Talk:Kakuro

Crosswords, Cross Sums, Kakuro and other names
Why is this the mathematical equivalent of a crossword? Logically if anything is, then it's a crossnumber (or "Number Word" as the Daily Mail used to call it inappropriately).

But this certainly can be considered one kind of mathematical 'crossword', along with the plain old crossnumber and others. -- Smjg 13:04, 16 September 2005 (UTC)


 * I agree with you on this one - in fact, apart from the grid, I see little correlation between Cross Sums and crosswords at all. Perhaps Figure Logic is closer, and maybe those Crossmath puzzles Dell Magazines publishes are more along the lines of a crossword, but ultimately I see completely different skillsets needed to solve all of them as opposed to crosswords.  - ZM Zotmeister 18:57, 16 September 2005 (UTC)

I don't think the link to http://www.kakuropuzzle.com/ belongs in this topic. The puzzles generated by the program don't even have unique solutions, and hence are not true Kakro. GLmathgrant 04:49, 2 November 2005 (UTC)


 * Confirmed and agreed. I'll be bold.  - ZM
 * Zotmeister 15:55, 2 November 2005 (UTC)

Where is it said the Japanese name is Kakro? Technically that's not even writable in the Japanese character set, the closest approximation being カクロ (kakuro), and one puzzle magazine actually using the katakana カックロ (kakkuro). The second gets around 100 times the initial Google hits of the former, including nikoli.co.jp which seems to host a lot of those sort of puzzles.

In fact, a quick check finds the Japanese page listed as カックロ (kakkuro) and no listings for kakuro. Still, it would be nice to have some kind of explanation as to what it actually means. Confusing Manifestation 16:21, 24 January 2006 (UTC)


 * Okay, I just did some patrolling, and what I now see is evidence of "peer pressure". You mention Nikoli.  They are the company that created the name カックロ, and they until just recently consistently transliterated their own title to romaji as Kakro  (the 'u' is silent anyway).  If you visit Nikoli's English pages, what you'll now see is inconsistent; their graphics, tutorials, and Puzzle Japan offerings all still say "Kakro", but their textual content and book sales form now read "Kakuro".  Best guess: the misspelling has become sufficiently widespread that they decided to use the incorrect one on their English pages to make sure people find their site when searching for the wrong term!
 * Until such a time that Nikoli changes all their "Kakro" references to "Kakuro", I believe the presentation of "Kakro" in the article is still correct.
 * At any rate, the "クロ" part is short for 'クロス', the English word 'cross'. (There's no 'u' in that either.)  - ZM
 * Zotmeister 21:36, 24 January 2006 (UTC)

Kakuro Combinations
Hi,

I created this page of Combinations for Kakuro: http://www.kevinpluck.net/kakuro/KakuroCombinations.html

I would like to submit it on this page if you all agree.

Thanks.


 * That - if accurate (I haven't completely proofread it) - is decidedly handier than the guide currently (and indirectly) linked to in the References. I for one think it would be a good idea to place a link to that chart directly in the Possible Sums section of the article.  - ZM
 * Zotmeister 18:15, 17 February 2006 (UTC)


 * Thanks Zotmeister, many people have found the table very useful some have gone as far as to describe it beautiful!
 * There is a beautifully colored Spickzettel for sums to 44 and eight cells with Kevin Pluck. That is alone optically a beauty. (Translated from above)
 * Yaaaay 21:00, 21 February 2006 (UTC)


 * If there is no further comments I shall add a short note to the Possible Sums section tomorrow with a link to the above.--Yaaaay 09:11, 1 March 2006 (UTC)


 * I think the author of the table went to great lengths to create as many references to unrelated commercial websites in the text as he could. What do bingo, casino games, online roulette games and webpage print software really have to do with a kakuro explanation? —Preceding unsigned comment added by 82.139.82.166 (talk) 09:20, 10 August 2010 (UTC)

Too many links
Does anyone else feel that far too many "Play kakuro here" links are being added? The point of external links is more to provide additional reference to the the article, not advertise a bunch of sites related to the topic that could just as easily be found with a Google search. Confusing Manifestation 01:10, 4 May 2006 (UTC)


 * Right, I am proposing removing all of the links save for: kakuro.com and kakuro.fluctuat.net. Why these two? Because they have semi-decent Alexa rankings and focus on the game. I will also add a link to Nikoli, which is currently absent. The rest of the links are just advertising and don't enhance the article in any way. Any complaints? Confusing Manifestation 11:43, 24 May 2006 (UTC)

