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 KenKen vs. CalcuDoku 
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Posted on: Sun Nov 27, 2011 4:45 am




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Post KenKen vs. CalcuDoku
Yesterday, I posted this message to my blog http://giuliozambon.blogspot.com, but I thought that probably some of you would find it interesting. THis is the first time that I try to show an image I stored on ImageShack. Previously, I stored them on one of my websites. The preview looks lousy, but I'll give it a try. Here it goes... OK. It din't work well. Second attempt using my website...

I found three websites that let you play daily KenKen (® Nextoy LLC) /CalcuDoku puzzles: http://www.kenken.com/, http://www.calcudoku.org/, and my website http://zambon.com.au/puzzles/calcudoku/daily/.

While the other two websites include puzzles of different sizes, and calcudoku.org also includes variants, my website only includes 9x9 puzzles. KenKen and CalcuDoku are the same puzzle, but their implementation is done by different people. Each implementation has a different feel and, on average, different levels of difficulty.

I know how my puzzles are developed, but, obviously, I have no idea what algorithms the other developers use. I thought it would be interesting to identify some of the differences from a statistical point of view.

For this purpose, I analysed 10 puzzles taken from each website. I know that 10 is too small a sample to make good statistics, but it was a lot of counting...

Anyhow, what follows is a summary of what I came up with. To avoid repeating the domain names, I will use K to identify kenken.com, Z for zambon.com.au, and C for calcudoku.org. ‘A’ indicates values obtained by averaging all. The triplets of numbers indicate minimum, average, and maximum values.

Number of cages: K=[31, 33.2, 38]; Z=[32, 34.3, 37]; C=[33, 34.2, 35]; A=[32.0, 33.9, 36.7].

The average number of cages is for everyone around 34. But it is interesting to note that K's spread is 7, Z's is 5, and C's only 2. This might indicate that, while K and Z do not set any limits to the number of cages, C determines the cages not completely as a result of random choices. This might be consistent with the fact that C sometimes presents puzzles that have the cages arranged in particular patterns (although none of the puzzles I randomly picked belonged to that group). It would be interesting to know what Patrick (C's developer) would have to say about this.

With larger samples, I expect that Z's (i.e., my) number of cages would turn out to be normally (i.e., randomly) distributed. Actually, as I generate the puzzles, I don't need to do the counting, because the computer automatically lists for the number of cages. I can check it out right now.

...

It turns out that the number of cages calculated for 100 Z's puzzles is [32, 34.83, 38].

The following image shows how the normal distribution (the magenta squares) fits to the measured values (the blue diamonds; these are the default of Excel and I didn't bother to change them). The vertical bars represent a standard deviation from the normally distributed values. In other words, if the distribution reflects reality, there is a 68.2% probability for each measurement to fall within the bars. At the very least, the plot confirms that the number of cages in my puzzles is not in disagreement with a normal distribution. I confess I would have been shocked if it had not been so, because the distribution is the result of several [pseudo]random choices...

Image

The following table summarises the counts of operation codes and cage sizes.
Image

C has about 6 times the number of 1-cell cages that K and Z have, and half the number of 2-cell cages. I will go out on a limb and say I believe that such differences are not due to statistical fluctuations within the samples. C also seems to have fewer divisions (1.3 vs. 3.5 and 5.5) and more cages with more than 3 cells (6.4 vs. 3.1 and 3.9). It seems reasonable to assume that the lower number of divisions (and perhaps subtractions) is due to the lower numbers of 2-cell cages.

In general, I have the impression that C's puzzles are more difficult than those of K and Z, and it seems reasonably safe to assume that the higher number of large cages is a contributing factor.

To deduce more from such a small sample would be inappropriate.


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Posted on: Mon Nov 28, 2011 4:18 pm




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Post Re: KenKen vs. CalcuDoku
Nice, interesting post :-)
giulio wrote:
indicate that, while K and Z do not set any limits to the number of cages, C determines the cages not completely as a result of random choices. This might be consistent with the fact that C sometimes presents puzzles that have the cages arranged in particular patterns (although none of the puzzles I randomly picked belonged to that group). It would be interesting to know what Patrick (C's developer) would have to say about this.

