## Kenken

For fans of Killer Sudoku, Samurai Sudoku and other variants

### Kenken

It looks as if the next thing to learn is Kenken, now pushed by The Times in London who were amongst the first if not the first in the UK with Sudoku and Killer Sudoku.

Here is the launch article in yesterday's paper. The examples in the paper (if not the interactive version) became quite complicated quite quickly and then much harder when the ( +.-, x, /) clues were omitted (see puzzles nos16-18)

I suppose that I will have to try it out but what with already having to do the crossword, the killer and the sudoku before starting work ...
Bigtone53

Posts: 413
Joined: 19 September 2005

Bigtone

They are interesting to do (and create), try some based on ZD's Algebraic Killer idea from last year:

http://www.djape.net/sudoku/forum/viewtopic.php?t=1014

It also posts you to Udosuk's combination tables.

Note also Sudokoguy's algebraic sudoku:

http://sudokuguyblog.blogspot.com/search/label/algebraic%20sudoku

HATMAN
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

Thanks HATMAN

This is todays EASY. To my mind, it is anything but. I am going to have to reset my mind on these things!
Bigtone53

Posts: 413
Joined: 19 September 2005

### re: KenKen

in the Mar.25 KenKen ( size = 6 ),
obviously we recognize
• 6+ in 3 cells = {1,2,3}
• 18+ in 4 cells = {6,5,4,3}
-- would be nice to similarly recognize some cases for multiplication etc

e.g.
• 24x in 4 cells = {1,2,3,4}
• 120x in 3 cells = {6,5,4}
• 5- in 2 cells = {6,1}

a reader commented that the subtraction can go in either direction
-- this is true !!
( likewise for division )
e.g.
r4c2 = 1 ! ( not 6 due to the 120x )

Pat

Posts: 3964
Joined: 18 July 2005

Has anyone tried today's Times KenKen?

[url]http://entertainment.timesonline.co.uk/tol/arts_and_entertainment/games_and_puzzles/article3626793.ece?Submitted=true [/url]

Either I am mistaken or there must be a problem
The 600X in the middle must be 6554.
The 60X in row 4 must be 61 (in whatever order)
which means the 600X in row 4 must be 54
Leaving only 2 and 3 in row 4 for a 3- ???

Anyone spot a problem?

sorry for the nasty url, the url code does not seem to work...
Agrajag

Posts: 3
Joined: 28 March 2008

Duh

I had completely fixated that 6x MUST be 6x1. Completely ignored the 2x3 possibility.

I think I was kind of thinking of 6/ (division)

I will now go hang my head in shame
Agrajag

Posts: 3
Joined: 28 March 2008

People based in London UK will be aware of the upcoming Mayoral election, which is basically a straight fight between the incumbernt Ken and the main challenger Boris. Both are well-known by their first names alone.

A letter in The Times today suggests that in the interests of politcal balance, perhaps the paper should introduce a puzzle called BorisBoris.

Bigtone53

Posts: 413
Joined: 19 September 2005

Luckily I live just outside London (the other end of my road is inside), but if I was voting I'd go for a change of idiot. Given what Ken's done just imagine what Boris might manage!
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

Having muddled along with some pretty basic KenKens over the last week or so, The Times produced a right snorter yesterday. You can try it here
Bigtone53

Posts: 413
Joined: 19 September 2005

What's annoying me is the number of times I forget that cages can have repeats. Which given I've created over 50 of ZD's Repeat Killers is particularly galling.
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

HATMAN,

Understood. These days Killers are my favourites. I have the same problem as you do with Kakuro (right name?) where numbers can be repeated in the same line/column. No problem with the concept but hard to switch into!
Bigtone53

Posts: 413
Joined: 19 September 2005

Bigtone53

In that case you will enjoy a Kakuro variant I posted on DJApe's forum:

http://www.djape.net/sudoku/forum/viewtopic.php?t=1244
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

Bigtone53 wrote:Having muddled along with some pretty basic KenKens over the last week or so, The Times produced a right snorter yesterday. You can try it here

I did it, that one ain't that tough, just needed an X-wing plus a few cage conflictions.

Here is a walkthrough:

Triple click to read what I wrote:6+ cage = [1212|2121]
=> r5c45=r6c56=r56c5={12} (NP @ r5,r6,c5)
400x cage = [4455|5544]
=> r2c56=r23c5=r12c6={45} (NP @ r2,c5,c6)
9+ cage cannot have 6 (can't be {6111})
144x, 432x cannot have 5 (indivisibility)
300x cage = {5526|5534}
=> 5 @ c12 locked @ r56c1+r45c2, r4c2 must be from {2345}
=> r5c1 must be from {3456}, r5c2+r6c1 must be from {345}
=> 6 @ r6 locked @ r6c234 => min r6c2*r6c3*r6c4=3*4*6=72
=> 360x cage: max r4c3*r5c3=5 => r45c3=[13|14|15]
=> HS @ r4: r4c2=5 => r5c12+r6c1={345} => HS @ r5: r5c6=6
Now r345c6={136|236}, product=1*3*6|2*3*6=18|36
=> 432x cage: r4c4*r4c5=12|24 => r4c45=[26|43|46]
=> r4c4 must be from {24} => r123c4 can't be {245}
=> r1c4*r2c4*r3c4 can't be 40
=> 720x cage: r1c35 can't be 18 => r1c3 can't have {36}
X-wing: 6 @ r36 locked @ r36c23
Now 6 @ c1 locked @ r24c1, 6 @ r3 locked @ r3c23
=> 144x cage = {66122|66114}
But 9+ cage must include at least a 1 (2+3+2+3>9)
=> r2c1+r3c12 can't include two 1s
=> 144x cage can't be {66114}, must be {66122}
=> r234c1=r3c123={126} (NT @ c1,r3)
=> r3c6=3 => r4c1456=[6432] => r1c5=6, r3c4=5
=> HS @ r2: r2c4=6 => r1c5*r2c4*r3c4=6*6*5=180
=> 720x cage: r1c3*r1c4=4 => r1c34=[41] => r1c12=[32]
=> 9+ cage: r2c2+r2c3=9-3-2=4 => r2c23=[13]

The rest are naked singles.

324165
213654
162543
651432
435216
546321

Pyrrhon has one of these in his site which is of similar difficulty:

http://www.sachsentext.de/en/algebra_square1.htm

udosuk

Posts: 2698
Joined: 17 July 2005

Matt

It is not so much about the difficulty of this one as the step change in difficulty from the others. I've done all the rest on paper with practically no pencil marks and I've now failed on this one four times.

Admittedly today was after work and down the pub immediate Guinness, today's KenKen was OK, then do some of this bad one, another Guinness - get a bit stuck, do DJAPES EASY, go home and start the food with a very large gin and tonic, go a bit further - and then the numbers start to get a bit (mentally) wobbly. However the red wine afterwards seems to has improved my typing skills.
HATMAN

Posts: 276
Joined: 25 February 2006
Location: Saudi Arabia

Pyrrhon has one of these in his site which is of similar difficulty:

http://www.sachsentext.de/en/algebra_square1.htm

Udosuk, Thanks for this. Perhaps I am gradually getting better but this did not seem as hard to me as the one I pointed out. As HATMAN says though, it was the sudden jump, rather than the absolute difficulty, which was the shock.
It is a miracle that I get any real work done these days with all these problems in The Times that I have to do each day before I start work
Bigtone53

Posts: 413
Joined: 19 September 2005

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