## Posts tagged ‘math’

### IDK Puzzles

I like logic, and I like beer, so it’s no surprise that this is one of my favorite online comics:

Not sure why that’s funny? There’s an explanation at www.beingamathematician.org.

Logic puzzles in which a protagonist states, “I don’t know!” are ubiquitous. Borrowing from texting culture, I’ve taken to calling these IDK Puzzles.

Every math person remembers the first non-routine problem they solved and, more importantly, the *feeling* they experienced when solving it. The first time I had that feeling occurred after solving a logic puzzle about three children’s ages that I discovered in a Martin Gardner book; now many years later, I don’t remember the title of the book, and the following is my best recollection of the puzzle:

Two neighbors are speaking. One asks the other, “I know you have three children, but how old are they?”

The other says, “The product of their ages is 72.”

The first neighbor says, “I still don’t know their ages.”

“Well,” says the other, “the sum of their ages is equal to our street address.”

The first neighbor again replies, “I still don’t know their ages.”

“I’m sorry,” says the other, “I can’t talk anymore, because I have to take my oldest child to the dentist,” and then leaves.

While saying good-bye, the first neighbor thinks, “Ah, now I know their ages.”

This puzzle is typical of the genre, in that it appears there is insufficient information, but those who persist will be rewarded. Can you figure out the three children’s ages?

A slightly different IDK Puzzle involves geometric shapes.

Two people are shown the following five shapes:

They are told that a prize has been placed under one of the shapes. One of the people is told the color, and the other is told the shape, but they are not allowed to share their information with each other.

They are asked, “Do either of you know where the prize is hidden?”

Both of them reply, “I don’t know.”

They are asked a second time, “Do either of you know where the prize is hidden now?”

Again, they both reply, “I don’t know.”

They are asked a third time, “What about now?”

They both reply, “Yes!”

Under what shape has the prize been hidden?

Enjoy solving those puzzles. Staying with the theme, let’s end this post with a logic joke of sorts…

Sam comes home from the grocery store with twelve gallons of milk. Pam asks, “Why’d you buy so much milk?”

“Because before I left, you told me to buy a gallon of milk, and then you said, ‘If they have eggs, buy a dozen.’ And they had eggs.”

Pam shakes her head at Sam’s response. But then she notices he hasn’t bought anything else and asks, “Where are the rest of the things we needed?”

“Remember how you told me to put ketchup on the list?” replies Sam.

“Yeah. So?”

“So I put ketchup on the list, but then I couldn’t read the other items!” Sam says. “But I remembered the eggs!”

### Interview: Kerry Schultz, Saucon Valley High School

It sounds like the start of a math joke: Did you hear about the mathematical economist who became a teacher? The punch line is, “Her name is Kerry Schultz,” which, admittedly, isn’t very funny, but it’s absolutely true. Kerry used to work as an analyst for JPMorgan Chase but now teaches calculus and computer science at Saucon Valley High School in Hellertown, PA.

Seniors selected Kerry to be the faculty speaker at the 2021 SVHS commencement. During her speech, Kerry gave the graduates some sage advice. “When you get the choice to sit it out or dance, I hope you dance,” she told them, drawing from Lee Ann Womack’s 2000 hit. She also referenced one of my favorite publications:

After a difficult last two years, I promised to avoid the pandemic topic, and I wanted to be sure to keep this on the lighter side. So I brought my favorite book,

Math Jokes 4 Mathy Folks. I’m pretty sure this book is the reason I was chosen to speak tonight.

As it turns out, Kerry and I have more in common than just our love of math jokes. We both have twins. (In fact, she has twin 10-year-old daughters and a 9-year-old son. I’ve never been good with numbers, but I’m pretty sure that means that, at one point, she had three kids under age two in her house. My goodness!) Like my wife and me, Kerry and her husband both love math jokes, math memes, and all things numeric. The two of them used to play The Game of 24 on long car rides; my wife and I played Dollar Nim with our kids.

