The New Sudoku Players' Forum

by **Mathimagics** » Wed Apr 03, 2019 7:00 am

I have now added Killer Sudoku to my variant repertoire, and here is a sample Jigsaw Killer puzzle.

These are affectionately known as "Texas Jigsaw Killers" over at the solver's forum (see here), an appellation that has less to do with the puzzle type that it does with chainsaws!

I have chosen not to use the traditional Killer presentation (dotted lines outlining the cages), I always found that a little messy, hence the 4-colour system for indicating the cages (yes, folks, MM finally went pastel!). And for a printer-friendly version, I have used a suggestion of tarek's, which (thanks to the 4-colour theorem), gives a pretty good result, with a nice "woodgrain" effect).

: TJK-099.png (12.55 KiB) Viewed 982 times

Print friendly: Show

Solution: Show

by **Mathimagics** » Wed Apr 03, 2019 7:40 am

One of the nice things about this variant is that there are software solvers that support it - Ruud's "SumoCue" and Richard Broughton's "Sudoku Solver" (SS).

Ruud created a one-line format, and the SS program supports this format, so you can paste the puzzle definitions directly into SS, which has a suite of Sudoku solving techniques, and some that are particular to Jigsaws and Killers (eg "Law of Leftovers", "Law of 45", "Split Cages").

SS has a scoring (rating) system, and this puzzle gets a rating of 0.95, which puts it in the "medium" difficulty class.

The "SumoCue" definition string for the puzzle above is:

SumoCue definition: Show

My puzzle definitions use a simple 3-line (81 character) format:

Jigsaw layout string

Cage layout string

Solution (or cage-sum list)

Code: Select all: AAABBBBBCAAABBBBCCAAADDDCCCEEEEDCCCFEEEEDFFFFEGGGDFFFFGGGDDDHHHGGIIIIHHHGIIIIIHHH AABBCCDDEFAABCGDEEFFHHHGDDEIIJJKLLLMIJJJKNNNMIOOOKNNMMPQQRSSSTTPPQRUVWWTPQQUUVVWW 378465219561738924294316875952841367713692458427589136839257641146973582685124793

The cage layout string is just a cell-to-cage assignment list, exactly as for Jigsaw layouts. Note that all characters beyond "Z" (90) are printable up to "~" (126) so that gives us 62 cage index characters, which is more than enough.

Cage sums can be obtained from the solution string, or alternatively, the solution string can be replaced by a comma-separated list of sums.

by **tarek** » Wed Apr 03, 2019 12:14 pm

This is great. What is lovely is your effort to make it possible to print out in several formats including B&W. I think feedback from P&P solvers will help to see if this is worth the effort.

Rating is obviously your next hurdle and is good to know that several freely available solver programs are available. You can probably batch solve/rate puzzles that you like to select from and present to your targeted audience.

The issues which advances players particularly look for in a puzzle is the rating but also how narrow and uncluttered the solution path is. This is an added challenge for puzzle makers which requires more effort in selecting suitable puzzles

Well done

Tarek

by **Mathimagics** » Wed Apr 03, 2019 1:42 pm

Thanks, tarek!

I have updated the "Print-friendly" image above. The format now shows the sums more clearly - I was using transparent background mode, I have replaced this with non-transparent mode. The fill patterns are more distinctive, I think. I replaced the "horizontal line" and "vertical line" patterns with solid light-grey and diagonal cross-hatch. That still leaves me with a 5th colour option (white) which is needed in case we have cells that are not assigned to cages.

Puzzle rating is always subjective, of course, and becomes even more so with Jigsaw layouts and Killer cages thrown into the mix. I have developed an increasing level of admiration for Richard's "SS" program, if the puzzle can't be solved with all the techniques enabled, it's usually an indicator that it's going to be extremely challenging for P&P solvers. The ability to select/deselect various techniques and get a revised score is really nice, too.

The "Texas Jigsaw Killer Archive" thread is full of examples of people trying different techniques and producing alternative walkthroughs for the harder puzzles.

My solver is far less elaborate, singles + cage-completion checking, combined with recursion (T&E / guessing), but it can solve anything. "Cage completion" checks are the secret weapon, and is a method I learned from my Kakuro solver - I think that SS calls them "cage eliminations".

So far I have found that the number of guesses required by my solver is a fairly good predictor of the likely SS rating.

Cheers
MM

by **Mathimagics** » Wed Apr 03, 2019 9:37 pm

I've posted a new puzzle here : TJK-102.

An improvement to the rendering process is the ability to look for and employ 3-color mode where possible for the cages.

by **Mathimagics** » Thu Apr 04, 2019 8:51 am

Ok, perhaps a final adjustment to the Killer Cage colouring algorithm is warranted …

Consider these two renderings of the same layout:

: 3Cv4C.png (15.15 KiB) Viewed 950 times

The 3-coloring on the left is cute, but has various instances of two cages that are diagonally adjacent and have the same colour.

This, I have decided, offends my aesthetic sensitivities ( :shock:

), and so I have changed the colouring rule - no two neighbouring cages should have the same colour.

This makes 3-colourings far less likely to occur, but has no impact on 4-colorability, it just produces a better result.

by **Hajime** » Thu Apr 04, 2019 11:14 am

Very well done; also nicely and thought-out colored. I like it !

The New Sudoku Players' Forum

Texas Jigsaw Killer

Texas Jigsaw Killer

TJK Definition Strings

Re: Texas Jigsaw Killer

Re: Texas Jigsaw Killer

Re: Texas Jigsaw Killer

Cage Colouring

Re: Texas Jigsaw Killer