[tt] NYT: KenKen: New Puzzle Challenges Math Skills
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KenKen: New Puzzle Challenges Math Skills
The New York Times, 9.2.9
[related material added.]
February 9, 2009
By WILL SHORTZ
KenKen, which starts in The New York Times today next to the
crossword puzzle, is a new numerical logic puzzle from Japan. The
name means loosely "cleverness squared."
KenKen shares some properties with sudoku. Each is a pure logic
challenge in which numbers are filled in the squares of a grid.
Unlike sudoku, though, in which the numbers act solely as symbols
(letters or pictures would work as well), KenKen requires
The rules are simple: Fill the grid with digits so as not to repeat
a digit within any row or column, and so the digits within each
heavily outlined box (called a cage) go together using the
arithmetic operation shown to make the target number indicated.
Two new KenKen puzzles will be presented in The Times each day from
Monday through Saturday. The first is a four-by-four-square puzzle
that increases in difficulty from easy to medium as the week
progresses. The second is a six-by-six-square puzzle that goes from
medium to hard.
KenKen was invented in 2004 by the Japanese educator Tetsuya
Miyamoto, who founded and teaches at the Miyamoto Math Classroom in
Tokyo. Students attend his class on weekends to improve their math
and thinking skills. Mr. Miyamoto said he believes in "the art of
teaching without teaching."
He provides the tools for students to learn at their own pace using
their own trial-and-error methods. If these tools are engaging
enough, he said, students are more motivated and learn better than
they would through formal instruction.
About 90 minutes of class time each week is set aside for solving
puzzles, usually designed by Mr. Miyamoto. The most popular one has
Given Mr. Miyamoto's philosophy of not instructing, one hesitates to
offer advice for solving KenKen, but here are some starting tips:
¶Fill in any single-square cages immediately.
¶Look for cages whose target numbers are unusually high or low for
their number of squares. Often these have unique answers. For
example, in a six-by-six puzzle, two squares with a sum of 11 must
be filled with 5 and 6, in some order. Three squares with a product
of 10 must be 1, 2 and 5.
¶Remember that cages can repeat numbers, as long as the numbers do
not appear in the same row or column. For example, a three-square
L-shaped piece with a sum of 6 could be filled with 1, 2 and 3 or 1,
1 and 4 (with the 4 in the middle square of the L).
¶Note that the order of the numbers in cages with subtraction and
division doesn't matter.
¶Don't forget that each row and column must contain every digit.
When you have exhausted arithmetic, use sudoku logic.
And now you're on your own.
Of What They Are Each a Piece - Wordplay Blog
December 7, 2008, 6:00 pm
Of What They Are Each a Piece
By Jim Horne
Monday, Dec. 8, 2008, crossword by Sarah Keller
*Across Lite, Solution
*Monday puzzle in other papers
Mata Hari Mata Hari, circa 1905. (Hulton Archives/Getty Images)
Sarah Keller constructs early-week puzzles. That means she can't be
too nefarious but she can still have fun. "Nose-in-the-air type" is
the clue to two crossing answers. I still find it a little jarring
when that déjà vu moment momentarily makes me think I must have made
There are four long clues today and our job as solvers is to
determine of what the starts are each a piece. You'll note that I
think it's amusing to find the most awkward possible way to avoid
ending a sentence with a preposition. We'll see if my editor leaves
it. The theme is standard Monday fare but there are a few fun fill
words that help out.
"Radius neighbor" won't fool seasoned solvers but it's an early-week
example of leading us to a wrong assumption. The radius here is the
bone near the ULNA. James AGEE appears yet again. Standard clues
refer to his screen play The African Queen or his posthumously
published Pulitzer Prize winner A Death in the Family.
The bawdy word of the day is BAWD clued as "Madam" meaning a brothel
proprietress. I remember that word being clued once as a "house
I do many kinds of puzzles and since Will Shortz has recently been
enthusiastic about the KENKEN variety I thought I'd check them out.
You've probably heard people say they don't want to try Sudoku
because they're not good at math. There's no math involved, of
course. If you happen to be a numbers person, that might be
KENKEN puzzles combine what you know about Sudoku with simple
arithmetic. Unlike Sudoku, there are no numbers pre-entered in the
The 4 by 4 puzzles are simple enough to do using the Flash applet on
the Web page. So is the easy 6 by 6. The medium one might need to be
printed out. I find the hard 6 by 6 doable but very difficult. Your
mileage may vary.