The comparison ends when it comes to exercise, though. I’m active, but Kerry runs at 4:30 a.m. most mornings, because she spends her afternoons taking kids to their various activities (soccer, baseball, football, swimming, cross country, and golf). She’s finished 10 marathons and hopes to run the Chicago Marathon in 2022. (I’ve also never been asked to speak at a graduation. Yet.) In her limited downtime, Kerry enjoys traveling or reading a good book on the beach.

I caught up with Kerry when a friend forwarded her picture from the Lehigh Valley Press. As it turns out, Kerry has a fascinating story about her path to education.

**Can you tell us how you got to Saucon Valley?**

I went to college with the hopes of becoming a math teacher, but others convinced me that I was “too smart” for that. So I graduated from Colgate University in 2000 with a degree in mathematical economics, and I went to work as an analyst at JPMorgan Chase in midtown Manhattan. Some might say it was glamorous, with lots of fancy meals and car service home every night — but I hated pretty much everything about it.

I was working in midtown on September 11, 2001, and my brother was working on the 90th floor of the South Tower. He was extremely lucky to escape the attack on the World Trade Center, but many of his co-workers did not. This was a pivotal day for me. I realized life was way too short to spend it doing something I hated. In the following weeks, I began looking for graduate programs in mathematics education. In 2002, I enrolled at Lehigh University, and in 2004, I began teaching middle school math in the Saucon Valley School District.

**What is your current role?**

I taught middle school math for five years while obtaining my principal certification from Lehigh. I then became a Coordinator of Academic Services and later an Instructional Coach for Math, all in Saucon Valley. In 2015, I requested a return to the classroom and was thrilled to be asked to teach high school math. I have been in the high school for five years now, teaching Algebra 2, Pre-Calculus, Calculus, and AP Computer Science Principles. I absolutely love my job!

**And if you weren’t teaching math?**

I’d love to be a professional athlete or work in an athletic setting — maybe a statistician for the NY Mets!

**What’s your favorite thing about teaching?**

The kids! It’s important to get to know each and every one of my students as best I can. Nothing is better than knowing I have made a difference in the life of a student. Sometimes it’s by helping them solve a difficult problem, sometimes by building their confidence, sometimes by showing up to their lacrosse game, and sometimes it’s simply by being there when they’ve had a rough day. The relationships I’ve built with students over the years are by far the most important thing to me.

**What is your favorite math joke(s)?**

My oldest favorite has to be, “What did 0 say to 8?” Now that I teach computer science, I really like, “There are 10 kinds of people: those who understand binary, and those who don’t.”

**Which math joke(s) do your students like best?**

The jokes that poke fun at mathematicians tend to be class favorites. “What do you call a beautiful woman on the arm of a math graduate student? A tattoo.” And, “What’s the difference between a large pizza and a mathematician? A pizza can feed a family of four.”

**What’s the funniest thing you’ve ever said during class? Or maybe, what’s the funniest thing that’s ever happened in class?**

This is definitely a case of “you had to be there,” but one year I had an Honors Calculus student convince me, with the help of her classmates, that after high school she was going into the family business of designing chairs. I was skeptical at first, but they were so believable and had so many details, they had me convinced for days. They told me that her family designed chairs for Nicki Minaj, and to this day I can’t hear that name without dying of laughter.

**What is your favorite area of mathematics? Is that also your favorite thing to teach?**

I don’t have a personal favorite, but I definitely love teaching calculus. Calculus is a great challenge for many students, but most of them are willing and able to put forth the effort to succeed. I enjoy helping students work through the difficulties, and I’m just as excited as they are when it all starts to make sense. It is fantastic when you see the light bulb go on!

### There Are Two Types of People…

It’s estimated that there are 7.9 billion people in the world, and counting. But in many ways, it’s fairly easy to divide us all into two types.

