## Archive for August, 2017

### My Insecurity Over Security Codes

Every time I attempt to access one of my company’s applications via our single sign-on (SSO) system, I’m required to request a validation code that is then sent to my smartphone, and then I enter that code on the login page.

It’s a minor nuisance that drives me insane.

The purpose of the codes are to provide an additional level of security, but given how un-random the codes seem to be, it doesn’t feel very secure to me. This screenshot shows some of the codes that I’ve received recently:

Here’s what I’ve observed:

- Every security code contains 6 digits.
- The first 3 digits in the code form either an arithmetic or geometric sequence, or the first 3 digits contain a repeated digit.
- Similarly, the last 3 digits in the code form either an arithmetic or geometric sequence, or the last 3 digits contain a repeated digit.

As an example, one of the codes in the screenshot above is 421774. The first 3 digits form the (descending) geometric sequence 4, 2, 1, and the digit 7 appears twice in the second half of the code.

I believe the reason for these patterns is to make the codes more memorable to those of us who have to transcribe them from our phones to our laptops.

This got me thinking. The likelihood of someone correctly guessing a six-digit code is 1 in 1,000,000. But what is the likelihood that someone could correctly guess a six-digit code if it adheres to the rules above?

If you’d like to answer this question on your own, stop reading here. To put some space between you and my solution, here’s a security-related joke:

“I don’t understand how someone stole my identity,” Lily said. “My PIN is so secure!”

“What’s your PIN?” Millie asked.

“The year of Knut Långe’s death,” Lily replied.

“Who is Knut Långe?”

“A King of Sweden who usurped the throne from Erik Eriksson.”

“And what year did he die?”

“1234.”

(Incidentally, Data Genetics reviewed 3.4 million stolen website passwords, and they found that 1234 was the most popular four-digit code. The researchers claimed that they could use this information to make predictions about ATM PINs, too, but I don’t think so. All this shows is that 1234 is the most commonly *stolen* password, and therefore this inference suffers from survivorship bias. Without having data on all the codes that were *not* stolen, it’s impossible to make a reasonable claim. But, I digress.)

To determine the number of validation codes that adhere to the patterns I observed, I started by counting the number of arithmetic sequences. With only 3 digits, there are 20 possible sequences:

- 012
- 024
- 036
- 048
- 123
- 135
- 147
- 159
- 234
- 246
- 258
- 345
- 357
- 369
- 456
- 468
- 567
- 579
- 678
- 789

But each of those could also appear in reverse (210, 975, etc.), giving a total of 40.

There are far fewer geometric sequences; in fact, only 3 of them:

- 124
- 139
- 248

And again, each of those could appear in reverse, giving a total of 6.

Finally, there are 10 × 9 × 8 = 720 three-digit numbers with no repeated digits, which means there are 1,000 ‑ 720 = 280 numbers with a repeated digit. (Here, “number” refers to any string of 3 digits, including those that start with a 0, like 007 or 092.)

Consequently, there are 40 + 6 + 280 = 326 possible combinations for the first 3 digits and also 326 combinations for the last 3 digits, which gives a total of **326 × 326 = 106,276 possible validation codes**.

That means that it would be about 10× more likely for a phisher to correctly guess a validation code that follows these rules than to guess a completely random six-digit code. But said another way, the odds are still significantly against a phisher who’s trying to steal my code. And quite frankly, if someone wants to exert that kind of effort to pirate my access to Microsoft Word online, well, I say, go for it.

### 8-15-17

Today is a glorious day!

The date is 8/15/17, which is mathematically significant because those three numbers represent a Pythagorean triple:

But August 15 has also been historically important:

- It’s the birthday of some famous people, including Jennifer Lawrence, Kerri Walsh-Jennings, Napoleon Bonaparte, Julia Child, and Ben Affleck, as well as some not-so-famous people, including one of my sisters, one of my aunts, one of my uncles, and my maternal grandfather.
- The Mayflower departed from Southampton, England, on August 15, 1620.
- The Panama Canal opened to traffic on August 15, 1914.
*The Wizard of Oz*premiered at Grauman’s Chinese Theater on August 15, 1939, and exactly 40 years later,*Apocalypse Now*was released.- In 1945, the Japanese surrendered on August 15.

But as of today, August 15 has one more reason to brag: It’s the official publication date of a bestseller-to-be…

Like its predecessor, this second volume of math humor contains over 400 jokes. Faithful readers of this blog may have seen a few of them before, but most are new. And if you own a copy of the original * Math Jokes 4 Mathy Folks*, well, fear not — you won’t see any repeats.

What kind of amazing material will you find on the pages of * More Jokes 4 Mathy Folks*? There are jokes about school…

An excited son says, “I got 100% in math class today!”

“That’s great!” his mom replies. “On what?”

The son says, “50% on my homework, and 50% on my quiz!”

There are jokes about mathematical professions…

An actuary, an underwriter, and an insurance salesperson are riding in a car. The salesperson has his foot on the gas, the underwriter has her foot on the brake, and the actuary is looking out the back window telling them where to go.

