## Six Degrees of Titillation

It was 75° today. If you live in Honolulu, Karachi, Gaberone, or Rio de Janeiro, that might not strike you as unusual. But let me assure you that during late February in Crofton, MD, a temperature that high is rather unexpected.

But no complaints. It was nice to wear only a t-shirt and no jacket, and it allowed me to use this joke at the start of my presentation:

What a beautiful day! When I was invited to this event, I suspected it’d be close to 20° outside. I just didn’t realize it’d be Celsius.

Horrible, ain’t it? But don’t worry… I’ve got more:

- Do math majors receive degrees or radians?
- If it’s 0° today, and it’s supposed to be twice as cold tomorrow, how cold is it going to be? (Stephen Wright)
- Are you a 45° angle? Because you’re acute-y.
- Why did the obtuse angle go to the beach? Because it was more than 90°.
- Are you cold? Go sit in a corner. It’s 90° over there.
- Why didn’t the circle go to college? It already had 360 degrees.
- I asked the trigonometer what the weather was like, and he said it was 15π/16 outside.
- The number you dialed is imaginary. Please rotate your phone 90° and try again.
- What brand of deodorant did the angle use?
*Degree*.

## A Mathematical Thank-You Note

I recently sent a copy of **More Jokes 4 Mathy Folks** to a friend of an acquaintance, and today I received a thank-you letter from the recipient. I think the letter is worth sharing, so here you go:

Patrick —

Thanks so much for sending me

… I’ve already annoyed my entire family, and I’m only 46/111 through the book. (I think your work here is done.)More JokesI can’t provide a formal proof, but empirically speaking, this is the best collection of math jokes known to exist. Honestly, I enjoy the blend of quips and jokes; almost everything I read translates well into a groaner I can splice into my physics classroom repertoire!

Hoping you don’t object to the informality of my “stationery” — thought you’d appreciate the utility of engineering paper.

^{1}Thanks again! Best,

RobP.S. I noticed — when I looked up your address (ed. note:

STALKER!) — that we only live about seven root two^{2}minutes apart. How would you feel about raising a pint some evening? I’d love to hear about your work and exchange a few quips!

This is one of the nicer letters I’ve received, and it was fun to be reminded that not all mail needs to be electronic. And you can bet that some of those compliments will be used on a promotional flyer soon!

^{1} Quarter-inch quadrille paper, if you must know.

^{2} He had correctly written the irrational number as

but since LaTeX looks like shit as inline text, I converted it to straight English.

## The Beer Paradox

From Gene Weingarten’s recent column, “Rhymes Against Humanity,” in the January 28 edition of the *Washington Post Magazine*:

An infinite number of mathematicians

Walked into a bar on one recent night,

And, under the strangest of barroom conditions,

What followed quite nearly became a big fight.“I’ll have a pint,” said the first to the ’tender.

“I’ll have a half,” said the next fellow down.

“I’ll have a quarter,” said the third (no big spender).

“Give me an eighth,” said the next, like a clown.The bartender fumed and grew suddenly pale

Then, calmly, he turned and he went to the spout

Drew up two pints, set them down at the rail.

Said, “Enough of this nonsense — you all work it out.”

This is an MJ4MF original, though like Gene’s, it’s based on a stale, old joke:

With my head in an oven

And my feet on some ice,

I’d say that, on average,

I feel rather nice!

What other classic math jokes can be easily converted to poems? Or have already been?

## Stupid Stats

C’mon, now… really?

Uterine size in non-pregnant women varies in relation to age and gravidity [number of pregnancies]. The

mean length-to-width ratio conformed to the golden ratioat the age of 21, coinciding with peak fertility.

Claiming that a uterine golden ratio coincides with peak fertility is highly suspect. The good folks at Ava Women claim that, “Most women reach their peak fertility rates between the ages of 23 and 31.” Information at Later Baby states, “Female fertility and egg quality peak around the age of 27.” And WebMD says, “A woman’s peak fertility is in her early 20s.” So, there seems to be some debate about when peak fertility actually occurs. Consequently, this strikes me as retro-fitting, and it seems that Dr. Verguts and his colleagues may have played loose with the age of peak fertility in order to make a connection to the golden ratio.

In their defense, though, it’s not the first time that folks have gone uptown trying to find a connection to the golden ratio. A claim by The Golden Number states, “[The DNA molecule] measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral,” and 34/21 ≈ 1.6190476, which is approximately equal to φ, 1.6180339.

