## Archive for July, 2010

### Radio Interview: Create a Fun Math Experience

Tonight, I had the privilege of being a guest on Teacher Talk radio, hosted by Teacher Jen. We talked about creating fun experiences in the math classroom, and guess what? I told some jokes. We also talked about appropriate uses of humor, fun things to do in the classroom, and the old adage, “Never smile until after Christmas!”

You can listen to the full interview at Teacher Talk Radio.

### The Cost of Good Grades

A quick joke that I just heard:

A math professor was giving an exam to his students. When the test ended, the students handed in their tests. The professor noticed that one of the students had attached a $100 bill to his test with a note that read, “One dollar per point.”

The next class period, the professor returned the tests to students. The student got back his test — and $64 change.

### Movie: Fermat’s Room

I’m not sure that the indie film Fermat’s Room deserved to win four awards or deserved a nomination for “Best Film” at the Sitges International Film Festival, but it’s got enough gems to keep mathy folks entertained for almost 90 minutes.

Take, for instance, this great line:

The more you study logic, the more you value coincidence.

In a moment, I’ll tell you about all the great math problems within the film. But first, let me tell you a little about the movie itself.

The general idea (without being a spoiler) is this: Four mathematicians are trapped in a shrinking room. Every so often, a math puzzle appears on a PDA, and they have one minute to enter the correct answer. If they take longer than a minute, the room starts shrinking — literally. Behind each wall is a hydraulic press that pushes toward the center until the correct answer is entered. While working out these riddles, there are two greater puzzles that they are attempting to solve — who would have done this, and how can they escape?

My favorite scene is when the young, brash, theoretical mathematician and the middle-aged, stoic, applied mathematician think they may have found a way to stop the hydraulic presses. “Will it work?” asks the theoretical mathematician.

“The only way to find out is to do it,” says the applied mathematician.

Upon hearing this, the young mathematician starts writing equations on a piece of paper, attempting to prove (theoretically) that their solution will work. The applied mathematician, who has already started to implement the solution, shakes the theoretical mathematician’s shoulder, as if to say, “No, really, we need to try it and see if it works, not just prove that a solution exists.”

It’s a fantastic and not-so-subtle commentary on the tension between theoretical and applied mathematicians. I laughed out loud.

But it’s got more than just great lines. It contains a treasure trove of famous math puzzles. I’ve listed several of them below — without context, so as not to spoil the movie; and without solutions, so as not to spoil your fun in solving them. Enjoy!

- En que orden estan los siguentes numeros?
**5, 4, 2, 9, 8, 6, 7, 3, 1**

(Note: It’s a huge hint that this problem is presented in Spanish. If presented in English, the order of the numbers would be different, and the problem would read as follows: What is the order of the following numbers?**8, 5, 4, 9, 1, 7, 6, 3, 2**) - Three boxes contain marbles. One box contains red marbles, another contains blue marbles, and the third contains a mixture of red and blue marbles. The boxes are labeled “Red,” “Blue,” and “Mixture,” but none of the boxes contains the correct label. What is the least number of marbles you could remove to know the contents of each box?
- You have two egg timers, one that measures four minutes and one that measures seven minutes. How can you use them to measure exactly nine minutes?
- (This one’s my favorite from the movie. I originally read it in a Martin Gardner book.) A professor tells his students, “I have three daughters, and the product of their ages is 36. How old are my daughters?”

His students work on the problem for a few minutes, then a woman in the class says, “I’m sorry, professor, but that’s not enough information to solve the problem.”

“Ah, yes,” he says. “I should have told you that the sum of their ages is equal to my house number.”

“I’m sorry, sir,” she says. “That is still not enough information to solve the problem.”

The professor asks, “Will it help if I tell you that the oldest one plays piano?”

“It will,” says the woman. “I now know the ages of your daughters.”

Based on the information, can you determine the ages of the professor’s daughters?