There are two types of people:

- Those who think the world can be divided into two types of people.
- Those who don’t.

The earliest known usage of the two-types format was by Mark Twain:

There are basically two types of people: people who accomplish things, and people who claim to have accomplished things. The first group is less crowded.

The potential origin of the two-types meme, as we know it today, may have been this ubiquitous math and computer science joke:

There are 10 types of people in the world: those who understand binary, and those who don’t.

A modification of that joke has appeared more recently for the uber-geeks:

There are 10 types of people in the world: those who understand ternary, those who don’t, and those who mistake it for binary.

Physicist C. N. Yang, who won the Nobel Prize in 1957, is credited with this version:

There are two types of math books: those you cannot read beyond the first sentence, and those you cannot read beyond the first page.

Two of my favorites were included in **More Jokes 4 Mathy Folks**:

There are three types of people: positive, negative, and relative.

There are two types of people: those who are wise, and those who are otherwise.

The number of modifications to the format are nearly infinite. To create your own, choose the number of things you wish to compare; choose the type of things you wish to compare; describe that number of things, making sure that two of them are diametrically opposed, as to cause an incongruous and humorous result; if possible, be self-deprecating in one of the descriptions; and finally, determine if you want it in paragraph form or as a bulleted list. For instance,

There are two types of math jokes:

- Those that are funny.
- Those that have appeared on this blog.

See? It’s not hard. Now you try. The following mathy examples can serve as inspiration.

There are three things I hate:

- People who can’t do simple math.
- Irony.

There are three things I hate:

- Bulleted lists.
- Lazy people.

There are two kinds of statistics:

- Those you look up.
- Those you make up.

There are three kinds of lies:

- Lies.
- Damned lies.
- Statistics.

There are two kinds of people. Avoid both of them.

There are two kinds of people:

- Those you want to drink with.
- Those who make you want to drink.

On the web, you’ll find all manner of visual adaptations of the meme.

There are two types of people:

There are two types of people:

And finally, there are two types of bloggers:

- Those who would write a blog post about the world containing two types of people.
- Those who would Google it first to see that there about 24,000,000 results for “there are two types of people.”

### Mathy One-Liners

To keep my edge, I read joke books and watch comedians. I modify the jokes I read and hear to fit my particular needs and, sometimes, I just steal a joke outright. I’d feel bad about doing this if I profited from it, but there is little to be gained by dropping a one-liner at a neighborhood happy hour.

I just finished *1001 One‑Liners and Short Jokes* by Graham Cann. It compensates with quantity what it lacks in quality. Although most of the jokes are not good — and many rely on British English, and others reference British culture, so they’re lost on me — there are more than a few chestnuts in the mix. I used this modification of one of his jokes while having dinner with my in-laws recently:

I don’t like coffee. It’s just not my cup of tea.

It garnered guffaws from my mother-in-law and groans from my sons, so it had the intended effect.

Another joke from the book is mathematical:

When I was two, I was really anxious because my age had doubled in just one year. I thought, “If this keeps up, by the time I’m six, I’ll be 90!”

It’s a terrible joke, not least because I’m unaware of any toddler concerned about their age. But more importantly, it’s wrong. If your age doubled from one to two in a year, then it would double to four by age three, to eight by age four, to 16 by age five, and to 32 by age six. Graham Cann clearly hasn’t studied exponential growth.

The following are other mathy jokes from the book, most of which I’ve modified at least slightly.

- I took an algebra test at school yesterday. My kleptomania is getting out of hand.
- For the three o’clock race, I backed a horse at ten to one. It came in at a quarter past four.
- One of every four frogs is a leap frog.
- My gun is made from a dozen pigs. It’s a 12-boar.

