Posts tagged ‘puzzle’

AWOKK, Day 7: KenKen Puzzle for 2016

Good day, and welcome to Day 7 of the A Week of KenKen series. If you’ve stumbled onto this page randomly, you should definitely check out some of the fun we’ve had previously…

Well, here it is, September 25, a mere 269 days into the year, and I am only now presenting you with a KenKen puzzle based on the year. I suppose I can take some solace in the fact that I’m presenting the following 2016 KenKen puzzle before the year is over. Little victories.

You might note that the puzzle has the following attributes:

  • The numbers 2, 0, 1, and 6 are featured prominently as individual cells.
  • Every target number uses (some combination of) the digits 2, 0, 1, and 6.
  • There are two large cages — one in the shape of a 1, the other in the shape of a 6 — each with a product of 2016.

This puzzle follows the standard rules of KenKen, but there is one major exception: although it is an 8 × 8 puzzle, instead of using the digits 1‑8, it uses 0‑7.

KenKen 2016 Puzzle

If you’re stuck, just fill in the squares randomly. There are only 108,776,032,459,082,956,800 different Latin squares of size 8 × 8, and your chances of guessing correctly are even better since 4 cells are already filled in.

As it typical of all puzzles presented on this blog, I am not posting the solution. At least, not yet. Maybe someday. If you beg. Or send me money. But not today.

September 25, 2016 at 5:05 am Leave a comment

AWOKK, Day 6: KenKen Glossary

KENgratulations! You’ve made it to Day 6 of MJ4MF’s A Week of KenKen series. If you happened to miss any of the fun we’ve had previously…

Robert F. Fuhrer is a toy inventor with a knack for coming up with creative names, including Crocodile Dentist, Gator Golf, T.H.I.N.G.S. (Totally Hilarious, Incredibly Neat Games of Skill), Rumble Bugs, Missile Toe (literally, a rocket in the shape of a toe), and many others. As the president of Nextoy, LLC, which holds the registered trademark for KenKen®, Bob now uses his creative naming abilities for the appellations of KenKen-related products.

The word that started this post, KENgratulations, is just one of his many linguistic creations. I rather like the term he coined to describe the computer application that randomly generates KenKen puzzles.

KEN·er·tor n. the “machine” (computer application) used to automatically generate KenKen puzzles

Quick! We need more 6 × 6 puzzles. Crank up the Kenerator!

The name conjures images of a machine from Willy Wonka.

Oompa, loompa, doom-pa-dee-do,
I’ve got a perfect puzzle for you…

Numbers and operations go in, puzzles come out.

The Kenerator

Bob can also take credit for the following:

KEN·cil n. a pencil used to solve KenKen puzzles

I prefer kencils rather than pens when solving KenKen puzzles.

KEN·grat·la·tions n. an expression of praise for solving a KenKen puzzle

Kengratulations for solving that puzzle in less than 7 years!

KEN·thu·si·ast n. someone who likes to solve KenKen puzzles

Most Kenthusiasts solve more than one KenKen puzzle a day.

There’s no doubt, Bob is good. But as you saw in a previous post, I’ve got a knack for coining terms, too…

KEN·tath·lon n. competition involving multiple KenKen events

I complete a Kentathlon consisting of a 4 × 4, 5 × 5, and 6 × 6 puzzle every morning.

e·go·KEN·tric adj. a person who thinks that they are better than others at solving KenKen puzzles

He’s completely egokentric, even though he’s never won a KenKen tournament.

KEN·tral of·fice n. where KenKen puzzles are made

The Kenerator resides in the kentral office.

KEN·te·nar·i·an n. person who has solved 100+ KenKen puzzles

He became instantly addicted to KenKen puzzles; he became a kentenarian in less than 3 weeks.

su·per·KEN·te·nar·i·an n. person who has solved 100+ KenKen puzzles in one day

She became a superkentenarian by completing all the puzzles in Ferocious KenKen on Saturday.

KEN·ta·gon n. the arena in which KenKen tournaments take place (analogous to the Octagon, the eight-sided chain-link enclosure used for Ultimate Fighting Championship matches, though usually less violent)

Enter the kentagon, prepare to solve!