1. December 7, 2008 7:39 pm
Our puzzle has a common example of RAS Syndrome. PIN Number
being (Personal Information Number) Number. Oh, RAS Syndrome is
(Redundant Acronym Syndrome) Syndrome.
2. December 7, 2008 7:57 pm
My déjà vu moment was filling in PSST at 32A and momentarily
thinking that it's still Sunday.
(PSST, it still is Sunday).
3. December 8, 2008 2:00 am
I was solving the puzzle and thinking that someone was sure to
mention that PIN NUMBER is redundant and that PSST is an echo of
Sunday's crossword. PhillySolver and mike didn't waste any time
taking care of business.
Fine puzzle for Monday. Kind of an unusual grid, and I'd guess
the seven-letter middle entry is the reason for that.
I must confess I've become an addict to KENKEN the past couple
of weeks. I find the first five levels range from quick to
not-too-hard-to-knock-off. The harder 6×6's, though, are quite a
good challenge. I am not a big sudoku solver-I do a few a
week-but they seem a little tedious now, filling in all the
candidates by hand. The KENKEN interface is great, and kudos to
whoever is responsible for it. (If I had one request, it would
be to add an "undo" button to reverse the last entry. I
sometimes mis-enter a number and it screws up the remaining
candidates.) Fun puzzle.
-- john farmer
4. December 8, 2008 6:45 am
Yep. Two days in a row! A person could get PSST-off. Or, to
paraphrase Winston Churchhill, perhaps this is something up with
which we should not put.
5. December 8, 2008 7:37 am
Took up Emmet Logan's challenge this morning and only filled in
the across clues. Was UNDONE by 43-a: "Not yet taken care of",
which I thought must be INLINE or ONLINE (on line is New Yawk
for in line, fyi). And I've never heard of Debbie Meyer (sorry
Deb), so that area was tricky. But overall it was fun and I'll
try it again tomorrow. Thanks Emmet!
Jim, does your editor allow you to end sentences with
6. December 8, 2008 8:07 am
Jeez Will-I'm still trying to learn Kakuro, now Kenken! Enjoyed
today's puzzle by Sarah Keller.
7. December 8, 2008 9:47 am
@PhillySolver - You might appreciate this puzzle:
8. December 8, 2008 9:53 am
this one brought to mind "it don't mean a thing if it ain't got
nice puzzle! lotsa good non-theme fill, too -- like the
symmetrically balanced (and sorta related "geographic")
EUROPE/OREIDA pair, ENAMEL, JUNTA and ARDENT. also enjoyed the
poetic proximity of ICIER RIME and INNER NINNY.
kudos to keller -- and shortz, of course!!
9. December 8, 2008 9:55 am
oh -- and XANADU!!
10. December 8, 2008 10:29 am
Pseudolus (from A Funny Thing Happened on the Way to the Forum?)
Thanks for the puzzle ...ABS System is an oldie. Funny how dated
the whole thing felt.
11. December 8, 2008 10:42 am
On KENKEN, you can click on any given square and press the "c"
button for clear. I try to do the KENKEN in my head and find
that I can do so with first five levels, but not the hard 6×6,
which is quite challenging.
-- Steve Manion
12. December 8, 2008 11:13 am
The answer to 11 Down: "A.T.M. access code" works out to "pin
number." PIN has gained wide acceptance as an acronym meaning
"Personal Identification Number." The answer, therefore, is a
-- David W. Gillette
13. December 8, 2008 12:08 pm
Sorry, Saturday's puzzle should have been rejected 3 times. It's
not about being hard, or out-of-the-box, it's about following
silly, illogical strings to find answers. Yikes.
14. December 8, 2008 12:26 pm
Nice puzzle, especially for a Monday.
Does the unqualified appearance of a redundancy such as PIN
NUMBER in the NYT crossword signal anything?
I've been told that the pronunciation of "nuclear" will revert
to "nuclear" from "nucular" starting January 20, 2009. Hoping
the same will be true for "War of Terrorism."
-- Ms. Piggy
15. December 8, 2008 12:55 pm
I'm sure there are people who enter PIN "numbers" in ATM
"machines" but I expect better from the NYT Times.
16. December 8, 2008 5:14 pm
You're right about the C-button for clearing a number in a
KENKEN square. When you enter a number, though, it removes that
number from the candidates for the same row and column. So when
you clear a number, you need to re-enter the candidates or
you're likely to make a mistake. An "undo" button, if I had my
wish, would be able to re-add the candidates that were deleted
when the number in the square was first entered.
It only is a problem when I miskey a number, and at first I was
doing that a lot. Getting better though.
