KenKen is a type of arithmetic and logic puzzle which was invented in 2004 by Japanese math teacher Tetsuya Miyamoto.

Like Sudoku, the goal in KenKen is to fill a square grid with numbers so that each number appears exactly once in each row and each column of the grid, an arrangement known as a Latin Square . But whereas Sudoku has 3×3 boxes superimposed on the main grid with the additional constraint that each box must contain each of the digits from 1 to 9, in KenKen the additional constraint comes in the form of arithmetic relations imposed on connected groups of grid cells (generally known as cages).

The clue for each cage consists of a target number and a basic arithmetic operator (one of +, -, x or ÷); meaning that the numbers in the cage can be combined (in some order) using that operator to yield the desired target. Numbers may be repeated in a cage, as long as they are not in the same row or column.

Another difference between Sudoku and KenKen is that a normal Sudoku starts with several of the grid cells already filled in, so the goal is to find numbers consistent with those starting numbers. In contrast, a KenKen grid starts out empty and you have to figure out all the numbers for yourself, although some KenKens contain cages consisting of a single cell; the “clue” for such cages is the target number (with no operator specified).

KenKen grids come in various sizes, usually ranging from 3×3 up to 9×9, and they may use all 4 of the basic arithmetic operators or a restricted subset of them. Cages generally consist of 2 or 3 cells, but much larger cage sizes occur, especially in the larger grids. The variations in grid size, operators used, and cage size and shape allow for a huge range of difficulty in KenKens, so it’s possible to generate simple puzzles that are suitable for young children, and it’s also possible to generate extremely difficult puzzles to challenge even highly talented adults.

I wanted to post an image of a typical 6×6 KenKen grid here from Wikipedia but unfortunately the forum software won’t display it.

The name KenKen is a trademark, as is KenDoku. The official KenKen site is http://www.kenken.com/ ; various periodicals publish KenKens using the official name, but other sites use names like Calcudoku, Mathdoku, and CanCan to avoid trademark infringement. One of my favourite alternative sites is http://krazydad.com/inkies/ which has many hundreds of puzzles in PDF format for easy printing.

KenKen puzzles are fun to solve and highly addictive. :) They can be a great way to practice mental arithmetic that kids can enjoy, but they also develop logic skills and encourage scientific thinking: solving KenKens frequently involves making hypotheses about cage or cell contents that you then need to prove or disprove.

This thread is for general KenKen-related chit-chat, especially the discussion of KenKen techniques and strategies.

I very much doubt that anyone here will be interested.

sibeen said:

I very much doubt that anyone here will be interested.

Jenna Likes Suduko from what I recall and may like the next challenge opportunity,

wish i could be but words are easier for me than numbers.

a little bit like matrices?

Boris said:

wish i could be but words are easier for me than numbers.

+1

I do like Sudoku although that’s a logic puzzle with nothing to do with math.

I did successfully do a few 3×3 KenKen though :)

Maths. Maths. We do Maths here. It’s a contraction of Mathematics. It has to have the s on the end.

It seems to be a geographic thing, which I’ve never thought about before:
http://www.dailywritingtips.com/math-or-maths/

Since we adhere to the UK stylings, “maths” is correct. Well there you go.

sibeen said:

I very much doubt that anyone here will be interested.

Apart from you, me, Alex, Dark Orange, and occasionally Divine Angel. :)

I tried to interest DV, but to no avail. But I’m hoping that mathematically-inclined people like TRD, mollwollfumble, KJW, Wocky & Diddly-Squat will check them out.

I never got into Sudoku, and initially dismissed KenKen. But a few months ago I was reading a free edition of The College Mathematics Journal (a publication of the Mathematical Association of America) which was dedicated to the great popularizer of recreational mathematics, Martin Gardner. It contained an article entitled Triangular Numbers, Gaussian Integers, and KenKen and I became intrigued.

Here’s a link to the whole CMJ issue: http://www.maa.org/pubs/cmj_jan12.html

Probably have a look when I’m less busy.

Talking of mathematically inclined people, have you had a look at:
http://www.mathlesstraveled.com/

Some interesting stuff there sometimes.