KEN·o·pause n. the period in a puzzle solver’s life when KenKen ceases to be fun

Kenthusiasts who have entered kenopause usually solve fewer than one puzzle a day, on average.

KEN·i·ten·tia·ry n. where KenKen solvers are locked up if they’re caught cheating (syn prism)

If you copy off your neighbor at a KenKen tournament, you’ll be sent to the kenitentiary.

KEN·al·ty n. a disadvantage imposed on a puzzle solver at a tournament for an infringement of the rules

He was given a 15-second kenalty for “using a kencil in an unsafe manner.”

KEN·ais·sance n. the period from roughly 2008 to 2010 when KenKen puzzles experienced tremendous growth in popularity, likely the result of publication in The Times (London), the NY Times, and other newspapers

Harold Reiter’s interest in KenKen started long before the Kenaissance.

KEN·der·foot, n. an amateur; someone who has solved only a few KenKen puzzles

He’s such a kenderfoot; he doesn’t even know the X-wing strategy!

KEN·den·cies n. the habits of a KenKen solver; analogous to a “tell” in poker

He has a kendency to complete all of the addition cages before attempting any subtraction cage.

hy·per·KEN·ti·late n. to breathe heavily while solving a puzzle (usu., a result of having difficulty)

At the 2013 KenKen International Championship, she started to hyperkentilate when she had trouble with a difficult 6 × 6 puzzle.

September 24, 2016 at 5:05 am Leave a comment

AWOKK, Day 5: Harold Reiter’s Puzzles

You’ve made it! Today is Day 5 in MJ4MF’s A Week of KenKen series. In case you missed the fun we’ve had previously…

Like Thomas Snyder, Harold Reiter believes that human-generated KenKen puzzles are superior to those created by computer. But Harold pushes the envelope by developing variations on KenKen that include Primal KenKen, 3-D KenKen, n × n KenKen puzzles that use numbers other than 1‑n, and Clueless KenKen — which contain no clues and, contrary to popular belief, were not invented by Cher Horowitz. Recently, in fact, he sent me a No-Op KenKen puzzle that used the floor function.

The following standard KenKen puzzle is one of Harold’s “Big Letter” puzzles. One of the cages forms a capital E, and he made this puzzle for a friend whose name began with — wait for it — the letter E.

Harold Reiter - Big E PuzzleNo-Op KenKen Puzzles have target numbers in the cages but no operations. All the typical rules of KenKen apply, but it’ll take a little more thought to determine which operation is needed in each cage. The following is Harold’s “No-Op 12” puzzle.

Harold Reiter No-Op 12And the piece de resistance of Harold’s creations — though he says the idea for this one actually came from his daughter, Ashley — is the following 3‑D KenKen. Here are Harold’s instructions for this puzzle:

In the puzzle below, there are 48 lines. Each must contain exactly one of the digits 1, 2, 3, and 4. The 16 cages are identified by letters. Each cage is either additive or multiplicative, and the target number for every cage is 12 — meaning that the numbers in the cells of every cage either add or multiply to give 12. Ken you solve it?

This one might need a little more explanation. The four layers of the puzzle work together; for instance, the two A’s on the top layer and the two A’s on the second layer form a four-number cage with a target number of 12. Similarly, the four G’s on the second layer and the lone G in the third layer form a five-number cage with a target number of 12. All standard KenKen rules apply and are extended to three dimensions — no repeat of a digit in any row, column, or tube vector.

I prefer this presentation of the puzzle, which looks like a 3‑D tic-tac-toe board:

Harold Reiter - 3D KenKen Layers

But Harold’s presentation of it gives you a blank version side-by-side with the original, so you have a place to record your work:

Harold Reiter - 3D KenKen

The KenKen world is indebted to Harold for creating interesting puzzles and for sharing them with a new generation of students at his local math events.

For more of Harold’s puzzles, and for suggestions on how to create your own, check out KenKen, Thinking Globally.

September 23, 2016 at 5:05 am Leave a comment

AWOKK, Day 3: KenKen Times

Today is Day 3 in MJ4MF’s A Week of KenKen series. In case you missed the fun we’ve had previously…

Yesterday, I introduced you to the KENtathlon.