There are Tom Swifties…

“13/6 is a fraction,” said Tom improperly.

And, of course, there are pure math jokes to amuse your inner geek…

You know you’re a mathematician if you’ve ever wondered how Euler pronounced Euclid.

Hungry for more? Sorry, you’ll have to buy a copy to sate that craving.

To purchase a copy for yourself or for the math geeks in your life, visit **Amazon**, where * MoreJ4MF* is already getting rave reviews:

For quantity discounts, visit **Robert D. Reed Publishers**.

### Mo’ Math Limericks

I’ve posted limericks to this blog before. Quite a few, in fact.

But a friend recently sent me *The Mathematical Magpie*, a collection of math essays, stories and poems assembled by Clifton Fadiman and published by Simon and Schuster in 1962. Coincidentally, one section of the book is titled *Comic Sections*, the name of a mathematical joke book written by Des MacHale in 1993. (I contacted Professor MacHale several years ago, and he suggested that we swap books. Best. Trade. Ever.) Des MacHale is Emeritus Professor at the University of Cork, a mere 102 km from Limerick, Ireland… which brings us full circle to today’s topic.

*The Mathematical Magpie* contains quite a few limericks, one of which you have likely heard before:

There was a young lady named Bright,

Who traveled much faster than light.

She started one day

In the relative way,

And returned on the previous night.

Despite a variety of other claims, that limerick was written by Professor A. H. Reginald Buller, F.R.S., a biologist who received £2 when the poem was published in *Punch*, and he “was more excited at the check than he was later when his book on fungi was published.”

You may not, however, be familiar with Professor Buller’s follow-up limerick about Miss Bright:

To her friends said the Bright one in chatter,

“I have learned something new about matter:

As my speed was so great

Much increased was my weight,

Yet I failed to become any fatter!”

Here are a few other limericks that appear in *The Mathematical Magpie*:

There was an old man who said, “Do

Tell me how I’m to add two and two?

I’m not very sure

That it doesn’t make four —

But I fear that is almost too few.

Anon.The topologist’s mind came unguided

When his theories, some colleagues derided.

Out of Möbius strips

Paper dolls he now snips,

Non-Euclidean, closed, and one-sided.

Hilbert Schenck, Jr.A mathematician named Ray

Says extraction of cubes is child’s play.

You don’t need equations

Or long calculations

Just hot water to run on the tray.

L. A. GrahamFlappity, floppity, flip!

The mouse on the Möbius strip.

The strip revolved,

The mouse dissolved

In a chronodimensional skip.

Frederick Winsor

And though it’s not a limerick, this one is just too good not to include for your enjoyment:

A diller, a dollar,

A witless trig scholar

On a ladder against a wall.

If length over height

Gives an angle too slight,

The cosecant may prove his downfall.

L. A. Graham

Finally, I leave you with a MJ4MF original:

With my head in an oven

And my feet on some ice,

I’d say that, on average,

I feel rather nice!

**Got any math poems or limericks you’d like to share? We’d love to hear them!**

### Just Sayin’

Heidi Lang is one of the amazing teachers at Thomas Jefferson Elementary School. When she’s not challenging my sons with interesting puzzles and problems, she’s entertaining them with jokes that make them think. On her classroom door is a sign titled *Just Sayin’*, under which hangs a variety of puns. Here’s one of them:

Last night, I was wondering why I couldn’t see the sun. Then it dawned on me.

That reminds me of one of my favorite jokes:

I wondered why the baseball kept getting larger. Then it hit me.

Occasionally, one of her puns has a mathematical twist:

Did you know they won’t be making yardsticks any longer?

And this is one of her mathematical puns, though I’ve modified it a bit:

When he picked up a 20‑pound rock and threw it 5,280 feet, well, that was a real milestone.

I so enjoy reading Ms. Lang’s *Just Sayin’* puns that I decided to create some of my own. I suspect I’ll be able to hear you groan…

- He put 3 feet of bouillon in the stockyard.
- When the NFL coach went to the bank, he got his quarterback.
- She put 16 ounces of poodle in the dog pound.
- The accountant thought the pennies were guilty. But how many mills are innocent?
- His wife felt bad when she hit him in the ass with 2⅓ gallons of water, so she gave him a peck on the cheek.
- Does she know that there are 12 eggs in a carton? Sadly, she dozen.
- When his daughter missed the first 1/180 of the circle, he gave her the third degree.
- She caught a fish that weighed 4 ounces and measured 475 nm on the visible spectrum. It was a blue gill.
- When Rod goes to the lake, he uses a stick that is 16.5 feet long. He calls it his fishing rod.
- What is a New York minute times a New York minute? Times Square.
- I wanted to dance after drinking 31 gallons of Budweiser, so I asked the band to play the beer barrel polka.
- The algebra teacher was surprised by the mass when she tried to weigh the ball:
*b*ounces.

And because this post would feel incomplete without it, here’s probably the most famous joke of this ilk:

- In London, a pound of hamburger weighs about a pound.