Archive for December, 2014

Results of Hold On… How Many Copies? Contest

As predicted, I did not meet my self-imposed deadline of posting the winner of the Hold On… How Many Copies? contest on Saturday. But I think you’ll agree I have a good excuse. When I woke at my in-laws on Saturday morning, my wife and kids surprised me with the pronouncement that we’d be spending the day at the Museum of Mathematics in New York City. (A post about that coming soon. It was awesome!) But after a full day of mathematical thinking and a late dinner, I didn’t have the energy to post results last night.

So, sue me.

But without further adieu, I can now announce the winner. Not before some data analysis, though.

The ten responses were:

{21, 137, 301, 333, 392, 429, 453, 595, 1637, 3142}

With a range of 3,121 and an average of 744, there was quite a spread to the data.

I certainly love the optimism of the respondent who predicted that 3,142 copies were sold! But with Q1 = 390 and Q3 = 559, the responses of 1,637 and 3,142 would both be considered outliers. Indeed, the actual number was lower than either of those guesses, but you won’t hear me complain about selling 634 copies of Math Jokes 4 Mathy Folks from Dec 15 to Dec 21!

The winner guessed 595 copies. Well done! He or she will be contacted via email or can contact me directly at patrick@mathjokes4mathyfolks.com.

For what it’s worth, I would not have won my own contest. Knowing that sales vs. rank is generally exponential but also knowing that sales decline during the third week of December, I used a purely linear regression to generate a guess of 473 copies. This would have resulted in a third-place finish. Oh, well. I take solace knowing that a third-place finish is far superior to where I would have placed if I had sponsored a marathon instead.

So, thanks to everyone who bought a copy of the book last week. Wow! Who would’ve thought sales would still be that brisk five years after publication! For that matter, thanks to everyone who’s ever bought a book. This has been an incredible ride!

Thanks, also, to those of you who entered the contest. Sorry if you didn’t win, but I hope you had fun playing.

Happy holidays!

Hold On… How Many Copies?

How many copies of Math Jokes 4 Mathy Folks do you think sold last week?

Why would you want to make a prediction? Well, lots of reasons…

• Like the author (and readers) of this blog, you’re a math geek.
• You swoon at the sight of data.
• You’ve never met a puzzle you didn’t like.
• You want to show the world how awesome you are.
• You’d like to win a signed copy of Math Jokes 4 Mathy Folks, some cool MJ4MF stickers, and a surprise gift, all shipped to you in exclusive MJ4MF packaging!
• All of the above.

If you’re reading this blog, then you surely love being alive in the Age of Big Data. I love it, too, and I devour any data that I can get my hands on.

Amazon feeds my desire by providing two valuable pieces of data about Math Jokes 4 Mathy Folks. First, they provide the sales rank for the book, which is updated hourly. Second, they provide weekly sales data. The downside to this latter stat is the delay in its release — they provide data for Monday-Sunday, but it isn’t released until the following Friday. The upside is that big dorks like me use the time from Monday through Thursday to make predictions.

The chart below shows the average sales rank and weekly sales for Nov 24 through Dec 14. (The “average sales rank” is the average of the sales ranks for the seven days each week. Although it’s updated hourly, I don’t have the time to check it that frequently, so I rely on Author Central, which reports the sales rank at the end of each day.) It also shows the average sales rank (but not sales) for last week, Dec 15‑21.

 Week Amazon Sales Rank (Weekly Average) Weekly Sales Nov 24-30 4,742 114 Dec 1-7 3,437 279 Dec 8-14 2,390 435 Dec 15-21 2,063 ?

The question: How many copies of MJ4MF were sold last week?

Oh, sure… I could just wait until Friday to find out — but what fun would that be?