Arrow Numbers
In Variants you write Arrow Numbers as a variant. But I search in internet and I couldn’t find any Arrow Numbers with characteristics as you describe. Where I find this Arrow Numbers? Miguel Monsanto 13:57, 25 Jul 2006

I'd like to second this. When I first found "Cross Sums" puzzles (mid 1980s in the UK), they had this additional non-repeating constraint. Where does the name "Arrow Numbers" come from? [David Brain]

Since I found one publisher that still has the constraint but does not use a separate name for it, I inserted a mention in the main descriptive section and removed the undocumented Arrow Number 'variant' name. Lhmathies (talk) 15:21, 27 January 2009 (UTC)

Change article title to Kakuro
The name Kakuro seems to be used more commonly now than the name Cross Sums (or the two are combined into Kakuro Cross Sums), so this article title should probably be changed to either Kakuro or Kakuro Cross Sums. If you search for Kakuro and "Cross Sums" on Google, there are more results for Kakuro, and most of the results for "Cross Sums" are from websites with Kakuro in the title, or the sites mention Kakuro.


 * Reluctantly, I have to agree. The name Kakuro has penetrated the market rather completely at this point.  --Suttkus 16:16, 9 November 2006 (UTC)


 * I support this motion. I've only ever seen it listed as "Kakuro", and most of the other language Wikipedias list it under that name too. FreakyFlyBry 05:26, 2 January 2007 (UTC)


 * I agree, too. I'm going to go ahead and make the change -- if anyone has any problem with it, feel free to revert. Roman à clef 22:36, 5 January 2007 (UTC)
 * Done. Insert complaining here. :) --Roman à clef 23:01, 5 January 2007 (UTC)

NP complete?
The only reference that Google knows to the claimed proof of NP-completeness of Kakuro is in this article. It references a pdf file that is no longer found. Is this a hoax?


 * The NP-completeness of Kakuro is proved in this article . --Pitan 23:03, 28 November 2006 (UTC)

Detailed Kakuro Tables
I added some tables to the kakuro sums [] but they were rejected quite fast. It's an extension of the tables in Killer Soduko.

In all honesty the Kakuro sections in the present Kakuro-page are of very little value for a Kakuro player.

Anyone that does Kakuros will know that using the full tables are the most common tool for solving Kakuros. You're practically lost without them. (With practice you won't need them after a while though.)

If the full tables take up so much space, then maybe they can somehow be reduced here. They are nonetheless a key trait of playing kakuro. You will find them in most Kakuro books on the first pages...

I would like to hear what others have to say to this....?

129.206.101.136 16:36, 28 March 2007 (UTC)


 * Please put them back if you think they're appropriate. I felt that they were unnecessary but that's just one opinion. --Tony Sidaway 22:23, 28 March 2007 (UTC)

I agree that a lot of people use the full tables -- I resort to them myself occasionally -- and they are particularly useful here where beginners may be looking for the article. I have a memory aide chart which I use (and can reconstruct quickly in pencil even if I don't have it to hand) that could cut down the section on minimums and maximums but I don't know if it would be helpful in the article since it's not as intuitive to other people as it is to me. (And I don't know how to insert it.) It's here if anyone is interested.) CD216.236.252.234 18:23, 5 April 2007 (UTC)


 * Individual aptitudes vary widely. Until I saw the tables in the article I'd no idea that such things had been tabulated, or that they were of use. To me it has always looked like a simple matter of mental arithmetic.  I've just added an external link to a table of combinations. --Tony Sidaway 18:45, 5 April 2007 (UTC)

I haven't seen any Kakuros (I started doing them as Cross Sums many years ago) on the net that push me to the full tables. I generally only use them when I'm trying to see if using one digit forces another, and that pretty rarely. But as a beginner I worked out the entire list, and looking at it helped me learn the patterns which make solving easier. The link to the complete set is probably sufficient for this purpose, as long as it stays reliable. CD192.80.65.234 19:55, 5 April 2007 (UTC)

Kakuro is not a linear programming problem
Right now the following text is present in the first paragraph:

In principle, Kakuro puzzles are integer programming problems, and can be solved using matrix techniques,...

I can't agree with this statement. Yes, making a sum of the block equal to the specified number is a restriction allowed in linear programming. But you have to enforce the inequality of every two numbers inside a horizontal or vertical block. Thus you need a restriction of a form $$a_{ij} \neq a_{kl}$$. This type of restriction is not allowed is linear programming problems.