- Thirty percent of car accidents in Sweden involve a moose. I say it’s time that we stop letting moose drive. (For the record, that statistic is likely fabricated. It’s estimated that there are 4,500 car accidents involving moose every year, but there are far more than 15,000 car accidents annually.)
- Did you hear about the constipated accountant? He tried to work it out with a pencil — but he couldn’t budget.
- To the man who invented zero: Thanks for nothing.
- Statistically, six of seven dwarfs are not Happy.
- I, for one, like Roman numerals.
- If every human in the world laid down end‑to‑end along the equator, most of them would drown.
- Ninety-nine percent of politicians give the rest of them a bad name.
- Light travels faster than sound, which is why some people appear bright until you hear them speak.
- I tried to change my password to “14 days,” but my computer said it was too week.

There were 288 others that I chose not to share, because they were two gross.

### Happy as L!

On Wednesday, I’ll complete my 50th trip around the Sun. To celebrate, my friend Kris sent me a card with a wonderful Roman reminder of my age:

Thanks, Kris!

Here are two relatively easy math problems associated with my birthday:

- On Wednesday, how many days old will I be?
- What are the four positive integer factors of the answer you got to Question 1? (Hint: One of the factors is the number of
**weeks**old that I’ll be.)

I recently wrote a book called One Hundred Problems Involving the Number 100. To celebrate my 50th birthday, here are ten problems involving the number 50:

- There are 50 puppies to be adopted at a shelter, and 98% of them are hounds. How many hounds must be adopted so that 90% of the remaining puppies are hounds?
- Let A = 1, B = 2, …, Z = 26. Find two common English words for which the product of the letters is 50.
- What’s the least possible product of two prime numbers with a sum of 50?
- While finding the sum of the numbers 1‑10, I got distracted and omitted some numbers. The sum of the remaining numbers was 50. How many different sets of numbers could I have omitted?
- The square numbers are 1, 4, 9, 16, …, and the non-square numbers are 2, 3, 5, 6, 7, 8, 10, 11, and so on. What is the 50th non-square number?
- Choose three numbers so that one number is selected in each row and each column. What’s the sum of the three numbers?

- A two-player game is played on this number rack with five rows of 10 beads. One player chooses to be Odd, the other Even. The players take turns. On each turn, a player may slide one, two, or three beads from the middle to the side of the rack. Beads moved to the side cannot be moved again. When all beads have been moved, the Odd player earns one point for each row with an odd number of beads on each side, and the Even player earns one point for each row with an even number of beads on each side. The player with the most points wins. What is the optimal strategy, and who should win?
- How many people must be present to have a probability of 50% that two of them will share a birthday?
- Insert only addition and subtraction symbols to make the following equation true:

9 8 7 6 5 4 3 2 1 = 50

- What’s the area of the square? (Inspiration from Catriona Agg, both for the puzzle and for the reduction in words.)

Answers will be posted on my birthday — St. Patrick’s Day! Stop back on Wednesday!

### Change the Vowel

The following puzzle contains a clue within each clue. The answer, of course, fits the clue, but each answer is also one of the words within the clue with its vowel sound changed. For instance, the clue “the distance from the top of your hat to the sole of your shoes” contains the word *hat*, and if you change the vowel sound from a short *a* to a long *i*, you get *height*, which fits the description.

As always, there’s a catch. Every answer to the clues below is a mathy word.

- The number of permutations of three different colored socks.

- This value is the same for 3 + 1 and 2 + 2.
- Do this with two odd numbers and you’ll get an even number.
- Three hours before noon.
- You may fail to correctly expand (
*a*+*b*)(*c*+*d*) if you don’t remember this mnemonic. - One represents this fractional portion of toes on the hoof of a deer.
- The last element of a data set arranged in descending order.
- The measure of central tendency made from the most common data points.
- The number of contestants ahead of third place if there’s a tie for first place.
- If the leader is forced to drop out of a race, the runner-up takes over this place.
- The square root is needed to calculate the length of the hypotenuse in this type of triangle.
- The graph of the declination of the Sun during a year can be approximated by this type of curve.