Instead, I constructed several mathematical models, and then I tweaked them to predict how many books were sold. The tweaks were based on some things I’ve learned over the past couple of years:

• Holiday sales are most vigorous in the first two weeks of December. They slow down a bit in the third week. Consequently, a sales rank of 1,655 on Dec 1 does not equal a sales rank of 1,655 on Dec 21.
• The long-term trend is not linear. In fact, this graph from Foner Books shows that it’s logarithmic.

Which brings us to the contest. Go to the Google form and enter your prediction and email address. (The email is only so I can contact you if you win.) Closest guess to the actual number of sales will win the grand prize. In the event of a tie, a winner will be randomly selected (or if I’m feeling generous, maybe there will be multiple winners… it’s hard to predict my disposition on any given day).

So, what are you waiting for? Open Excel or SPSS or your stat software of choice, muddle through a few regressions, and submit your entry!

Winners will be announced on Saturday, December 27, 2014. The exact time will depend on what time I roll out of bed, what activities my wife and kids propose for the day, and my particular disposition on Saturday. On second thought… safest if you check back on Sunday.

Good luck!

What Do You Call…

A question from Brain Quest Grade 4:

Alex responded correctly.

Parallel.

Eli responded belligerently.

It’s not just mathematicians. Everyone who knows that would call them “parallel.”

How do you like that? Not only is my son mathematically literate, but he’s a sarcastic smart-ass, too. I couldn’t be more proud.

In honor of Eli…

What do you call a two-headed canary?
A binary.

What do you call a geometer who spent all summer at the beach?
Tan gent.

What do you call the circuit board on your spouse’s mother’s computer?
The motherboard-in-law.

What do you call two fishermen who fish standing up?
Vertical anglers.

What do you call a number that can’t keep still?
A roamin’ numeral.

What do you call a math teacher who loses control of his pupils?
Cross-eyed.

Great Dates

Today is a great date, and I almost missed it!

12/13/14

Today’s date (in U.S. format) is the last time this century that the month, date, and year are consecutive numbers. If you choose not to celebrate this momentous occasion, you’ll have to wait almost 89 years for this to happen again.

Another great date with consecutive numbers happened 5 years ago.

8/9/10

That’s the date that Math Jokes 4 Mathy Folks was published.

And I rather like 12/11/14. That’s just two days ago, when Math Jokes 4 Mathy Folks reached a rank of 2,210 on Amazon. That’s the highest sales rank it’s ever received. Woo-hoo!

Every year around this time, there is a significant spike in sales of MJ4MF. Ostensibly, it’s a good gift to give your engineer husband, statistician wife, or geometry teacher. And I am ecstatic that so many people are enjoying the book. But I’m wondering if we can blow the roof off of the Amazon rank; with a concerted effort, can we get the ranking of MJ4MF to below 1,000?

Here’s my request:

If you’re thinking of buying Math Jokes 4 Mathy Folks from Amazon for someone as a gift this holiday season, please make your purchase of MJ4MF between noon and midnight ET on Tuesday, December 16. (Use this conversion chart if you’re in a different time zone.)

Ordering by Tuesday, December 16 will still allow the book to arrive in time for Christmas or the last night of Chanukah, especially if you have Amazon Prime.

Since Amazon sales rank is based on a 24-hour period, any purchase on Tuesday will help with the ranking, so we don’t need to be much more specific than that.

And if you’re not thinking of buying Math Jokes 4 Mathy Folks this holiday season, well, what the hell is wrong with you? All the cool people are doing it.

Mental Math and the MCWC

How long would it take you to find the sum of 2 two-digit numbers?

Or 4 four-digit numbers?

Okay, let’s get really crazy… how long would it take you to find the sum of 10 ten-digit numbers?

You can decide whether you’ll do the calculation in your head, on a calculator, or with paper and pencil. Your choice.

With a calculator, it took me 91 seconds to find the sum of 10 ten-digit numbers.

Without a calculator, the winner of the Mental Calculation World Cup 2014 needed only 242 seconds to complete 10 problems in which participants were asked to add 10 ten-digit numbers. On average, that’s just 24 seconds to do in his head what took me a minute-and-a-half with technology.

