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Double CalcuDoku
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Posted on: Fri Dec 02, 2011 9:14 am

Posts: 54
Joined: Thu Nov 03, 2011 8:52 am
Double CalcuDoku
I am reposting this article from my blog.

I imagine that you are familiar with the double Sudokus like the following one:

I though: wouldn't it be nice to make overlapping CalcuDocus? Well, here is the first one I generated:

As you can see, I overlapped a 3x3 area. To explain how this works, I have coloured the puzzle, which is normally in B&W. The two squares are two normal CalcuDokus, but the green area belongs to both the yellow and the blue puzzles.

Notice that cages can cross the boundary. For example, the right-side cell of the 2-cell cage "2:" belongs to both puzzles, while its left-side cell only belongs to the yellow puzzle.

As I don't like puzzles that admit multiple solutions, I ensured that the program delivers a unique solution. The interesting thing with overlapping CalcuDokus is that they can overlap by any amount of rows and/or columns, while Sudokus, to maintain the integrity of the boxes, can only overlap by 3 or 6 rows and/or columns.

For the time being, my program only supports an overlapping of 3 rows and 3 column, but I am going to parameterise it. Then problem is not in generating and solving the puzzle, but in displaying it.

Concerning the name to give to these puzzles, I thought that Niken would be a nice possibility. This is because "Ni" means "two" in Japanese and KenKen (which is a registered trademark of Nextoy LLC) is much more widely known than CalcuDoku. In any case, "CalcuDoku", as a name, is quite long on its own. As "Ken" is a normal Japanese word (which, as you probably know, means "wisdom"), I don't believe that Nextoy could accuse me of infringing their trademark. I could also call it KenTwo or TwoKen but, somehow, it doesn't seem right. Also Kenni is not good. What do you think?

Posted on: Fri Dec 02, 2011 11:11 am

Posts: 690
Joined: Fri May 13, 2011 6:51 pm
Re: Double CalcuDoku
giulio wrote:
...
I though: wouldn't it be nice to make overlapping CalcuDocus? Well, here is the first one I generated:
...
Concerning the name to give to these puzzles, I thought that Niken would be a nice possibility ... "Ni" means "two" in Japanese ... I don't believe that Nextoy could accuse me of infringing their trademark...

Curious and interesting, I'll solve it today. What about "nicalc"? (no trademark) reserving "...calc" for three or four overlapped and "samuraicalc" for the five overlapped. Additionally, you could add a digit for the number of rows (columns) overlapped like "nicalc3" in this case (or even "samuraicalc2345" if different overlaps in the four corners).

And, since the size of the overlap is not a problem, you may design one smaller, like 5x5 "samuraicalc2" or a 7x7 "samuraicalc3" not so difficult to print.

Posted on: Fri Dec 02, 2011 12:19 pm

Posts: 2192
Joined: Thu May 12, 2011 11:58 pm
Re: Double CalcuDoku
giulio wrote:
I though: wouldn't it be nice to make overlapping CalcuDocus? Well, here is the first one I generated:

Yes, that's a nice idea, I saw that at djape's site a while back
(overlapping Calcudoku)
(he also does the 5 overlapping puzzles in
a few sizes, and calls them "Calcudoku Samurai").
giulio wrote:
Concerning the name to give to these puzzles, I thought that Niken would be a nice possibility. This is because "Ni" means "two" in Japanese and KenKen (which is a registered trademark of Nextoy LLC) is much more widely known than CalcuDoku

It depends a bit on the country. I'm guessing that because of the marketing there, "KenKen" is more
widely known in the US.
You'd be interested to know that for a long time now "calcudoku" is a more popular search term
through which people find my site than "kenken" (queried almost twice as much)(but this may
be of course because for "kenken", my site is only 6th on Google, and everybody ends
up going to the festive kenken.com )

Patrick

Posted on: Fri Dec 02, 2011 12:37 pm

Posts: 54
Joined: Thu Nov 03, 2011 8:52 am
Re: Double CalcuDoku
clm wrote:
What about "nicalc"? (no trademark) reserving "...calc" for three or four overlapped and "samuraicalc" for the five overlapped. Additionally, you could add a digit for the number of rows (columns) overlapped like "nicalc3" in this case (or even "samuraicalc2345" if different overlaps in the four corners).

And, since the size of the overlap is not a problem, you may design one smaller, like 5x5 "samuraicalc2" or a 7x7 "samuraicalc3" not so difficult to print.

It sounds logical, but people would find the numbering confusing. I also find that "calc" is OK together with "Doku", but without it, it's much less appealing. All in all, I'll stick with Niken.
pnm wrote:
Yes, that's a nice idea, I saw that at djape's site a while back
(overlapping Calcudoku)
(he also does the 5 overlapping puzzles in
a few sizes, and calls them "Calcudoku Samurai").

And I thought it was my original idea...

