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The solution of a 6x6 and a 9x9 puzzles with "strange cages"
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Posted on: Mon Nov 14, 2011 6:04 pm

Posts: 2258
Joined: Thu May 12, 2011 11:58 pm
Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca
Wrt. the 9x9: I stopped my solver after one hour, after which about 22 x 10^9
possible solutions had been tried (testament to the poor quality of my solver

I'm thinking the 9x9 is too "open ended", and most likely completely unsolvable
by a human (unless there's some key solving technique that I'm missing)

Patrick

Posted on: Mon Nov 14, 2011 7:18 pm

Posts: 2258
Joined: Thu May 12, 2011 11:58 pm
Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca
My solver took half an hour to compute all solutions for the 6x6.

It found 6492 solutions.

The difficulty rating is 183.

Here are a few solutions:

465123
126345
342561
514632
231456
653214

645123
326541
214635
563412
431256
152364

542163
326541
614325
453612
231456
165234

142635
326541
465312
654123
231456
513264

(these were solution number 10, 100, 1000, and 6492 found)

Patrick

Posted on: Mon Nov 14, 2011 10:50 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca
pnm wrote:
In addtion, I like to reduce typing as much as possible

Note that in my suggested format:

6
31,+,a1b1c1a2c2a3b3c3

I could reduce it still by one character by defining:

6
+31,a1b1c1a2c2a3b3c3

(Also note that for the single cage you wrote:
2,b2
and as a result, I had to add a special case to the converter such that
it detects an operator is missing..)

"31+" (a1-b1-c1-a2-c2-a3-b3-c3);

- quotes
- parentheses
- dashes
- a space
- a semicolon at the end...

Granted, the dashes make the cell list a bit more readable.

Patrick

It was only a suggestion (to make compatible both things), I see the difficulties, and in fact a more concise expressions are much better for the solver, you are right, but I was thinking that you could implement "any" expression. Well, your text form is an easy and convenient way to avoid graphics and be able to quickly transmit you some puzzle configuration from time to time (by the way, yes, I did not notice that the + was required for the single cells too). For my new "international terminology" it would be necessary to create a totally new compiler (in case of translating that language to a representation, for instance...). But we are talking about two different things in fact because the idea of the "terminology" is more to have a tool to explain the full process of the solution of a puzzle, or part of the process, etc.. I am thinking now in prepearing examples of the solutions of the puzzles using the PowerPoint, will see..., that gives better quality than the video transmisions, undoubtedly, and it would permit the players to advance very slowly just by clicking the keyboard, etc., at that time the insertion of the notes could be in this "international terminology" and not in English, Spanish or any other language (of course it would be necessary to insert a "reference" to that language with a call to the Forum of the www. calcudoku.org; the PowerPoint permits additionally to add the voice in any language).

Posted on: Mon Nov 14, 2011 11:38 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca
pnm wrote:
Wrt. the 9x9: I stopped my solver after one hour, after which about 22 x 10^9
possible solutions had been tried (testament to the poor quality of my solver

I'm thinking the 9x9 is too "open ended", and most likely completely unsolvable
by a human (unless there's some key solving technique that I'm missing)

Patrick

Very curious. If a 6x6, even knowing the exact compostion of the cages, has 6492 solutions (by spinning those numbers around the central "hole" of the cages and combining the 4 cages to a valid grid) (I suppose excluding symmetries), how many a 9x9 would have?. The number of different diagrams (excluding symmetries), just the "configuration", before stablishing the cages, that is, the restrictions, is 3 for a 3x3 (with the 1's in the diagonal, the 2's in the diagonal and the 3's in the diagonal); for the 4x4 I think is 108 (in three classes, 36 with one pair of equal corners, 36 with two pairs of equal corners, and 36 with all four corners different), etc. The number of valid grids grows almost "in vertical" and we know the very high number, 6,671 x 10 ^ 21 of valid "sudoku grids" (9x9).

