37:38:39:40:41:42:6154:6154:43:1544:1544:1544:44:45:2325:46:1548:6154:47:6147:48:49:2064:2325:50:1548:51:52:6147:6147:53:2064:2325:

Solution:
239716548
457298361
861534729
573942186
682153497
914867235
796321854
348675912
125489673

[tarek]

Is the question about the minimum number of caged cells in a killer puzzle where a cage has at least 2 cells and no givens?

I haven't explored that at all.

[999_Springs]

here is my contribution

are you asking for minimum number of cages, or minimum number of cells occupied by cages?

it turns out that you can use the approach for minimum givens on larger sudokus in this thread to create killer sudokus. the trick is to notice that replacing each "row" of givens by one cage with the biggest or smallest possible sums forces all the cages to be solved one after another

if you allow for repeated digits in cages, for the 3x3 case you get a 1-cage killer sudoku that looks like this

Code: Select all

X........
XXXX.....
XXXXXXX..
XX.......
XXXXX....
XXXXXXXX.
XXX......
XXXXXX...
XXXXXXXXX

X = 165

the solution is isomorphic to the canonical grid. i actually came up with this killer sudoku myself in 2012 and posted it to my facebook, but it only got 8 likes and 12 comments (5 of the comments were me) so i'm sorely disappointed that my facebook friends aren't as enthused by low clue killers as you guys are. i didn't post it here because this forum was completely dead in 2012. i also cross posted it to motris's blog here

now if you disallow repeats in cages, you can split this cage into separate cages in each row, and get rid of the last cage because it doesn't do anything. then if you want to consider least cells in cages you can move the cages with 5-8 cells to the other side of the row to make them smaller. so you get this (i've shuffled the rows and columns to make it symmetric)

Code: Select all

AA.......
........B
.....CCCC
DDD......
.........
......EEE
FFFF.....
G........
.......HH

A = 17
B = 1
C = 10
D = 24
E = 6
F = 30
G = 9
H = 3

which has 8 cages, 20 occupied cells, and is trivially easy to solve

by tarek's standards this thing has a tiny flaw in that there are two one-cell cages, so i'm thinking of the most efficient way to get rid of them. the "obvious" way to do it is to replace the one-cell cages by their row complements to get this 8-cage killer with no singles:

Code: Select all

AA.......
BBBBBBBB.
.....CCCC
DDD......
.........
......EEE
FFFF.....
.GGGGGGGG
.......HH

A = 17
B = 44
C = 10
D = 24
E = 6
F = 30
G = 36
H = 3

however, if you care about the minimum number of occupied cells, this wouldn't be optimal. i've come up with a way to replace the single cages with two doubles each, if you allow diagonal cages like hatman is doing. the solution of this one is the same as the one above except i swapped c1 with c2 and c8 with c9 to get the diagonal cages to line up

Code: Select all

AAII..B..
.......B.
.....CCCC
DDD......
.........
......EEE
FFFF.....
.G.......
..G..JJHH

A = 17
B = 6
C = 10
D = 24
E = 6
F = 30
G = 14
H = 3
I = 3
J = 17

which has 26 occupied cells and no singles. i'm wondering whether a better design is still possible for this idea with the canonical grid. unfortunately any of these puzzles will be trivially easy and boring to solve

hatman, your link doesn't work

edit: fixed typos and explicitly added the 8-cage no singles killer

[tarek]

here is my contribution

I like this very much! You always look at things from a different angle (and lose mobile phones in the process). Brilliant!

Tarek

[Mathimagics]

hatman, your link doesn't work

The unmangled link is http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=3&t=804

[HATMAN]

999_Springs

This is stunningly impressive and definitive on the subject.

I did not come across your motris post in 2012 and it is strange to be led back to some of my old stuff.

If we make it more difficult by requiring every cage to have at least three solutions (two would be a bit trivial), where can you get to?

Please explain the mobile phone bit.

Cheers

Maurice

[mith]

The subject of fewest caged cells in a killer came up elsewhere, and specifically we were trying to do it using only 2-cell cages. I managed to match the 26 cell minimum with this added restriction:

https://f-puzzles.com/?id=yfo7azjv

Wouldn't be too surprising if 24 is possible, at some point I'm planning to script a search for one.

[mith]

Got it down to 12 and then 11 dominoes today, still placing by hand:

https://f-puzzles.com/?id=yfyy99be

10 dominoes feels in reach of a computer search... 9 is almost certainly impossible.

[999_Springs]

mith i can't load those links (tried 2 browsers and both show blank pages) - do you have an image or text representation for them?

Please explain the mobile phone bit.

see hardest 17 clue and hardest 19 clue. haven't looked at what happens when you want 3+ options per cage, sorry

really want my phone back, those 2019 memories i hadn't backed up were so valuable to me gopro and passport would be nice to have too

[mith]

That's strange. I'll post text version of those later (attaching images doesn't seem to be working on here lately).

But for now...

https://f-puzzles.com/?id=yhodu9bk

Code: Select all

.........
AA...BB..
C...DE...
C...DE...
.........
.FF....G.
.H.II..G.
.H.......
.....JJ..

A = 6
B = 5
C = 5
D = 3
E = 5
F = 17
G = 12
H = 16
I = 17
J = 4

I can't believe that exists, much less that I found it by hand. I've been dancing around uniqueness the last 24 hours and finally got there this morning.

I don't think I'll be trying to improve on that by hand Maybe a computer search at some point for a 19 caged cell puzzle.

[mith]

I've also now found an 8 cage 20 cell version (four 2-cell and four 3-cell)... and a 7 cage:

Code: Select all

.....A...
.B..AAAA.
.B..CCC..
.B.CC....
..D.....E
..DDD...E
..FF...EE
..F......
.....GG..

A = 16
B = 9
C = 17
D = 26
E = 30
F = 24
G = 3

Total number of cells can almost certainly be improved - I have a 7 cage 20 cell with 2 solutions. (And a 9 cage 19 cell with 14 solutions - not sure if I'll get there by hand on that on, we'll see.)

[mith]

Got it down to 7 cages, 19 cells last night. And am surprisingly close on 18 cells (3 solutions is my best currently). Surprisingly low on 17 cells even (70 solutions), though I’m still doubtful that one is possible.

[Mathimagics]

If you haven't yet found 18-cells, can we see some of your 19-cell instances?