Answers

- six

- sum
- add
- nine
- FOIL
- half
- least
- mode
- two
- first
- right
- sine

### 100 Problems for the 100th Day of School

In May 2020, I delivered a webinar titled *One-Hundred Problems Involving the Number 100*. Every problem included a problem that somehow used the number 100, maybe as the number of terms in a sequence, the length of a hypotenuse in inches, or the number of digits written on a whiteboard. At the end of the webinar, NCTM President Trena Wilkerson challenged me to create a collection of 100 problems for which the answer is always 100.

So, I did.

My process was simple. I just wrote problem after problem with little concern for topic or grade level. Some of the problems were good; others were not. Some of the problems were difficult; others were easy. Some of the problems required knowledge of esoteric math concepts; others required nothing more than the ability to add and subtract. But I wrote 100 problems, then I reviewed them and deleted those that weren’t good enough. Then I wrote some more, and cut some more, and so forth, until I finally had a collection of 100 problems that were worthy.

And I’m going to share all of them with you in just a minute. But first, a math problem for which the answer is** not** 100.

As I said, I wrote the problems as they came to me, not necessarily in the order that I’d want to present them. But to keep track of things, I numbered the problems 1‑100. Since they were in the wrong order, I had to rearrange them, meaning that Problem 92 in the draft version eventually became Problem 1 in the final collection; Problem 37 became Problem 2; Problem 1 became Problem 3; and so on. You get the idea. So, the question…

You have a collection of 100 items numbered 1‑100, but the items are out of order. When you arrange the items in the correct order, how many would you expect to be labeled correctly? (Less generically, how many of my problems had the same problem number in the draft version and the final collection?)

The solution to that problem is more beautiful than I would have initially guessed. Have fun with it.

Without further ado, here is the collection:

**Problems with 100 as the Answer**

My goal was to release these problems in time for the 100th day of school, which most schools celebrate in late January or early February. I hope this collection reaches you in time. And I present the problems one per page, so you can decide which one(s) you’d like to use with your students. If you teach algebra, then perhaps you’ll print and share Problems 46 and 53; if you teach third grade, perhaps Problem 2 will be more appropriate. But the problems cover a wide range of topics and difficulty levels, so feel free to use whichever ones you like. (Be forewarned, though. The answer to **every** problem is 100, so unless your students are absolutely terrible at identifying patterns, you probably won’t want to share every problem with them. At least, not at the same time. I’m sharing this collection in time for the 100th day of school, but feel free to use any problem at any time.)

My favorite problem in the collection? I like Problem 47:

Above the bottom row, each number in a square is the sum of the two numbers below it. What value should replace the question mark?

Feel free to let me know if you or your students have a favorite.

p.s. – Bonus points if you can identify the origin of the 100 in the image at the top of this post.

### My 0.04 Seconds of Fame

In 2017, I attended the International KenKen Championship and filmed the final round, which I posted previously on this blog. But filmmakers Louis Cancel, Chris Flaherty, and Daniel Sullivan were there that day, too, and their cameras were significantly more sophisticated than my Samsung S8. Their footage of the competition, coupled with myriad interviews of competitors, organizers, and the inventor of KenKen himself, Tetsuya Miyamoto, has resulted in a new documentary, * Miyamoto and the Machine*, recently released by

*The New Yorker*. It tells the story of KenKen’s origins and attempts to answer the question, “Can a computer make puzzles as beautiful as those created by humans?”

Many aspects of the film will appeal to kenthusiasts, but my favorite moment occurs at 17:14. Competitor Ellie Grueskin is competing in the finals, and just over Ellie’s left shoulder is a barely visible, occasionally funny, middle-aged math guy holding — wait for it — a Samsung S8!

Yep, that’s me. I’m a star!

You have to ask yourself, what kind of monster would author such a shamelessly self-promotional post and not even provide one KenKen puzzle for the reader to enjoy? Definitely not me, so here you go.