-- john farmer
17. December 8, 2008 5:24 pm
Is the photograph which accompanies the Sarah Keller Wordplay
article actually Theda Bara, instead of Mata Hari as the tag
-- Lucile Redmore
18. December 8, 2008 5:41 pm
Regarding 69 Across -- "Upper house members: Abbr." For eight
years I worked for a member of the U. S. House of
Representatives. He and his colleagues firmly rejected any
notion of the Senate being the upper house. They viewed the
House and Senate as being two equal bodies. Bob Auman, Raleigh,
-- Bob Auman
19. December 8, 2008 6:48 pm
I think PIN number is an example of Syndrome Syndrome. And a
fine one at that.
20. December 8, 2008 7:49 pm
Lucile, I can see the resemblance but that alluring photo is of
the spy, not the actress.
-- Jim Horne
21. December 9, 2008 8:41 am
Dude! PINNUMBER is just so wrong: one enters a PIN at an ATM.
PINUMBER could be technically correct, though odd. Now had the
clue been, "`ATM Machine' access code," it might've been OK.
-- wayne kitsteiner
22. December 9, 2008 8:54 am
I believe there was en error in Monday's puzzle: Neptune's realm
is the Mediterranean, NOT the ocean, which is ruled by Oceanus.
-- Sebastian Dunn
23. December 9, 2008 10:46 am
Love the KENKEN puzzles.
The word `miskey' in J. Farmers comment looks pleasantly odd in
24. December 9, 2008 3:30 pm
i thought this one was mildly boring. i'm still on Sunday's,
though, which is proving to be fun and tough.
25. December 16, 2008 6:44 pm
I am totally addicted to these KenKen puzzles too!
Also, for anyone out there who might be interested, I found
another place to play online games at
26. December 18, 2008 7:15 pm
Looks like there is a Google Gadget to play KenKen puzzles
directly from your google.com/ig homepage or Google Desktop.
The KenKen/Kendoku gadget is available at:
Grid-Irony - Wordplay Blog
January 31, 2009, 6:00 pm
By Jim Horne
Mia Hamm Forward Mia Hamm of the Washington Freedom during the WUSA
game against the Carolina Courage at the SAS Soccer Park on April 5,
2003 in Cary, North Carolina. (Grant Halverson/Getty Images)
Sunday Puzzle »
By Victor Fleming and
Feb. 1, 2009
*Across Lite »
*XWord Info Solution »
*Syndicated crossword »
Premium Crosswords is available through subscription only.
After two recent Sundays recognizing a new guy in the White House,
today's puzzle celebrates an event that all Americans, whether they
hail from red Cardinal states or yellow and black Steeler states,
can get behind. It's time to set aside our differences, pick up our
beer and potato chips, and focus on the one American activity that
can unite us all in troubled times -- wagering on sports
Victor Fleming and Matt Ginsberg have combined forces to bring us an
oversize (overtime?) tribute to one of the biggest TV shows of the
year. There is no mention at all of the ads, unless the TWO MINUTE
WARNING tells us how long we have to look for more dip before play
resumes. Could any companies afford to run Super Bowl ads this year?
"F, monetarily" followed by "F, musically" is cute. Constructors and
editors must be especially pleased when they find opportunities like
that. The latter is not E SHARP which doesn't fit anyway. This is
one of those traps that takes advantage of the convention that the
first letter of clues is always capitalized. FORTE is always
lower-case f in music. I used to tell people that "playing loud is
my forte" but nobody ever laughed.
Only Shakespeare could compare DEATH to a lover's pinch. I'm glad I
don't have to write this blog in iambic pentameter. Kenilworth is a
novel by Sir Walter Scott. "It is the privilege of tale-tellers to
open their story in an inn -- the free rendezvous of all travellers
-- and where the humour of each displays itself without ceremony or
The "1993 triple-platinum Frank Sinatra album" is DUETS. In this
very odd collection, singers who were still alive sang along to
Sinatra tapes and the producer Phil Ramone did his digital magic to
make it seem like they were collaborating. It didn't work for me.
What did work was seeing MIA HAMM in the grid, a great athlete in
the sport the rest of the world calls football.
So, which is more fun for you this weekend, the game or the puzzle?
And if you're getting up, could you grab me another beer?
1. January 31, 2009 7:20 pm
It's the puzzle for me all the way. I'll be AT LARGE, doing my
usual avoidance therapy on the whole shebang. You folks have
-- Alan J.
2. January 31, 2009 8:10 pm
At least today's themed answers weren't puns, as I
originally feared (you know, ball would be bawl, etc.). As it
was, I couldn't wait to finish -- which is about how I feel
about the game.
