Archive for August, 2011

QRack the CODE on this Qrossword

My eighth-grade English teacher told us, “You must learn the rules of grammar. They are very important, and you can not feel comfortable breaking them until you thoroughly understand them.” I believe this philosophy also applies to crossword puzzles. Typically, crossword puzzles must be constructed so that the grid is rotationally symmetric. Recently, I created a crossword puzzle, but I had a very good reason for violating the symmetry rule, so I did.

I now present the puzzle for your enjoyment. Enjoy.

QRack the CODE Qrossword Puzzle

Many mathy folks enjoy crossword puzzles. But in case you’re visiting just for the jokes and have no interest in crossword puzzles, here are a couple of jokes for you (crossword-related, of course).

A gentleman heard a rumor that the Pope might be taking the same flight to Italy. He thought, “This is great! I’ve been a Catholic my whole life, and I might get to meet the Pope!”

The man takes his seat. A few minutes later, the Pope sits in the seat next to him. Shortly after take-off, the Pope pulls out a crossword puzzle. After a few minutes, the Pontiff turns to the man and says, “Excuse me, sir. Do you know a four-letter word for ‘woman’ that ends U-N-T?”

The man thought for a few seconds. “Your Holiness,” he said, “I think the word you’re looking for is AUNT.”

“Oh, of course,” said the Pope. “Do you have an eraser?”

The following crossword joke could easily be modified for a plane geometry class.

Showing his map of attractions to a local, the tourist said, “Sir, I understand that a shrine to the creator of the crossword puzzle is near here. Do you know how to get there?”

The local pointed to a spot on the map. “You’re here,” he said. “The shrine is three down and four across.

August 31, 2011 at 12:36 pm Leave a comment

A Puzzle of Few Words

HangmathWinston Churchill once said, “The short words are the best, and the old words best of all.”

Today’s post contains several puzzles, the answer to each is a short word, and at least one of the answers is a very old word, indeed.

But first, a joke about words and math:

Teacher: Use the word announce in a sentence.
Student: Yes, ma’am. Announce is one-sixteenth of a pound.

The first puzzle is about the game Hangman.

In the game of Hangman, the first player thinks of a word and reveals the number of letters. The second player then guesses letters. If a guessed letter is in the word, the first player reveals the position(s) of every occurrence of that letter within the word. If the guessed letter is not in the word, then the second player receives a body part for a man who is hanging from a gallows (hence the name, Hangman). If the entire man is completed before the word is guessed, the second player has been hanged and loses.

Various versions of the game use hangmen with different numbers of body parts. The number of parts typically ranges from 7 to 13. The Hangman game at www.playhangmangames.net contains 7 body parts, and my sons play a version with 11 body parts:

Hangman - 11 Parts

Jon McLoone at the Wolfram Blog ran a simulation to determine the best words for the game of Hangman. Of course, you could just click on that link, but it might be more fun to think about the following question before you do:

What is the best word to use when playing Hangman? And does the best word change, depending on how many body parts are in the version you play?

Surprisingly, McLoone found that there is a single best Hangman word, for any game with 8 to 13 body parts. A strong hint is included at the bottom of this post.

The second puzzle is a product value puzzle, in which the product value of a word is equal to the product of the value of the letters. Specifically,

Assign each letter of the alphabet a value as follows: A = 1, B = 2, C = 3, and so on. The product value of a word is the product of its letters. For instance, the word CAT has a product value of 60 because C = 3, A = 1, T = 20, and 3 × 1 × 20 = 60.

One fun puzzle based on this set-up:

Find an “acre” word, which is a word with a product value of 43,560, the number of square feet in an acre.

The (unique) answer happens to be one of my favorite English words.

Turning this idea around, another variation is as follows:

Find a four-letter English word with the largest possible product value.

According to Scrabble Australia, there are 16,739 four-letter words. However, many of those would not be considered common — such as euoi (an impassioned cry), nabk (berries you’ve never tasted, from a plant you’ve never seen), and zizz (a short sleep). The last of these examples has an impressive product value of 263 = 17,576, but it’s not the highest. Not even close, in fact; its product value is only 7.8% of the largest product value for a four-letter word.

You can explore similar puzzles with the Product Value Calculators on the MJ4MF website.

Hints for all three puzzle appear below the following joke about words and math:

A boy was told to write an essay about his favorite subject. He wrote, “I really love math,” and turned in his essay. Returning his paper, the teacher said, “Sorry, your essay needs to be at least 100 words.” So he wrote, “I really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really, really love math.”

Hints

The best Hangman word (according to McLoone’s analysis) has a product value of 6,760.

The defintion of the acre word is “alternating layers of silt or clay, usually of contrasting colors, that comprise an annual cycle of deposition in a body of still water.” That doesn’t help? Then just enter 43,560 into the second form on the Product Value Calculators page.