I will now delete the sentence mentioning linear programming, and please let me know if I'm wrong in my argumentation. Actually, there is a fundamental reason why Kakuro is not a linear programming problem: Linear programming restrictions always specify a convex polytop of vectors, whereas a set of answers to a specific Kakuro puzzle might not be convex:

1 2 4 5 - is a valid block

1 3 3 5 - is an invalid block

1 4 2 5 - is a valid block,

the convexity fails.

Thus, there is no simple reduction from Kakuro to linear programming.


 * To whom it may concern, I've added back a reference to integer programming. Integer programming is a subcase of linear programming, where the solutions are limited to integer values.  Mathematically, the concern about whether a programming "system" can be called by that name has to do with whether or not the problem can be posed in such a way as to match the general form.  Kakuro can be formulated as a linear programming problem with special constraints.  It is more easily formulated as an integer programming problem, since that naturally requires integer solutions (as a special constraint) on the linear programming problem.  Having said that, Kakuro is not identical to a generic integer programming problem.  It is a special case, with special constraints, such as being limited to integers 1 to 9, no row/column repeats, etc.  Those special constraints can be formulated fairly easily as boolean-valued integer (0 or 1) constraints.  In other words, there's nothing fundamentally disqualifying about the special constraints required of Kakuro beyond integer programming in general that would mean that it's not an integer programming problem.  — Preceding unsigned comment added by 70.247.163.191 (talk) 16:07, 17 June 2016 (UTC)

Link for review: kakurohelper.com website (javascript tool)
Hi. I wrote a kakuro helper javascript application at http://www.kakurohelper.com. It can be a great help when solving the puzzles, but is easier to read than the complicated tables. It's not software that needs to be purchased or downloaded or anything, it's just a webpage that calculates the sums in javascript. If there are no objections, I'd like to add it to the External Links section. There doesn't appear to be anything like this linked right now, just places to play or tables or strategies. This is something different.

http://www.kakurohelper.com

Thanks!
 * How is a webpage that calculates the sums in javascript not software that needs to be [] downloaded ? Is this some new sort of Zen koan like the sound of one hand clapping?
 * Sniping aside ... the reason I came here was because I wondered if anyone had ever seen a Kakuro-like which uses the hexadecimal digits rather than the decimal digits? Such variants are (relatively) common for Sudoku, and it appears an obvious step for Kakuro, so I'd be a little surprised if it had never been done. OK, these are done for fun and a "hexa-doku" takes about 4 times more time than 4 similar Sudokus, so I'd expect similar scaling for "hexa-kuro".

Aidan Karley (talk) 10:57, 27 October 2008 (UTC)

First cite
Not to diminish the awesomeness of Cross Sums, but the cite http://www.conceptispuzzles.com/articles/kakuro/index.htm claiming "Kakuro" is second only to Sudoku is actually quoting this article, thus it is circular and should be removed. —Preceding unsigned comment added by Penguinwithin (talk • contribs) 04:01, 8 April 2008 (UTC)

Proposed tutorial
I proposed the following tutorial for the links section (I am the creator of it): Learn by example: Step-by-step kakuro tutorial. The tutorial was removed as spam, however I think it could be a beneficial guide for people who want to see how to solve a puzzle step-by-step. I'm sorry it was perceived as spam - that is not the intent. I only want it posted if people find it beneficial. Anyone have any feedback on it? —Preceding unsigned comment added by 24.245.27.77 (talk) 21:19, 19 April 2009 (UTC)
 * It's still a link to an ad-driven website that you yourself created, so it's still spam. DreamGuy (talk) 23:11, 19 April 2009 (UTC)
 * The kakuro combinations link was submitted by the individual who created it and there are ads on that page. By that definition it would be "spam". However, others agreed that it was a helpful tutorial... Is that the threshold? Just trying to better understand. Thanks. Also, if I removed ads from the tutorial pages would that "help" at all? Thanks, again. —Preceding unsigned comment added by 24.245.27.77 (talk) 13:58, 26 April 2009 (UTC)

Dead link for Android Kakuro application mentionned
Android Kakuro application mentionned at the end of the article is a dead link : https://play.google.com/store/apps/details?id=by.squareroot.kakuro. It would be great to update link with an existing application. You can find a lot of Kakuro Android applications from Google Play Store : https://play.google.com/store/search?q=Kakuro. Ssaurel (talk) 08:13, 1 April 2015 (UTC) ssaurel

Odd/even
The first Kakuro's I met had light shading of some cells, to contain odd digits, while white cells should contain even digits. I do not know if this is a common variant, deserving a mention in the Variants section.--Nø (talk) 15:34, 30 September 2017 (UTC)