Though this guy — an honest-to-goodness biologist — seems to disagree:

I’ve also heard folks say that people are perceived as more beautiful if certain bodily proportions are in the golden ratio. The most extreme example of this that I’ve found involves the teeth:

…the most “beautiful” smiles are those in which central incisors are 1.618 wider than the lateral incisors, which are 1.618 wider than canines, and so on.

In a study of 4,572 extracted adult teeth, Dr. Julian Woelfel found the average width of the central incisor to be 8.6 mm. If the teeth in a beautiful smile follow the geometric progression described above, well, that would imply that the first molar would be just 8.6 × 0.618^{5} ≈ 0.8 mm wide, which isn’t reasonable and, moreover, is not even remotely close to the average width that Dr. Woelfel found for the first molar: approximately 10.4 mm.

But all of these claims involving the golden ratio are not even close to being the stupidest statistics I’ve heard in my life. Mary Anne Tebedo made a remark on the floor of the Colorado State Senate in 1995 that may hold that distinction:

Statistics show that teen pregnancy drops off significantly after age 25.

Of course, it’s hard to call that a *statistic*, since it’s completely nonsensical. Maybe it’s only the stupidest *statement* I’ve ever heard.

Then there’s this one, from the *New York Times* on August 8, 2016, which couldn’t be more useless:

No presidential candidate has secured a major party nomination after an FBI investigation into her use of a private email server.

Well, duh. Email didn’t even exist before the 1970’s. Moreover, besides Hillary Clinton, has *any* presidential candidate ever had their use of a private server investigated by the FBI? This is like saying, “No one has ever been named *People*‘s Sexiest Man Alive after writing a math joke book.” (Not yet, anyway.)

Randall Munroe made fun of these types of “no politician has ever…” claims in 2012 with his cartoon *Election Precedents*:

And it’s true:

But perhaps my all-time favorite is one that Frank Deford — may he rest in peace — included in his piece “The Stupidest Statistics in the Modern Era” on NPR’s Morning Edition:

He’s [Brandon Phillips] the first National League player to account for as many as 30 steals and 25 double plays in one season.

About this stat, Deford commented, “Steals and double plays together? This is like saying, ‘He’s the first archaeologist to find 23 dinosaur bones and 12 Spanish doubloons on the same hunt.'” (I sure am going to miss him.)

The preponderance of dumb stats shouldn’t come as a surprise, though. A recent study found that people deemed real news headlines to be accurate 83% of the time and fake news headlines to be accurate 75% of the time. So, if we can’t tell truth from fiction, how can we possibly distinguish useful statistics from inane?

If you’d like to test your ability to detect fake news, check out Factitious from American University.

## WODB, Quora Style

The following puzzle was recently posted on Quora:

Which of the following numbers don’t belong: 64, 16, 36, 32, 8, 4?

What I liked about this puzzle was the answer posted by Danny Mittal, a sophomore at the Thomas Jefferson High School for Science and Technology. Danny wrote:

64 doesn’t belong, as it’s the only one that can’t be represented by fewer than 7 binary bits.

36 doesn’t belong, as it’s the only one that isn’t a power of 2.

32 doesn’t belong, as it’s the only one whose number of factors has more than one prime factor.

16 doesn’t belong, as it’s the only one that can be written in the form

x, where^{y}xis an integer andyis a number in the list.8 doesn’t belong, as it’s the only one that doesn’t share a digit with any other number in the list.

4 doesn’t belong, as it’s the only one that’s a factor of all other numbers in the list.

I suspect that Danny has visited Which One Doesn’t Belong or has read Christopher Danielson’s *Which One Doesn’t Belong*. Or maybe he’s just a math teacher groupie and trolls MTBoS.

But then Jim Simpson pointed out the use of “don’t” in the problem statement, which I had assumed was a grammatical error. Jim interpreted this to mean that there must be two or more numbers that don’t belong for the same reason, and with that interpretation, Jim suggested the answer was 32 and 8, since all of the others are square numbers.

Don’t get me wrong — I don’t think this is a great question. But I love that it was interpreted in many different ways. It could lead to a good classroom conversation, and it makes me consider all sorts of things, not the least of which is standardized assessments. How many times have students gotten the wrong answer for the right reason, because they interpreted an item on a state exam or the SAT differently than the author intended? And how many times have we bored students with antiseptic questions, only because we knew they’d be free from such alternate interpretations? Both scenarios make me sad.

## Four, or F**k You?

If you asked a student, “How many sides does a quadrilaterals have?” and you received the following response…

…well, you might be upset.