Holy smokes!

Competitors at the MCWC do a number of mental calculation tasks. The following exercises will give you an idea of the computations that they do.

Exercise 1. Sum of 10 ten-digit numbers.

$\begin{array}{r} \mathbf{4190187220}\\ \mathbf{3967093178}\\ \mathbf{8567125486}\\ \mathbf{1005683165}\\ \mathbf{3635944647}\\ \mathbf{7645865467}\\ \mathbf{3506970235}\\ \mathbf{6710259450}\\ \mathbf{2 347 894 647}\\ \mathbf{\underline{ + 4 995 420 559}}\\ \end{array}$

Exercise 2. Multiplication of 2 eight-digit numbers.

$\begin{array}{r} \mathbf{18467941}\\ \mathbf{\underline{ \times 73465135}} \end{array}$

Exercise 3. Square root of a six-digit number.

$\mathbf{\sqrt{530179}}$

Exercise 4. Day of the week for a calendar date.

$\textbf{8 December 1721}$

Exercise 5. Multiplication of 3 three-digit numbers.

$\mathbf{184 \times 734 \times 635}$

These sample exercises are taken from the examples in the MCWC 2014 Official Rules.

If you were able to complete all five of those exercises in, say, less than 3 minutes, then you might be ready for MCWC 2016. (Note that for Exercise 3, you needed to be accurate to within 5 × 10-6.)

But if you’re like me, you’ll probably want to skip the competition and keep your calculator close at hand.

Birbiglia, Baby Boomers, and Computers

Mike Birbiglia said:

I didn’t realize I was good with computers till my parents bought one.

My wife’s cousin Natalie — now in her 60’s — has a more pragmatic explanation for why older folks are less tech-savvy than the average bear.

Perhaps Baby Boomers, having grown up during the Cold War, are afraid of what might happen if you push the wrong button.

Touché.

Many of us have love-hate relationships with computers. Some of us have hate-hate relationships with them. To wit:

There are two types of computers in the world: those that waste your time, and those that waste your time faster.

A computer once beat me at chess, but it was no match for me at kickboxing.

Men are like computers. They’ll do what you want, but not until they’re turned on and stroked in the right sequence.

A computer lets you make mistakes faster than any invention in human history, with the possible exceptions of handguns and tequila.

Problems in the MathCounts School Handbook are presented “shotgun style,” that is, a geometry problem precedes a logic puzzle and follows a probability question. (I worked for MathCounts for seven years and then served as a writer and chair of their Question Writing Committee, so I’m not unbiased.)

By comparison, textbooks often present 50 exercises on the same topic, each one only minimally different from the previous one. That tips the hand to students, methinks, and makes them realize, “Oh, I just need to do the same thing.” I prefer the MathCounts approach, where students have to dig into their bag of tricks to find a viable solution strategy.

With that in mind, here are a few problems I’ve encountered recently, each one not like the others.

Problem 1. The simple polygon is made from 73 squares, connected at their sides. What is the perimeter of the figure?

A simple polygon made from 73 unit squares.

Problem 2. What is the expected number of times that a six-sided die must be rolled to get each number 1–6?

Problem 3. A wall is to be constructed from 2 x 1 bricks (that is, bricks that are twice as long in one direction as the other). A strong wall must have no fault lines; that is, it should have no horizontal or vertical lines that cut entirely through a configuration, dividing it into two pieces. What is the minimum size of a wall with no fault lines? The figure below shows a 3 × 4 wall that has both horizontal and vertical fault lines.

A 3 × 4 wall with a fault line.

No answers, but here are some hints.

Problem 1. Look for a pattern.

Problem 2. Check out this simulation for the Cereal Box problem.

Problem 3. The smallest arrangement without a fault line is larger than 3 × 4 and smaller than 10 × 10.

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.