The case of the 6x6: with a rating of 183 it would be solvable by a human, even if the solution is not unique (one of those 6492), the program could return the "congratulations"; perhaps you may introduce some type of complementary (additional challeging puzzles), without points, without time limitation (neither 24 hours or 72 hours...) and just indicate (without names) "solved by 12 puzzlers..." and after some time, a month or so, put new ones, just for hobby.

Posted on: Tue Nov 15, 2011 12:12 am

Posts: 2258
Joined: Thu May 12, 2011 11:58 pm
Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca
clm wrote:
perhaps you may introduce some type of complementary (additional challeging puzzles), without points, without time limitation (neither 24 hours or 72 hours...) and just indicate (without names) "solved by 12 puzzlers..." and after some time, a month or so, put new ones, just for hobby.

What I should introduce is a "user puzzle" feature: simply upload a file
in that format, and it becomes a puzzle created by clm.

The solver would assign points to it based on difficulty level, etc...

Patrick

Posted on: Tue Nov 15, 2011 12:17 am

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca
pnm wrote:
Wrt. the 9x9: I stopped my solver after one hour, after which about 22 x 10^9
possible solutions had been tried (testament to the poor quality of my solver

I'm thinking the 9x9 is too "open ended", and most likely completely unsolvable
by a human (unless there's some key solving technique that I'm missing)

Patrick

Perhaps there are not many solutions and because of the high number of combinations in the case of the 9x9 it would have required more time to find the first solution. Here is the solution:

Posted on: Tue Nov 15, 2011 1:59 am

Posts: 530
Joined: Fri May 13, 2011 1:37 am
Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca
This kenken is beyond my ken

Posted on: Tue Nov 15, 2011 12:37 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca
pnm wrote:
My solver took half an hour to compute all solutions for the 6x6.

It found 6492 solutions.

The difficulty rating is 183.

Here are a few solutions:

465123
126345
342561
514632
231456
653214

645123
326541
214635
563412
431256
152364

542163
326541
614325
453612
231456
165234

142635
326541
465312
654123
231456
513264

(these were solution number 10, 100, 1000, and 6492 found)

Patrick

Now, knowing that there are 6492!!! solutions, it would probably be interesting looking for at least one. But, with a rating of 183, this requires some time. Here is one of those 6492 solutions:

Posted on: Tue Nov 15, 2011 3:06 pm

Posts: 2258
Joined: Thu May 12, 2011 11:58 pm
Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca
clm wrote:
Now, knowing that there are 6492!!! solutions, it would probably be interesting looking for at least one. But, with a rating of 183, this requires some time.

What's also interesting is how to modify the puzzle so there's exactly one solution...

I'm wondering if this could be programmed. The solver determines there are >= 2 solutions
(determined quite quickly), and then the puzzle is modified in a way that is known to reduce
the number of solutions (simple example: split a large cage into two), etc.

Patrick

Posted on: Tue Nov 15, 2011 8:38 pm

Posts: 700
Joined: Fri May 13, 2011 6:51 pm
Re: The solution of a 6x6 and a 9x9 puzzles with "strange ca
pnm wrote:
clm wrote:
Now, knowing that there are 6492!!! solutions, it would probably be interesting looking for at least one. But, with a rating of 183, this requires some time.

What's also interesting is how to modify the puzzle so there's exactly one solution...

I'm wondering if this could be programmed. The solver determines there are >= 2 solutions
(determined quite quickly), and then the puzzle is modified in a way that is known to reduce
the number of solutions (simple example: split a large cage into two), etc.

Patrick

We could try your idea and see what happens, I broke (in my solution) a big cage into two parts:

6
31,+,a1b1c1a2c2a3b3c3
2,+,b2
150,x,d1d2d3e3f3
4,+,e2
2,-,e1f1f2
3600,x,a4b4c4a5c5a6b6c6
3,+,b5
28,+,d4e4f4d5f5d6e6f6
5,+,e5

Here is the graphic anyway

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