And the four-letter word with the largest possible product value? It’s an anagram of the mythological river that divides Earth and the Underworld, as well as an anagram of the 70’s rock band that sang Come Sail Away and Mr. Roboto.

August 30, 2011 at 8:20 am Leave a comment

Dude, You’re Such a Cube

Today’s a good day to work in a cube farm, to hang out with a dorky friend so square that he’s a cube, or to cube out your glass with some lemonade and enjoy one last, lazy summer afternoon. We’re 53 years from the aweseomely cubic date of 8/27/64, but it’s still pretty cool that today’s month is 23 and the date is 33.

If you do enjoy a glass of lemonade today, be sure to keep it cold with an (ice)3.

Here’s a tree that’s appropriate for today:

Cube Root Tree

If you’re in the path of Hurricane Irene, please don’t stand under this tree! (Seriously, be safe today.)

August 27, 2011 at 8:21 am Leave a comment

Should Math Be Taught in Schools?

If you haven’t seen it, check out this video in which the 2011 Miss USA delegates were asked, “Should evolution be taught in schools?” Sadly, this is real.

Math In Schools

On a lighter note, a satirical video was created in which (fake) Miss USA delegates were asked, “Should math be taught in schools?” Happily, this is not real… though I fear it might reflect the actual sentiment of many folks.

August 24, 2011 at 12:32 pm 1 comment

Stupid Game

Question Mark“Let’s play a game,” a colleague said, bounding into my office. “I ask you a question, and if you don’t know the answer, you pay me $5. Then you ask me a question, and if I don’t know the answer, I pay you $5.”

“Sounds like a stupid game,” I said.

“Fine,” he huffed, and stormed away.

A half-hour later he was back. “What if you pay me $5, but I pay you $10?” he asked.

“I got work to do. Still not interested.”

He left, but then he came back 15 minutes later. “You pay me $5, and I pay you $50?”

The game may be stupid, but I’m not.

“Okay, fine,” I said.

“What are the Sylow theorems?” he asked.

I’m not a fan of finite group theory, and I don’t know the answer. Nor do I care. I reached into my wallet and handed him $5. “Okay, now my question,” I said. “What has three teeth and runs around in a circle all day?” I asked him.

He gave me a puzzled look, then left for his office. He first checked all of his reference books; nothing. He then tried every conceivable search in Google; nada. In desperation, he queried some of our colleagues; zilch. Frustrated, he returned an hour later, and stuck $50 in my face. I took the money without looking up from my computer and said, “Now leave me alone. I have work to do.”

“I’m not leaving yet!” he insisted. “What’s the answer?”

I reached into my wallet and handed him another $5.

August 22, 2011 at 9:48 pm Leave a comment

Why Are Math Jokes Funny?

There’s a demotivational poster that reads:

MATH JOKES
If you get them, you probably don’t have friends.

Perhaps.

You may not have friends, but if you laugh at a math joke, then you have something in common with the person who wrote, forwarded, or posted the joke. Is that person a friend? Maybe not, but she is at least a kindred spirit.

Harvey Penick wrote the book And If You Play Golf, You’re My Friend. For our crowd, if you laugh at math jokes, then you’re my friend.

This got me to thinking about what makes a math joke funny and why we enjoy them. I found my favorite answer to this question in the comments section of a webcomic. One comment suggested that part of the reason we find math jokes funny is that we “like inside jokes, probably because they exclude other people.” But a response to that comment suggested that shared dorkiness may be the reason:

It’s not that you laugh and think, “Neener, neener — I get it, and you don’t.” It’s that you realize you are not alone, and that sensation is bliss.

The mention of bliss reminded me of a joke…

Would you rather have eternal bliss or a ham sandwich?
A ham sandwich, because nothing is better than eternal bliss, and a ham sandwich is better than nothing.

If you laughed at that joke, take comfort in knowing that you’re not alone and that you’re my friend.

August 20, 2011 at 5:42 am Leave a comment

Eddie Gaedel, a Man of Stature

Sixty years ago today, baseball player Eddie Gaedel stepped to the plate for the only at-bat of his major league career. Standing just 3’7″ tall, he drew a walk on four straight pitches.

Why mention this on a math jokes blog? Gaedel’s uniform number was 1/8.

This reminds me of a math question that my friend Harold Reiter likes to use to start a class discussion about size of numbers.

Which of the following is the largest fraction?

1/2

1/4

1/6

1/8

It also reminds me of the priest who tells his congregation that he understands how difficult it is to tithe. “If you can’t afford to give 1/10 of your salary to the church,” he tells them, “then just give 1/9 or 1/8.”

