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9x9 twin
http://www.calcudoku.org/forum/viewtopic.php?f=16&t=245
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Author:  pnm  [ Wed Jun 20, 2012 12:53 pm ]
Post subject:  9x9 twin

I'm testing out 9x9 twins, below is a sample, how nice/easy/difficult is it?

Image

Author:  jomapil  [ Wed Jun 20, 2012 1:08 pm ]
Post subject:  Re: 9x9 twin

At first sight looks like very good and appealing.
This afternoon I'm going to solve it.

But, Patrick, if day after day, is already decided the puzzles, when are these new puzzles used?


P.S. - I finished the puzzle and it is very easy. Maybe around 30 points of your classification.

Author:  clm  [ Wed Jun 20, 2012 8:42 pm ]
Post subject:  Re: 9x9 twin

pnm wrote:
I'm testing out 9x9 twins, below is a sample, how nice/easy/difficult is it?

...


Nice, medium difficulty, the interesting thing is that the left and right puzzles can not be completely solved independently, that is, it exists the necessary interaction between them. If you try to solve, i.e., the left puzzle alone you arrive to a situation with the possibility of permuting a total of 14 cells by pairs (in rows 1 and 2 and in rows 3 and 4: a1-a2, b1-b2, e1-e2, i1-i2, a3-a4, h3-h4 and i3-i4). In the case of the right puzzle you arrive to a situation with 17 cells that can be permuted (d1-e1, d2-e2, d5-e5, a6-b6-d6-e6, a7-b7-c7-d7-e7, and c8-d8).

Author:  pnm  [ Wed Jun 20, 2012 8:50 pm ]
Post subject:  Re: 9x9 twin

clm wrote:
Nice, medium difficulty, the interesting thing is that the left and right puzzles can not be completely solved independently, that is, it exists the necessary interaction between them.

Hm, I need to look into that, because I'm pretty sure that right now
a potential twin puzzle is only approved if at least one of them has
a unique solution..

Author:  clm  [ Wed Jun 20, 2012 9:49 pm ]
Post subject:  Re: 9x9 twin

pnm wrote:
clm wrote:
Nice, medium difficulty, the interesting thing is that the left and right puzzles can not be completely solved independently, that is, it exists the necessary interaction between them.

Hm, I need to look into that, because I'm pretty sure that right now
a potential twin puzzle is only approved if at least one of them has
a unique solution..


If it facilitates your analysis, here is the detail.

Left puzzle: a1-a2 = [5,8]; b1-b2 = [4,8]; e1-e2 = [2,5]; i1-i2 = [2,4], two possibilities in rows 1 and 2.
a3-a4 = [4,6]; h3-h4 = [4,9]; i3-i4 = [6,9], two possibilities in rows 3 and 4.

Right puzzle: d1-e1 = 3-5 (the correct solution for the twin) or 5-3; d2-e2 = 9-2 (or 2-9); d5-e5 = 5-9 (or 9-5) these can be permuted in combination with a6-b6-d6-e6 = 7-1-4-3 (the correct sequence for the twin set) or 3-7-1-4 (the right puzzle alone); a7-b7-c7-d7-e7 = 3-7-2-1-4 (the correct sequence for the twin) or 7-1-4-3-2 (the right alone).
finally, c8-d8 = 4-2 (the correct) or 2-4 (the right alone).

Author:  jake4  [ Wed Jun 20, 2012 9:57 pm ]
Post subject:  Re: 9x9 twin

pnm wrote:
clm wrote:
Nice, medium difficulty, the interesting thing is that the left and right puzzles can not be completely solved independently, that is, it exists the necessary interaction between them.

Hm, I need to look into that, because I'm pretty sure that right now
a potential twin puzzle is only approved if at least one of them has
a unique solution..

I don't think clm is saying that there are multiple possible solutions. He's saying that you can't solve one of the puzzles independently, i.e. you have to look at the interactions between both puzzles to solve.

I'm so glad clm mentioned this, because I was thinking about whether we could get twin puzzles that were dependent on each other. And I was also thinking that clm would be the one to talk to about that. :)

Author:  pnm  [ Wed Jun 20, 2012 10:00 pm ]
Post subject:  Re: 9x9 twin

jake4 wrote:
I don't think clm is saying that there are multiple possible solutions. He's saying that you can't solve one of the puzzles independently, i.e. you have to look at the interactions between both puzzles to solve.

No, exactly, but as an easy way out for creating a twin with a unique solution,
the software requires (if I remember correctly), that at least one of them has
a unique solution. I think clm is saying neither of them have a unique solution
(by themselves).

Author:  clm  [ Thu Jun 21, 2012 12:20 am ]
Post subject:  Re: 9x9 twin

pnm wrote:
jake4 wrote:
I don't think clm is saying that there are multiple possible solutions. He's saying that you can't solve one of the puzzles independently, i.e. you have to look at the interactions between both puzzles to solve.

No, exactly, but as an easy way out for creating a twin with a unique solution,
the software requires (if I remember correctly), that at least one of them has
a unique solution. I think clm is saying neither of them have a unique solution
(by themselves).


Usually, when solving twin puzzles, I try just one (normally the left) because it makes it a little bit more difficult (and amused) (well, when I am in a hurry I use both to go faster [smile]). And many times with only the left, i.e., I have arrived to the full solution of the twin and found the unicity of this left side only (mainly in the 5x5's and 6x6's), without the need of the right puzzle, that's why I sent that post "The essential info in a puzzle" (in the section "Solving strategies and tips") because I'm convinced that in many cases the other puzzle contains only redundant info or info to easy the solution. The ideal situation, of course, is that both puzzles be related in such a way to make impossible to solve the full twin without the crossed info.

Well, this is the case in this 9x9, it needs both puzzles. I went first only with the left side and practically finished it until I found those possible permutations, so the solution for the left is not unique (and we need the right puzzle). Later I repeated the process using only the right puzzle and found again (almost at the end) that it also has more than one solution (permutations).

In this context, in my opinion, the puzzle is consistent as a good 9x9 twin, well "interleaved" (a different thing is the criteria used for the software, perhaps it would be more interesting that both puzzles have several solutions, separately, and a unique solution when considered together).

Author:  jake4  [ Thu Jun 21, 2012 4:29 pm ]
Post subject:  Re: 9x9 twin

clm wrote:
In this context, in my opinion, the puzzle is consistent as a good 9x9 twin, well "interleaved" (a different thing is the criteria used for the software, perhaps it would be more interesting that both puzzles have several solutions, separately, and a unique solution when considered together).

I like the idea of twins that have to be solved together, or interleaved, as clm put it. Especially for the smaller puzzles, say 5x5 and 6x6 twins; interleaving would make solving those more interesting (i.e., harder :) ).

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