Okay, just kidding, sort of. I was glad to see another stage
reference - TROD the boards - that's three days in a row, right?
And haven't we just recently seen ESTELLLA? And OXEYE?
Is Holden's little brother really ELLIE, or did I get something
wrong? I'll have to check that.
Okay, got to go. Got to start cooking the chili.
3. January 31, 2009 9:04 pm
I clearly know a lot less about football than I pretend to. The
only NEUTRAL ZONE that came readily to my mind is the one
separating the United Federation of Planets from the Romulan
Empire -- any breach of which was, I suppose, the height of
-- Peter S.
4. January 31, 2009 10:00 pm
After Saturday's, this was a snap. Loved the OFF cross- I'm too
tired to remember the numbers. Hope the Steelers do as well
5. February 1, 2009 12:18 am
Super Bowl not so super
Puzzle -- theme not so exciting
Game -- prospectively not so exciting in that the Giants aren't
in, damn that Plaxico, I heart Eli
Ads -- expect that no entity who received TARP funds would spend
$$$ here ... as if!
-- Ms. Piggy
6. February 1, 2009 4:09 am
OVULE/STAMEN was a nice cross.
7. February 1, 2009 5:09 am
In contrast with the other solvers this one was tough for me --
don't know much about football -- don't even know it is Super
After finally finishing the xword I went out for lunch and had
(chicken) SATAY. It is clued as "Asian Appetizer" since that's
what it is considered in the states. However here in Indonesia,
the place of origin of sate (local spelling), it is a dish --
main meal. There's an article in wikipedia:
I had 10 skewers + rice for 26,000 RUPIAH equivalent to $2.36
The xword database shows Rupiah was clued as Jakarta capital
(8/9/08). I hope next time SATAY will be clued as Indonesian
8. February 1, 2009 8:01 am
For me, ALLIE crosses STAPLED.
Neither the puzzle nor the superbowl. It's my mate's birthday.
Do you know how difficult it is to celebrate a Feb. 1 birthday
in a restaurant in America?The sports bars are SRO and the
better establishments close early in deference to their staff
who need to park it in front of a television. You can have your
beer. I guess it's cakes and ale for the likes of us
9. February 1, 2009 9:15 am
The game hasn't happened yet, so I can't answer your question
about which was more fun. I expect the game to win the day, and
for the Steelers to win the game.
And for me to win for best poem, since nobody's tried their hand
at the iambic pentameter you mentioned. Here's something (not
sure if it's proper iambic pentameter, but at least it covers
all of my mistakes) inspired by 24A, 106D, 87A and 100A,
Instead of EYE, I had a LIP
And I also put a TOE for TIP
But the silliest goof was IRE for TEE
And CEPTION for FERENCE near ruined me!
10. February 1, 2009 10:11 am
This may not be the appropriate format for this question - but
does anyone know how to print acrostics from the acrostic
archive in the one-page PDF format? The multi page format is a
pain. I'm not sure if it's the NYT or my computer (or me) that's
at fault, just can't solve THIS particular puzzle! Thanx.
-- Joe Keating
11. February 1, 2009 10:18 am
Could someone please explain 111 across? I got ATNO from the
downward crosses, but I have no idea how that relates to "5 for
B or 6 for C". I feel dense, but I can't see the connection.
12. February 1, 2009 10:26 am
At. no. = atomic number (see the periodic table).
13. February 1, 2009 10:30 am
I don't know where else to put this, but there is a mistake in
today's KENKEN. The upper right hand corner is a square with
four boxes and lists its sum as 23, which can't be done
according to the rules. Only 6-6-6-5 works, which necessitates
repetition of the 6 across and down.
I thought the NW was tough in today's puzzle and kept thinking
(unsuccessfully) of an NBA forward whose name ended in M.
-- Steve Manion
14. February 1, 2009 10:39 am
Never mind. just noticed it was an 8×6.
-- Steve Manion
15. February 1, 2009 10:50 am
We're with you Norteno: can't understand clues=atno. What are we
-- Gail and Bill
16. February 1, 2009 10:52 am
I was similarly stupefied by the results of my solving.