The Rev Dodgson said:

Probably have a look when I’m less busy.

Oh, good. I suspect that KenKen may be of interest to some of your Newton Excel Bach readers.

The Rev Dodgson said:

Talking of mathematically inclined people, have you had a look at:
http://www.mathlesstraveled.com/

Some interesting stuff there sometimes.

Ta. I don’t think I’ve seen that before.

KenKen is bad, m’kay?

Night before last I dreamt about it…

I got an app (or two) for my phone so I can do these while flying.

Interestingly enough, I can easily listen to an audiobook while doing sudoku but can’t listen to an audiobook while doing Kenken.

Carmen_Sandiego said:

Interestingly enough, I can easily listen to an audiobook while doing sudoku but can’t listen to an audiobook while doing Kenken.

That doesn’t surprise me at all – I usually have a very active internal monologue while I’m doing KenKens.

Here’s some KenKen stuff I posted the other night in Chat.

It can sometimes be useful to determine the parity of a cell or cage (i.e. is it odd or even).

It’s often possible to determine the parity of a cage without knowing any of the numbers it contains. Obviously, it’s easy to do for any + cages, but it’s also easy to do for – cages, since the difference between two numbers has the same parity as their sum.

If the product of a x cage is odd, then all the numbers in it must be odd, so it will have odd parity iff it contains an odd number of boxes. Similarly, if the result of a ÷ box is odd, then the sum of the two numbers it contains must be even.

> This thread is for general KenKen-related chit-chat, especially the discussion of KenKen techniques and strategies.

For KenKen I use what is called the “dot method”. Let’s suppose it’s a 3*3 KenKen. Then in each box keep track of the nine positions top-left, top-middle, top-right, middle-left etc to represent the digits 1 to 9 in turn. Whenever a number is eliminated by, for example, being too large or small or used elsewhere or having the wrong factors I place a dot in the eliminated position. Sooner or later all spaces will be used up in a box leaving only one possibility, then write the number in. No need ever to rub out.

I make mistakes. If you make a mistake in placing a dot then a single diagonal line through cancels the dot and to reinstate it put the second diagonal through making a cross. Very easy and saves on erasers.

Or just use trial and error.

I do them on an spreadsheet.

I’ve only done the one that appears in The Age. I can’t say it’s particularly challenging though, even when it’s rated ‘challenging’. But it serves as a brain reset before looking back to the other puzzles. The ‘easy’ 4×4 one, I can’t write it out as fast I can solve it.

One of the Enigma code breaker chaps used to do the Times cryptic crossword on the short train trip to work, he was a clever chap, well most of those boffin type chaps were clever chaps.

I know 2 Kens.

Ian said:

I know 2 Kens.

I ken 1 Ken laddie!

I’m working on a forum-friendly KenKen grid editor.
Here’s a sneak preview of the kind of output it (currently) generates.
This one comes from INKY_6H_b001_4pp.pdf, puzzle #4.

<style type="text/css"> table { position: relative; left: 0px; top: 0px; border: 2px solid ; border-collapse: collapse; } td { border: 2px dotted gray; padding: 0px 4px 2px 2px; width: 2.8em; height: 2.8em; vertical-align: bottom; text-align: center; font-weight:bold; } td.R { border-right: 2px solid ; } td.B { border-bottom: 2px solid ; } .target td { font-size: 0.7em; width: 4em; height: 4em; vertical-align: top; text-align: left; }
</style>

I working through the 6 × 6 hard one’s on inky. Down to below 15 minutes to complete one – unless I stuff up, which is still quite regular :)

sibeen said:

I working through the 6 × 6 hard one’s on inky. Down to below 15 minutes to complete one – unless I stuff up, which is still quite regular :)

That’s a pretty good speed, I reckon. I’m currently in the middle of book 60 of that set. I haven’t timed myself lately, but I think I average around 10 minutes, although some can take me 20 minutes or more. OTOH, some of the puzzles in the hard collection are actually quite easy and I can breeze through them in about 5 minutes.