My generator program can run in one of three modes:
1. cages of a random size but with a set maximum (e.g. max cage size 4)
2. a specific distribution (e.g., for a 5x5, create 1 cage of size 1, 3 cages of size 2, and 6 cages of size 3)(not always satisfied)
3. a specific layout (so all cages exactly specified, like the "patterned" puzzles on the site)
giulio wrote:
C has about 6 times the number of 1-cell cages that K and Z have, and half the number of 2-cell cages. I will go out on a limb and say I believe that such differences are not due to statistical fluctuations within the samples

True, the target for the 9x9 is 8 cages of size 1.
giulio wrote:
In general, I have the impression that C's puzzles are more difficult than those of K and Z, and it seems reasonably safe to assume that the higher number of large cages is a contributing factor.

If you send me the dates of the 9x9's you used from my site, and specifications for the 9x9's from yours,
I can compare the difficulty level using my solver.
(format spec is in this thread)

Patrick


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Posted on: Tue Nov 29, 2011 3:04 pm




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Post Re: KenKen vs. CalcuDoku
giulio wrote:
...I found three websites that let you play daily KenKen (® Nextoy LLC) /CalcuDoku puzzles: http://www.kenken.com/, http://www.calcudoku.org/, and my website http://zambon.com.au/puzzles/calcudoku/daily/.


The statistic is very interesting and it underlines the special characteristics of the calcudoku.org website (apart of the special functions, etc.). Though http://www.321monkey.nl/calcudoku follows a similar design to calcudoku.org (perhaps you have not included it for this reason, the case of the New York Times is irrelevant for this statistic since they do not provide a 9x9) I think that perhaps it would have been interesting to have included the 321money also in the results so comparing both C puzzles.

giulio wrote:

... In general, I have the impression that C's puzzles are more difficult than those of K and Z, and it seems reasonably safe to assume that the higher number of large cages is a contributing factor.

To deduce more from such a small sample would be inappropriate.


Probably the statistical inference obtained with a larger population of samples should not give very different results, I also have the same intuition, as you say, that the difficulty of the C's puzzles is due to the higher number of large cages; for instance, in today's Nov 29, 2011, we have 8 4-cell cages and 4 3-cell "-" cages so no matter if in the other hand we have 13 "individual" 1-cell cages, the puzzle is reasonably difficult even considering that the content of 4 of those 4-cell cages, the cages located in row 5 and column e, plus the content of cages f3-f4-g4, a8-a9-b9 and b7-b8-c7-c8 is quickly defined.


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Posted on: Tue Nov 29, 2011 4:32 pm




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Post Re: KenKen vs. CalcuDoku
clm wrote:
Though http://www.321monkey.nl/calcudoku follows a similar design to calcudoku.org

Note that you can go directly to the English version via www.321monkey.com.

I can confirm that the 9x9 puzzles on 321monkey use exactly the same generation code and difficulty range
as the ones on calcudoku.org :-)

Patrick


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Posted on: Wed Nov 30, 2011 2:28 am




Posts: 54
Joined: Thu Nov 03, 2011 6:52 am
Post Re: KenKen vs. CalcuDoku
Last night, I had prepared a reply to Patrick's reply to my original post but I lost the Internet connection and with it the message. And I hate to have to retype what I have already written once...

Anyhow, I only generate 9x9 puzzles. The program defines solution grid, shape and size of the cages, and operations at random with the following constraints (the numbers between parentheses are the settings for the daily calcudoku you find at http://zambon.com.au/puzzles/calcudoku/daily/):
    Maximum number of 1-cell cages (3)
    Ratio of number of 2-cell cages vs. 3-cell cages (5/2)
    Maximum number of 5-cell cages (3)
    Maximum number of 4-cell cages (4)
    Ratio of multiplications vs. sums vs. subtractions in 2-cell cages (15/27/55)
    Maximum number of cages that on their own admit in excess of 200 combinations of digits (2)
    No cage with more than 5 cells.