Posted on: Fri Dec 02, 2011 4:26 pm

Posts: 246
Location: Lisbon, Portugal
Joined: Sun Sep 18, 2011 5:40 pm
Re: Double CalcuDoku
Giulio, I didn't see in your site any samurai Calcudoku.
It will be fine if you publish one of those ( one per month ) or a little smaller double(?)8x8 samurai calcudoku ( one per week )!

_________________
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Posted on: Sat Dec 03, 2011 3:19 am

Posts: 54
Joined: Thu Nov 03, 2011 8:52 am
Re: Double CalcuDoku
jomapil wrote:
Giulio, I didn't see in your site any samurai Calcudoku.
It will be fine if you publish one of those ( one per month ) or a little smaller double(?)8x8 samurai calcudoku ( one per week )!

Thanks. I will. But I have first to get the Niken completed. It is still not working properly with overlappings other than 3x3.

To be consistent, I could call the Samurai CalcuDoku "SamuraiKen", but I like "CalcuSamurai" better. It would be consistent with "CalcuDoku".

Posted on: Thu Dec 08, 2011 8:08 am

Posts: 54
Joined: Thu Nov 03, 2011 8:52 am
Re: Double CalcuDoku
Again, I repost this from my blog http://giuliozambon.blogspot.com.
I can now generate Double CalcuDokus with any overlapping, although, at least for the time being, the overlapping region can only be a square. Here is an example of a 6x6 overlap:

I find puzzles with large overlaps more interesting. It makes it easier to exploit the fact that the cells of each row and columns that are not share must coincide. For example, in the above example, the three bottom cells of the middle column of the right puzzle include two singles: a 4 and a 2. This means that also the top three cells of the same column must include a 4 and a 2. As the 2-cell cage "9x" cannot possibly contain an even digit, it means that the they must be in the other two cells.

And here is an example of a 7x7 overlap:

The "edge effect" is particularly strong when the overlapping is 7x7, and makes the solution of the overall puzzle easier. To keep the difficulty at a challenging level, I have therefore tweaked the configuration parameters and made the individual puzzles a bit more difficult. Notice that in the above example there are three 5-cell cages and seven 4-cell cages.

I have just published a book with one hundred puzzles:

You can buy it in print from Lulu for US\$9.99 or in several eBook formats from Smashwords for US\$0.99.

Posted on: Fri Dec 09, 2011 11:38 am

Posts: 490
Joined: Fri May 13, 2011 1:37 am
Re: Double CalcuDoku
Niken sounds good to me as you'll probably require twice the "ken" to solve some of the ones you've generated.......as for me, they would probably be beyond me as I have only "one ken"

Posted on: Fri Dec 09, 2011 12:38 pm

Posts: 54
Joined: Thu Nov 03, 2011 8:52 am
Re: Double CalcuDoku
Actually, they are not more difficult than normal CalcuDokus. The edge helps, because the three (or two) cells on either side of the shared 6x6 (7x7) block must be the same (although obviously not necessarily in the same order). I have just generated the first full Samurai CalcuDoku. Here it is:

I know: it's a bit large. I would like to publish a book of them, but I would have to use a large-format page...
I haven't completely solved it yet, but I saw something interesting. To be expected, but nice nonetheless. For no particular reason, I started solving it from the top-right square. I was able to complete it without having to resort to the middle square and, when I completed it, I saw that there was an ambiguity: you could swap the values of two parallel pairs of cells. As each pair belonged to a single cage, it was a genuine ambiguity. But then, when I progressed towards the centre, as I had hoped and expected, the ambiguity was resolved, because the leftmost of the two pairs, fully contained within the overlap, was forced into one of the two alternatives.

I tried with an overlapping of 4x4 instead of 3x3, but it looked "squeezed", and with an overlapping of 2x2 it looked very spread out. I suppose, I am used to the Samurai Sudoku and find a "standard" overlapping more pleasing to the eye.

Before anybody asks, I am not going to develop a Samurai CalcuDoku with an overlapping of 5x5 or more. It wouldn't be clear at a glance where a puzzle would finish and when one would begin. In any case, to cater for the overlapping of three squares instead of two, I would have to redevelop the program and I don't think it would be worth the effort. Or not?

I just noticed that I haven't coloured the unused parts of the image like the forum's background. But perhaps it makes it easier to print. I was happy to see that the generation of cages and operations worked at once with the new set of overlapping squares. The only fiddly thing was the ASCII display that I use for debugging.

Posted on: Fri Dec 09, 2011 9:44 pm

Posts: 422
Joined: Fri May 13, 2011 2:43 am
Re: Double CalcuDoku
Fun. Not hard, but takes some time. It might help to see the borders more clearly where the overlaps occur. Perhaps the overlapped cells could be coloured? I discovered two unresolved ambiguities. It would be better to have a unique solution. Ambiguities are in the bottom-left 9x9. Cells c1-d1, c8-d8. Also cells h1-i1, h3-i3.

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