While completing a KENtathlon, my goal is to complete a 6 × 6 puzzle in less than 2 minutes; a 5 × 5 puzzle in less than 1 minute; and a 4 × 4 puzzle in less than 20 seconds. Even though the sum of those times for all three puzzles is 3 minutes, 20 seconds, my goal is a combined time of 3 minutes. It’s good to have goals.

Puzzle Size Goal Time Personal Best
4 × 4 0:20 0:12
5 × 5 1:00 0:27
6 × 6 2:00 1:29
KENtathlon 3:00 2:32

 

I don’t always perform well enough to meet those goals. And when I don’t, I repeat the same size puzzle again… and again… and again… for as many attempts as it takes to complete each puzzle in the allotted time. And when I’ve met the time goal for each puzzle individually, if the combined time isn’t satisfactory, then I start the whole thing over.

To say that I’m slightly obsessive would be like saying that the Pope is a little bit Catholic.

As you may have noticed in the table, I once finished a 4 × 4 puzzle in 12 seconds. The key word there is once. The stars were in alignment that day — it was an easy puzzle, and the dexterity of my thumbs and fingers was at an all-time high. Though I’ve attained 13 a handful of times, I’ve never replicated that 12-second feat.

12SecondKenKen

My fastest puzzle ever,
not Photoshopped.

 

That said, I regularly complete 4 × 4 puzzles in 14 or 15 seconds. With that being the case, you have to wonder if the 20-second goal is really a challenge. And what about the goal times for 5 × 5 and 6 × 6 puzzles?

Admittedly, my time goals are arbitrary, though not random. When I chose those goals, I had completed enough KenKen puzzles that I intuitively knew what felt right. Still, it wasn’t based on hard data… and if you’ve read this blog long enough, you know that that bothered me. A lot.

But what’s a boy to do?

I suppose a well-adjusted human might do nothing, think it’s not worth the trouble, and just let the whole thing go. But an obsessive numbers guy? Well, he’d painstakingly solve 132 KenKen puzzles, collect data on the amount of time each one took to complete, meticulously record the data in an Excel spreadsheet, and perform a thorough analysis. You may think that undertaking such a project is ludicrous; but to me, it was absolutely essential.

The graph below shows the results. The circular dots represent my median time for each puzzle size, and the square dots represent the upper and lower quartiles. For instance, the median time for 6 × 6 puzzles was 217 seconds, while the interquartile range for 6 × 6 puzzles extended from 163 to 284 seconds.

KenKen Time RegressionWhat this reveals is that my intuition wasn’t perfect, but not bad.

  • I completed 49% of 4 × 4 puzzles in less than the goal time of 20 seconds.
  • I completed 58% of 5 × 5 puzzles in less than the goal time of 1 minute.
  • But, I completed only 14% of 6 × 6 puzzles in less than the goal time of 2 minutes.

Further analysis revealed that I completed 40% of the 6×6 puzzles under 3 minutes, and that seems a bit more reasonable, so my new goal time for 6 × 6 puzzles is 3 minutes.

Now, I know you thought this analysis was completely unnecessary, but the proof is in the pudding. The results were invaluable. By considering the data, interpreting the results, and revising my goal time for 6 × 6 puzzles, the probability that I can now complete each size puzzle in the allotted time on the first or second try has increased from 16% to 39%. Or said another way, Remy’s morning walks now last an average of just 15 minutes, whereas some of them used to take an hour-and-a-half.

September 21, 2016 at 5:05 am Leave a comment

AWOKK, Day 2: The KENtathlon

You’ve come back! Great! Welcome to Day 2 of MJ4MF’s A Week of KenKen series. In case you missed the fun we had yesterday…

As the early riser in our family, I’m responsible for taking our dog Remy on his morning walk. Given his advanced age (13) and breed (golden retriever), our veterinarian says that I should walk him 15-20 minutes every morning.

But the length of Remy’s morning walk is completely independent of any professional recommendations. Instead, it depends entirely on the amount of time it takes me to solve a 6 × 6, a 5 × 5, and a 4 × 4 KenKen puzzle.

I call it the KENtathlon.