### Good Day for a Math Joke

I believe that every day is a good day for a math joke, but Drew at www.toothpastefordinner.com apparently thinks I’m in the minority…

Though it’s not math-related, the following is my favorite TFD joke. I appreciate artists who recognize the irony in a situation and are willing to make fun of themselves.

### What’s in a Name?

The product value of a word can be calculated as follows:

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.

During a recent webinar, I introduced participants to my collection of Product Value Puzzles. The following product value puzzle is credited to John Horton Conway:

Find an English word with a product value of 3,000,000.

Finding the solution is up to you. But I will give you some good news — there’s not a unique answer. In fact, there are two English words that satisfy the conditions of the problem.

What most folks found interesting, though, are the Product Value Calculators on my web site. With these two tools, you can:

- Enter an integer value, and the first calculator will return all words in the English language whose product value equals the number you enter.
- Enter a word, and the second calculator will return the product value.

One of the participants during the webinar said that her middle school students, when confronted with any type of math puzzle involving words, will first apply the rules of the puzzle to their name. Apparently, I’m not much different from a middle school kid, because that’s what I did, too. Turns out, my name has a product value of 1,710,720:

Patrick = 16 × 1 × 20 × 18 × 9 × 3 × 11 = 1,710,720

So, then I wondered, “Are there any other words that have a product value of 1,710,720?” Of course, I could have used the Product Value Calculators to find the answer, but that would have been unsatisfying. With a little trial-and-error, I found that blackboard also has a product value of 1,710,720:

blackboard = 2 × 12 × 1 × 3 × 11 × 2 × 15 × 1 × 18 × 4 = 1,710,720

There were three things about solving this problem that I really enjoyed:

- My strategy involved substitutions: I replaced a letter or a pairs of letters by other pairs of letters that have the same product value. For instance, the
*t*and*c*in*Patrick*could be replaced by*o*and*d*, because both pairs have a product value of 60. - Calculating the product values for
*Patrick*and*blackboard*reveal two distinct factorizations for 1,710,720. - How cool is it that I’m a mathy folk, and my name and
*blackboard*have the same product value?

(Incidentally, my boss David found that his name and the word *chalk* have the same product value. Some would argue that its numerological destiny that we work together and are friends.)

So now I’ll offer the challenge to you. **Can you find a word that has the same product value as your name? **Good luck!

Of course, if that’s more thinking than you care to do right now, you could just access the product value calculator. But what fun would that be?

### Make Money with Fractions

An act of Congress on July 17, 1861, gave the Treasury Secretary the authority to print U.S. currency. For a variety of reasons, it wasn’t until several years later that the Treasury Department actually began printing; in the interim, private firms printed the notes in sheets of four, sent them to the Treasury Department where the seal was affixed *by hand*, and then the sheets were cut apart with scissors. (How far we’ve come!)

Did you know that the U.S. government will replace worn out or damaged money if three-fifths of it is still identifiable? Similarly, two-fifths will earn the bearer half the face value.

Perhaps the U.S. government is not terribly good with fractions. (This is not surprising. A recent government report claims that five out of four government employees do not understand fractions.) Even an elementary student knows that 3/5 + 2/5 = 1. So why is the government willing to give you 150% of a bill’s value if you divide it in the ratio 60:40?

If you want to make a quick buck (or a quick $50), here’s my suggestion: Go to the bank, get a fresh $100 bill, then cut it as shown:

As divided, the left portion is 3/5 of the original bill, and the right portion is 2/5 of the original bill. Now you can exchange the left portion for a new $100 bill, and you can exchange the right portion for $50. That’s a 50% return on your money, which is better than almost every blue-chip stock in the history of NASDAQ and the NYSE.

With policies like this, is it any wonder there’s a national deficit?

* NOTE: It is illegal to purposely mutilate U.S. currency. The above post is satirical. Do not try this at home. If you do, we at MJ4MF hereby absolve ourselves of all responsibility.