I don't plan for any 1-cell cage at all, but when the program defines the cages, it can be that it has to cut a cage short because it cannot proceed with its intended size. That's how the 1-cell cages can come about. If, at the end of the cage generation phase, there are too many 1-cell cages or too many cages that admit more than 200 combinations, the program starts afresh but keeping the same pseudo-random seed.

I introduced the 200-combination limit because I didn't want to end up with puzzles that are too difficult to solve, and introduced the constraints that seemed reasonable (at least at the time). I defined the constraints by trial and error, until I got the program to generate puzzles I was pleased with. As a starting point, I inferred my parameters from the KenKen puzzles available online.

In the not-so-distant future, I would like to develop puzzles with a given pattern of cage shapes, because I find the symmetry of some of Patrick's puzzles very pleasing. I also like very much the 5-cell cage that looks like a W (the only 5-cell cage that spans 3 rows and 3 columns). Also Patrick's use of additional operations can make for interesting puzzles.

But, before that, I want to complete an extension of CalcuDoku that I have never seen anywhere. When I have it ready, you'll be the first one to know (well, perhaps I will post it first on my blog http://giuliozambon.blogspot.com/ [smile] ).


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Posted on: Sat May 12, 2012 9:25 pm




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Post Re: KenKen vs. CalcuDoku
hi giulio

I visited your website and was intrigued by your puzzles. I would like to try solving them, but I prefer solving large puzzles offline. I can figure out no way either to print out your daily puzzles or to copy them into my own computer, so it's not possible for me to solve them. Do you have any suggestions?


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Posted on: Sat May 12, 2012 9:42 pm




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Post Re: KenKen vs. CalcuDoku
pnm wrote:
I can confirm that the 9x9 puzzles on 321monkey use exactly the same generation code and difficulty range
as the ones on calcudoku.org :-)

I read this post again now by coincidence (visited the thread because of cecileb's recent post),
and: this is no longer true. The 9x9 puzzles on 321monkey are easier than the ones on
calcudoku.org (and have been so for a while now)

Patrick


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Posted on: Sat May 12, 2012 10:21 pm




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Joined: Fri May 13, 2011 12:11 am
Post Re: KenKen vs. CalcuDoku
cecileb wrote:
hi giulio

I visited your website and was intrigued by your puzzles. I would like to try solving them, but I prefer solving large puzzles offline. I can figure out no way either to print out your daily puzzles or to copy them into my own computer, so it's not possible for me to solve them. Do you have any suggestions?

What I would do:

Your keyboard hopefully has some sort of Print Screen option. Probably abbreviated PrntScr.

Hit that with the puzzle on the screen.

Then, use the paste function to paste that image into Paint or any other image related program, and print that. You'll have some additional things around it, but you'll at least get the part you need to print.


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Posted on: Sat May 12, 2012 11:37 pm




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Post Re: KenKen vs. CalcuDoku
pnm wrote:
clm wrote:
Though http://www.321monkey.nl/calcudoku follows a similar design to calcudoku.org

Note that you can go directly to the English version via www.321monkey.com.

I can confirm that the 9x9 puzzles on 321monkey use exactly the same generation code and difficulty range
as the ones on calcudoku.org :-)

Patrick

What's wrong with this forum? I just received a message that something had been posted, and then discovered that the date of this message from Patrick is completely off: 2011-05-12 squeezed between a 2011-11-29 and a 2011-11-03...


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Posted on: Sun May 13, 2012 12:05 am




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Joined: Tue Apr 24, 2012 5:47 pm
Post Re: KenKen vs. CalcuDoku
As for solving puzzles offline on your computer, I'd also suggest using the print screen button on your keyboard. But, starling already beat me to it! [lol] In fact, I do it all the time.


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