Here are three puzzles for you to solve as a KENtathlon. The order in which you solve them doesn’t matter. I don’t even care if you take a break between puzzles. The only thing I would recommend is that you complete each puzzle in one sitting with no break — but, hell, this is for fun, so I don’t much care if you ignore that suggestion, too.

Kentathlon 6x6

Kentathlon 5x5

Kentathlon 4x4

Post your combined time for all three puzzles in the comments.

If you’d like to compete against other KENthusiasts, you can register for the KenKen International Championship, to be held in New York City on December 18. (Unfortunately, registration isn’t open yet… check www.kenken.com in the coming months for details.)

September 20, 2016 at 5:05 am Leave a comment

A Week of KenKen, Day 1: Introduction

Welcome to A Week of KenKen (AWOKK). Every day this week, the MJ4MF blog will feature a new post about the number puzzle that Sudoku wishes it could be. That’s right — seven days, nothing but KenKen.

Here’s a list of the posts that you’ll see in coming days:

  • Day 1: Intro (that’s today!)
  • Day 2: The KENtathlon
  • Day 3: KenKen Times
  • Day 4: My KenKen Puzzles
  • Day 5: Harold Reiter’s Puzzles
  • Day 6: KenKen Glossary
  • Day 7: KenKen Puzzle for 2016
  • Day 8: KenKen in the Classroom

If the Beatles got nothin’ but love, babe, eight days a week, then I can certainly have a week with eight days of KenKen. Deal with it.

Today is an introduction, for those of you unfamiliar with KenKen. Here are the rules of the puzzle:

  • For an n × n grid, fill each row and column with the numbers 1 through n. A number may not be repeated in any row or column.
  • Each heavily outlined set of cells, called a cage, contains a mathematical clue that consists of a number and an arithmetic operation: +, –, ×, or ÷. The numbers in that cage must combine (in any order) to produce the target number using the mathematical operation indicated.
  • Cages with just one cell should be filled with the target number.
  • A number may be repeated within a cage, provided it’s not in the same row or column.

The New York Times crossword puzzle editor and Weekend Edition puzzlemaster Will Shortz explains KenKen in this short video:

Ready to try for yourself? Here’s a simple puzzle, which is dubbed an “easy” puzzle from the KenKen website:

Easy 3x3 KenKen

Too easy? Here’s a slightly more interesting one that I created:

Fun 3x3 KenKen

Did that whet your appetite for more? If you were a kid who could’ve held out for several minutes to get two marshmallows, then check back tomorrow for the next installment. But if you were a kid who just couldn’t wait and would’ve gobbled that single marshmallow immediately, then here’s your instant KenKen gratification:

Till tomorrow, happy solving!

September 19, 2016 at 5:05 am Leave a comment

Demitri Martin and Me

As I was watching If I by Demetri Martin, I realized something.

I love Demitri Martin, because I am Demetri Martin.

Not literally, of course. I didn’t inhabit his body and take over his soul. (Would if I could!) Nor is this blog a ruse that appears to be written by Patrick Vennebush when it is, in fact, written by Demitri Martin. I just mean that he and I are about as similar as two people can be without entering the world from the same womb. Check out this list:

Demitri Martin Patrick Vennebush
He’s weird. (In a good way.) I’m weird. (No disclaimer.)
He did Mensa puzzles as a kid. I did Mensa puzzles as a kid.
He uses convoluted mnemonics to remember numbers. I use convoluted mnemonics to remember numbers.
He uses drawings and visual aids during stand-up performances. (See below.) I use drawings and visual aids during math presentations. (See below.)
He was influenced by Steven Wright, Emo Philips, Eddie Izzard, and Mitch Hedberg. I watched every Steven Wright performance on cable television when I was a teenager; my favorite joke is from Emo Philips; I own every Eddie Izzard CD; and one of my great regrets is that I never saw Mitch Hedberg perform live.
He was slated to play Paul de Podesta in Moneyball but was replaced by Jonah Hill. I wasn’t in Moneyball, either.
He was born in a prime number year (1973). I was born in a prime number year (1971).
He won a Perrier Comedy Award. I sometimes drink Perrier while watching Comedy Central.
He once attended class wearing a gorilla suit. I had no fashion sense in college.
He is extremely allergic to nuts. I’m not allergic to them, but I really don’t like crazy people.