"5 for B or 6 for C".=ATNO was nonsense to me. Thanks to Jamie
638 for revealing the connection. That answer was my reason for
visiting the Wordplay Blog today. As Nick Danger once said in
reply to Rocky Rococo's introduction of himself: "Thanks
half-pint, you just saved me a lot of investigative work." No
-- Eli Becker
17. February 1, 2009 10:53 am
Jim, are you suggesting that Sinatra was dead when "Duets" was
put together? He was very much alive--just not bothering with
the actual singing of duets with his singing partners. (Nat King
Cole was long dead when Natalie Cole's "Unforgettable" duet with
her father was cooked up, but Sinatra was...just lazy or a
-- Amy Reynaldo
18. February 1, 2009 11:20 am
Quijote, thanks for asking about ATNO and saving me the trouble.
I hesitate to bring up another one I didn't get, since I may
have made an error on the cross (it happens). This second one is
122A, clued as "Roman Power" for which I got VIS. Did I make a
mistake? If not, someone explain the answer.
19. February 1, 2009 11:20 am
To Gail and Bill and ElQuixoteNorte:
The chemical elements are distinguished by each having a
different number of protons in its nucleus. The element boron
(symbol: B) has five protons in its nucleus, and hence its
"atomic number," commonly abbreviated as At. No., is 5. Carbon's
At. No. is 6 and its symbol is C.
20. February 1, 2009 11:58 am
I'm another one for whom this was harder than Saturday's. First
I was trying to fit football teams into the clues, then lots of
errs. Like EYES for LIDS, TOTAL for RECAP, and the worst, RUDDER
for TILLER. (The former gave me EDDIE for the brother, which I
like better than ALLIE, even though the latter is right.) Nasty
spelling for THEATRE, e'en though it is clued correctly.
VIS is latin for power or strength, Wags.
OK, now I understand ATNO, but what about ADIN?
All in all, though, I would say it was a good, cleverly themed
Sunday puzzle. And it included that great trivia answer: What
word in English has 8 letters but only 1 vowel? 106A
21. February 1, 2009 12:04 pm
The thematic aspect was straightforward and copious (i.e., no
less than 11 thematic answers, most of them quite cute). For me
the nonthematic part was the trickiest aspect.
I'd like to add to the cryptic clarification by Jamie638
of "5 for B or 6 for C".=ATNO = AT. NO.
For those not into the perodic table, the point is that
5 is the atomic number (AT. NO.) for Boron (with symbol B) and 6
is the atomic number for Carbon (with symbol C).
I liked the cunning of the definitions for ACROSS 110, 111, 123,
On the other hand, Holden's little brother is obscure (at least
for a Canadian), while "Fully constituted, as a session of
Congress" is to me misleading for a word that is usually defined
as "complete in the sense of PLENARY session or meeting, the
part of a conference when all members of all parties are in
attendance or PLENARY power or PLENARY authority, the complete
power of a governing body".
22. February 1, 2009 12:22 pm
Wags, VIS is Latin for power.
Thanks, Byphate! I had STEELED for 1D, which may not make total
sense, but I accepted it as a Pittsburgh Steelers reference. Of
course that left "elenary" for 29A, which makes no sense at all,
but I just ignored it.
23. February 1, 2009 12:46 pm
Congrats to Serena for her big win Down Under. Not too many
ADIN's, as there were not many deuce points in a match that
lasted just 59 min. According to an article in yesterday's
paper, more Buffalo wings are eaten today than any other time
and its common for stores to RUNLOW due to the demand. I may
have to settle for SATAY instead. A fun puzzle. How 'bout IDO
24. February 1, 2009 2:00 pm
I don't care about or know anything about football but I enjoyed
the puzzle and was able to get the theme answers. I like when
the puzzle relates to the day, holiday, occasion etc. My
favorite clue was 38 A since the answer is my daughter's name. I
enjoy reading this blog and all the comments - you are all so
clever (and helpful to this novice puzzle solver).
25. February 1, 2009 2:06 pm
Appreciate the Firesign Theater reference, Eli! And meaningful
that it has something to do with chemistry, since Nick Danger
seemed so much funnier back in the old days with the indulgence
Got to go cheer dem Stillers.
-- John T.
26. February 1, 2009 6:26 pm
Thanks to sara for oxeye. We were down to the last three words
and going out of our minds. So, for you, it's Allie, not Ellie.
27. February 1, 2009 8:56 pm
Did the puzzle during the first half. Stumbled a few times,
places others have noted. I liked the bunch of Fs where the
F-clues' answers go. Are asterisks "stars" (as in the "10
starred clues")? Thought they were "asterisks".
Sunday's are perfect for topical themes, and this one fit well.
Also, important to me right now -
- an appearance by Nick Danger, Third-Eye (yay!) in the
- Bruce sang "10th Avenue Freeze-Out" and "Born to Run" rather
than the expected "The Rising" and "Born in the USA" at
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