After you solve the puzzle, definitely watch * Miyamoto and the Machine*. It’s 25 minutes well spent.

### Mathy Zoom Backgrounds

Do you seek the admiration of your colleagues or the respect of your students?

Do you wish to create the illusion that you’re funny and cool?

Do you long to be the envy of your virtual social circle?

Unfortunately, you’re reading a math jokes blog, which means there may not be much hope for you. But a possible start may be to download some of the math joke backgrounds below for your next online meeting. I’ve been using them for the past few weeks, and I don’t think it’d be an overstatement to say that I’m now the envy of the internet. I mean, I’ve got a face for radio, but you have to admit that I look pretty fantastic when there’s a math poem above my head and equations on either side of it:

And guess what? You can look that cool, too!

To use any of the images below, simply right click and “Save Image As…,” then install them as virtual backgrounds (Zoom, Google Meet). If you’d like a better look at any of them before deciding if they’re worth valuable memory on your laptop, just click on an image to open it full screen.

### Mathy Portmanteaux

The term *portmanteau* was first used by Humpty Dumpty in Lewis Carroll’s *Through the Looking Glass*:

Well, ‘slithy’ means “lithe and slimy” and ‘mimsy’ is “flimsy and miserable.” You see, it’s like a portmanteau — there are two meanings packed up into one word.

Interestingly, the word *portmanteau* itself is also a blend of two different words: *porter* (to carry) and *manteau* (a cloak).

Portmanteaux are extremely popular in modern-day English, and new word combinations are regularly popping up. Sometimes, perhaps, there are **too many** being coined. In fact, one author refers to these newcomers as *portmonsters*, a portmanteau of, well, *portmanteau* and *monster* that attempts to capture how grotesque some of these beasts are. An abridged list of portmonsters would include *sharknado*, *arachnoquake*, *blizzaster*, *snowpocalypse*, *Brangelina*, *Bennifer*, *Kimye*, *Javanka*, *fantabulous*, and *ridonkulous*.

Portmanteaux seem to proliferate most easily in B-movie titles, weather, and celebrity couples, but the world of math and science is not free from them. Here are a few mathy portmanteaux, presented, of course, as equations.

**ginormous** = *giant* + *enormous*, really big

**guesstimate** = *guess* + *estimate*, a reasonable speculation

**three-peat** = *three* + *repeat*, to win a championship thrice

**clopen set** = *closed* + *open set*, a topological space that is both open and closed

**b****it** = *binary* + *digit*, the smallest unit of measurement used to quantify computer data

**pixel** = *picture* + *element*, a small area on a display screen; many can combine to form an image

**voxel** = *volume* + *pixel*, the 3D analog to pixel

**fortnight** = *fourteen* + *night*, a period of two weeks

**parsec** = *parallax* + *second*, an astronomy unit equal to about 3.26 light years

**alphanumeric** = *alphabetical* + *numeric*, containing both letters and numerals

**sporabola** = *spore* + *parabola*, the trajectory of a basidiospore after it is discharged from a sterigma

**gerrymandering** = *Elbridge Gerry* + *salamander*, to draw districts in such a way as to gain political advantage (In the 1800’s, Governor Elbridge Gerry redrew districts in Massachusetts to his political benefit. One of the redrawn districts looked like a salamander.)

**megamanteau** = *mega* + *portmanteau*, a portmanteau containing more than two words, such as DelMarVa, a peninsula that separates the Chesapeake Bay from the Atlantic Ocean and includes parts of Delaware, Maryland, and Virginia

**meganegabar** = *mega* + *negative* + *bar*, the line used on a check so that someone can’t add “and one million” to increase the amount

(By the way, when Rutgers University invited *Jersey Shore* cast member Snooki Polizzi to speak to students on campus in 2011, they paid her $32,000, which is $2,000 more than they paid Nobel and Pulitzer Prize winning author Toni Morrison to deliver a commencement address six weeks later.)