 

One of Demetri’s drawings:

Ants Bears People

One of my drawings:Celsius Benchmarks

Oh, sure, I could list hundreds of other similarities between Demitri and me, but I think the list above is enough to see that the coincidence is uncanny. I mean, we practically live parallel lives.

Demetri used to sneak Mensa puzzle books — not muscle mags or girlie mags — into school to read during class. One of the puzzles purportedly from his Mensa Presents Mighty Mindbusters book:

If a crab-and-a-half weigh a pound-and-a-half, but the half-crab weighs as much again as the whole crab, what do half the whole crab and the whole of the half-crab weigh?

He said that solving problems from those books was validating.

When I got one right, I’d be like, “Yes! I am smart! These other idiots don’t know how much the crabs weigh.” But I do. Because I just spent Saturday working it out.

I solved puzzles like this, too. I don’t know if they made me feel smart, but I enjoyed the way I felt when I figured out a particularly tough one.

From the way he describes it, such puzzles may have had the same effect on both of us.

Whatever the reason, I spent a lot of time as a kid doing these puzzle books. And it came to shape the way I see the world. So now, as an adult, I see the world in those terms. For example, to me a phone number is always a sentence or an equation. Like my friend Becky…

He goes on to say that he remembers Becky’s phone number using a convoluted, mathematical mnemonic:

Beckys Number

That is, he converts the first three digits into an expression that is equal to an expression formed by the last four digits. He concludes that it’s “much simpler,” but it’s unclear how.

Now that’s some crazy, messed-up sh*t.

And I’d probably think it even weirder… if I didn’t do it, too.

One night many years ago, my roommate Adam asked for the number of the local pizza shop. I replied, “33, 13, 203,” because that’s how I saw it. Adam looked at me like I was nuts, and he was probably onto something.

My friend AJ’s street address is 6236, which I remember as 62 = 36.

My street address growing up was 1331, which I associated with the third row of Pascal’s triangle. (It also happens to be 113, but I didn’t know that at the time.)

I chose the four digits of my PIN because… no, wait, that wouldn’t be prudent.

My co-worker Julia’s extension is 2691. I used to remember this as 2 + 6 = 9 – 1, until I recognized a more elegant geometric mnemonic: the sequence 2, 6, 9, 1 forms an isosceles trapezoid on my office phone’s keypad — or it would, were the buttons equally spaced.

2691OnPhone

I can’t explain why I do this. Perhaps, as Demetri says, it’s the influence of all those puzzle books. Or maybe it’s just that the mental conversion to an equation gives the number meaning, making it more memorable. Or perhaps it’s that I’m wired to see the world through a mathematical lens, despite not wearing glasses.

Larry McCleary, author of The Brain Trust Program, claims that numbers are difficult to remember because “most of us don’t have any emotional attachment to particular numbers.” Mr. McCleary, I’d like you to meet my friend Demetri…

Demitri and I are both into anagrams.

Even when I walk down the street, things look a little different. The signs… the letters dance around. It becomes a little puzzle for me. So, say MOBIL, the gas station — that becomes LIMBO. STARBUCKS becomes RACKS BUST. CAR PHONE WAREHOUSE… AH, ONE SOUR CRAP — WHEE!”

Yeah, I do that, too…

demetri_martin_anagram

My first car was a CHEVROLET IMPALA, which transforms to COMPARATIVE HELL. Our neighbor’s son is CARSON, whom I jokingly call ACORNS. And I can’t see a STOP sign without also thinking of OPTS, POST, POTS, and TOPS.

If you’re reading this, you likely have some things in common with Demetri, too. What number mnemonics do you use, or what anagrams to do you see?

May 25, 2016 at 8:27 am Leave a comment

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About MJ4MF

The Math Jokes 4 Mathy Folks blog is an online extension to the book Math Jokes 4 Mathy Folks. The blog contains jokes submitted by readers, new jokes discovered by the author, details about speaking appearances and workshops, and other random bits of information that might be interesting to the strange folks who like math jokes.

MJ4MF (offline version)

Math Jokes 4 Mathy Folks is available from Amazon, Borders, Barnes & Noble, NCTM, Robert D. Reed Publishers, and other purveyors of exceptional literature.

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