Officially, Gaedel had 1 base‑on‑balls (BB) and 0 at-bats (AB). In baseball, a plate appearance does not offically count as an at-bat if the player is walked. This gave Gaedel an on-base percentage (OBP) of 1.000, the highest possible. As it turns out, he’s not the only player with an OBP of 1.000; nearly 30 others have accomplished the same feat.

The official formula for on-base percentage is

OBP = (H + BB + HBP) ÷ (AB + BB + HBP + SF)

where

  • H = hits
  • HBP = hits-by-pitch
  • SF = sacrifice flies

An interesting question is:

How can a player have a higher batting average than on-base percentage?

Though rare, it occasionally happens when a player has a relatively low number of at‑bats with few walks and several sacrifice flies. For instance, a player with 1 hit in 2 at-bats with a sacrifice fly would have a batting average of 0.500 and an on-base percentage of 0.333.

August 19, 2011 at 12:30 am Leave a comment

Good Jokes and Great Problems

You may or may not agree with the following contention. (Typing that sentence made me think, “The law of the excluded middle either rules or does not rule.”)

A good joke is like a good math problem…
You don’t expect the punch line,
And you have to think to figure it out.

One problem for which this maxim holds is Paper Pool. The problem can be found in the unit Comparing and Scaling: Ratio, Proportion, and Percent, which appears in the middle-grades Connected Math Project curriculum. It also appears in 1000 Play Thinks by Ivan Moscovich as Playthink 833: Reflected Balls.

The rules for Paper Pool are rather straightforward. Create a rectangular pool table with integer dimensions that has a pocket at each of the four corners. Then following the rules below, in which pocket will the ball land, and how many hits will occur?

  • The lower-left corner is always corner A, and the labeling continues counterclockwise with B, C, and D.
  • The ball always starts in corner A.
  • The ball is hit with an imaginary cue (a stick for hitting a pool ball) so that it travels at a 45° diagonal across the grid.
  • If the ball hits a side of the table, it bounces off at a 45° angle and continues its travel.
  • The ball continues to travel until it hits a pocket.

For example, a 5 × 3 table is shown below. Following the rules above, the ball will land in Pocket C after 8 hits. (Note that the initial strike by the cue stick at A and reaching the pocket at C are both counted as hits. You can disagree if you like, but using these conventions will make it easier to see some patterns.)

PaperPool - 5 x 3 Table

How many hits do you think will occur on a 5 × 4 table? Go ahead, take a second to think about it…

If you predicted that 9 hits would occur, you’re right:

Paper Pool - 5 x 4 Table

You can now see a pattern begin to emerge:

5 × 3 → 8 hits
5 × 4 → 9 hits

So, then, how many hits will occur on a 5 × 5 table? Given the pattern above, it would be reasonable to think that 10 hits would occur. But that would be wrong…

Paper Pool - 5 x 5 Table

Like the punch line to a good joke, this result was unexpected. At this point, most people want to figure out what’s going on.

If you’re like most people, then you can explore Paper Pool using the Online Paper Pool Tool at Illuminations.

Finally, here’s a joke that really does have an unexpected punch line.

Will you be able to attend the 2012 International Convention of the Barbershop Harmony Society in Portland?  You really should try to make it — it’s bound to be a harmonic function

Ouch.

August 15, 2011 at 9:46 am Leave a comment

MJ4MF Featured at NYTimes Numberplay Blog

A few weeks ago, I wrote about Dollar Nim, a number game that my wife invented for our boys while on a long car ride. Well, some folks at the NY Times liked the game so much, it’s the puzzle they featured on the Numberplay blog this week. Applause to Numberplay blogger Pradeep Mutalik, who posted an extension to the game that I look forward to investigating.

(Note: My previous post about Dollar Nim is inactive while this article runs at NY Times.)

August 8, 2011 at 11:32 pm 1 comment

Almost End of Summer

This is the point of the summer that, when I was a classroom teacher, I would start to panic, realizing that the start of the school year was just around the corner. “Oh, my goodness, they’ll be back in three weeks!” Now that I have an office job and kids of my own, it’s the point of the summer when I start to think, “Thank goodness, they’ll be back in school soon!”

For the teachers out there, here are a few jokes to ease you into the classroom…

Teacher: How far are you from the correct answer?
Student: Three seats, sir.

Teacher: Did your parents help you with these problems?
Student: Nope! I got them all wrong by myself.

Teacher: If I had five coconuts and gave you three, how many would I have left?
Student: I don’t know.
Teacher: Why not?
Student: Because all of our practice problems were about apples and oranges!

Teacher: If you got $10 each from 10 people, what would you have?
Student: A new bike!

And a joke that isn’t about the classroom, but was told to me by a high school student in a classroom:

What do you get when you cross a bridge with a bike?
The other side.

(Though maybe “bridge bike sine theta” is a better answer?)

August 7, 2011 at 2:54 pm 1 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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