But perhaps the student learned to count in binary on her fingers, where the right thumb is the register for 1, the right index finger is the register for 2, the right middle finger is the register for 4, and so on. Then the response above would be appropriate, despite appearances.

If you then asked, “Into how many regions will a circle be divided if 6 points are placed randomly on a circle, and each point is connected to every other point?” the student might appear to wave at you — or, she may just be telling you (correctly) that 31 regions would be created by holding up all 5 fingers. (In binary counting, all five fingers add up to 1 + 2 + 4 + 8 + 16 = 31.)

My sons learned to count in binary when, at age 5, they asserted that the highest you can count on your fingers is 10. “Actually,” I told them, “You can count as high as 1,023 on your fingers. If you want, I can show you how.”

Of course, they wanted to learn, and I was happy to teach them. There are at least four good reasons for teaching students to count in other bases, and “Dr. Peterson” at the Math Forum had this to say:

I taught my son to multiply in binary before he really learned it in decimal, because it’s easier; you have only the algorithm (method) with no multiplication tables to learn.

Knowing how bases work helps to develop number sense while clarifying the concept of place value. And not understanding place value leads to things like this…

My former boss shared this video with me on Facebook recently, and he asked,

Does this work with other numbers?

I had a fun time playing with that question, so let me now give you a chance to think about it. Can you find another pair of numbers that produce analogous incorrect results when multiplying and dividing? And if you’re feeling really ambitious, can you generalize to determine what types of number pairs will always give these kinds of incorrect results?

## 2017 KenKen International Championship

If you like puzzles and ping pong, then Pleasantville, NY, was the place to be on December 17.

More than 200 Kenthusiasts — people who love KenKen puzzles — descended on Will Shortz’s Westchester Table Tennis Center for the 2017 KenKen International Championship (or the KKIC, for short). Participants followed 1.5 hours of solving KenKen puzzles with a pizza party and several hours of table tennis.

The competition consisted of three rounds, with the three puzzles in each round slightly larger and more difficult than those from the previous round. Consequently, competitors were given 15, 18, and 20 minutes to complete the puzzles in the first, second, and third rounds, respectively.

Competitors earned 1,000 points for each completely correct puzzle, and 0 points for an incomplete or incorrect puzzle. In addition, a bonus of 5 points was earned for every 10 seconds in which a puzzle was turned in before time was called. So, let’s say you got two of the three puzzles correct and handed in your answers with 30 seconds remaining in the round; then, your score for that round would be

The leader after the written portion was John Gilling, a data scientist from Brooklyn, whose total score was 10,195. And if you’ve been paying attention, then you know what that means — Gilling earned 9,000 points for completing all of the puzzles correctly, so his time bonus was 1,195 points… which is the amount you’d earn for turning in the puzzles 2,390 seconds (combined) before time was called. The implication? Gilling solved all 9 puzzles from the written rounds — which contained a mix of puzzles from size 5 × 5 to 8 × 8 — in just over 13 minutes.

Wow.

As a result, Gilling, the defending champion, earned a spot in the Championship Round against Tess Mandell, a math teacher from Boston; Ellie Grueskin, a high school senior at The Hackley School; and Michael Holman, a technology consultant. In the final round, each of them attempted a challenging 9 × 9 puzzle, which was displayed on an easel for the crowd to see. Solving a challenging 9 × 9 is tough enough; having to do it as 200 kenthusiasts follow your every move is even tougher.

So, how’d they do? See for yourself…

When the dust settled, Gilling had successfully defended his title. For his efforts, he received a check for $500. But more importantly, he retained bragging rights for one more year.

If you think you’ve got what it takes to compete with the best KenKen solvers, try your hand at the 9 × 9 puzzle that was used in the final round. In the video above, you saw how fast Gilling solved it to win the gold. But even the slowest of the four final-round participants finished in under 15 minutes.

Again, wow.

Finally, I’d be failing as a father if I didn’t mention that my sons Alex and Eli competed in the Delta (age 10 and under) division. Though bested by Aritro Chatterjee, a brilliant young man who earned a trip to the 2017 KKIC by winning the UAE KenKen Championship, Eli took the silver, and Alex brought home the bronze. They’re shown in the photos below with Bob Fuhrer, the president of Nextoy, LLC, the KenKen company and host of the KKIC.

#proudpapa

For more KenKen puzzles, check out www.kenken.com, or see my series of posts, A Week of KenKen.