Light Humor and More on a Math Puzzle

We all need a break from the seriousness of math, so here are some (actual) amusing headlines. Before I get nasty comments, remember these are real!

1. Teachers Strike Idle Kids
2. Eye Drops Off Shelf
3. Miners Refuse To Work After Death
4. Hospitals Are Sued By 7 Foot Doctors
5. British Left Waffles On Falkland Islands

Ok, enough of the silliness...

I received several emails and comments about the math puzzle from the other day. Essentially, they all indicated that the problem was readily solved using technology.

First, here is the solution:
123456789 = 10821 x 11409

Aniket S., a computer science major from Solapur University, India, sent me the solution and the code she used in C++ to find the factors.

Both Mike Croucher and Pat Ballew, who emailed me, used the powerful new computing engine Wolfram Alpha to find the factors. As Pat pointed out, "the times they are a changin'...

In fact, I found the prime factors of 123456789 on the TI-89:

factor (123456789)
3^2 x 3607 x 3803

A few additional thoughts...
Is there anything special about the number 123456789? If we randomly permute the digits to, say, 586421739, we obtain the prime factorization 3^2 x 107 x 608953, which cannot be rearranged to form two 5-digit factors due to the 6-digit prime. Can you find a permutation of 123456789 which can also be factored into two 5-digit numbers?

If we make one change to the original number we can solve the puzzle:
123456784 = 10406 x 11864.

Have fun computing...

A Digit Problem from Florian for 'Constructivists!'

First a humorous aside from one of my friends on another message board. A friend emailed it to him so it's probably making the rounds of the web. In case you haven't seen it, here it is...

A recent study found that the average American walks about 900 miles a year.

Another study found that Americans drink, on average, 22 gallons of alcohol a year.

That means, on average, Americans get about 41 miles to the gallon.

Kind of makes you proud!



One of our new and devoted readers, Florian, contributed the following unusual digits by algorithmic construction problem. This is a wonderful example of a different type of solution, since a standard algebraic approach should prove fruitless. Florian is our resident computer scientist. That should help you understand how he devised this question.

Suppose a₁a₂a₃...a_n-16 represents an n-digit positive integer whose units' digit is 6. Find the least such positive integer satisfying the property that when the number is multiplied by 2, the result is 6a₁a₂a₃...a_n-1 , the n-digit number whose digits are the same as the original number except that each digit is shifted one position to the right and the rightmost digit '6' rotates to the leftmost position.

Have fun looking for this 18-digit number! Would a calculator be useful here?

Variations and Extensions:

Here is how one could modify this for middle schoolers:
(i) Give them the 18-digit number to start with (sorry, I'm not giving this away yet), have them multiply it by 2 using paper and pencil and see how long it takes for various students to see the surprising result. (Yes, Steve, they actually are expected to multiply with accuracy!)
I guarantee they will express surprise!
(ii) Now ask them to figure out how they could construct the digits of the mystery number, one digit at a time. Some will catch on quickly, others will need guidance.
(iii) What questions should occur to students as they are building this number? You may need to ask them if they believe this process eventually has to terminate.

Extension for the Very Highly Motivated (or for people like me who need to get a life!):

Construct the 42-digit number a₁a₂a₃...a₄₁5 (ending in the digit '5'), which when multiplied by 5 is of the form: 5a₁a₂a₃...a₄₁, in which the result has the same digits as the original number with each digit shifted one position to the right and the rightmost digit rotated to the leftmost position.

Note: Check my accuracy on this!

Calculus Humor?

From Savage Research, Humor...

Math Knowledge

Two mathematicians were having dinner in a restaurant, arguing about the average mathematical knowledge of the American public. One mathematician claimed that this average was woefully inadequate, the other maintained that it was surprisingly high.

"I'll tell you what," said the cynic. "Ask that waitress a simple math question. If she gets it right, I'll pick up dinner. If not, you do." He then excused himself to visit the men's room, and the other called the waitress over.

"When my friend comes back," he told her, "I'm going to ask you a question, and I want you to respond `one-third x cubed.' There's twenty bucks in it for you." She agreed.

The cynic returned from the bathroom and called the waitress over. "The food was wonderful, thank you," the mathematician started. "Incidentally, do you know what the integral of x squared is?"

The waitress looked pensive; almost pained. She looked around the room, at her feet, made gurgling noises, and finally said, "Um, one-third x cubed?"

So the cynic paid the check. The waitress wheeled around, walked a few paces away, looked back at the two men, and muttered under her breath, "...plus a constant."


I'm sorry, but that did make me smile! Reminds me of when I was teaching calc, I would tell my students that if they forgot the +C in an indefinite integral, their grade would be C+! Actually, I wasn't kidding...

BTW, there are many more of these at the above web site. Many are one-liners with that twisted sense of humor characteristic of Steven Wright or Jackie Vernon. I will not apologize for laughing!

Here are a few more...

1) Save the Whales -- collect the whole set.

2) If you believe in telekinesis, raise my hand...

3) The early bird may catch the worm, but it's the 2nd mouse that gets the cheese.

Ok, enuf' already (for now)...

My Favorite Ole and Lena Math Joke

Have you submitted your vote yet in the MathNotations poll in the sidebar?

A few years ago we visited our niece and nephew in Minnesota and fell under the magical spell of the land of 1000 lakes. Minnesotan's self-deprecating humor is refreshing, innocent and, as corny as it may appear, I am proud to say I enjoy it!

There are even websites you can visit to read Ole and Lena jokes which have been around since the first immigrants arrived.

Here is one of my favorites from the book, Ole and Lena, Live via satellite, Adventure Publications (in Scandinavian vernacular):

Littler Ole: Our math teacher tought she could stump us with a hard question. She asked, "Dis may take you a vhile to figure, but how many seconds are dere in a year?"

Lena: Dat must haf taken a lot of figuring, Little Ole.

Littler Ole: No, I hardly had to tink. I told her twelve.

Lena: Twelve?

Littler Ole: January 2nd, February 2nd, March 2nd,...

Ok, stop groaning now and admit it made you smile!

Sequel to "What did Pi say to i?" and more...

I can't believe I'm doing this but one of my students asked me if I heard the other half of the joke. Here's the original:

"What did pi say to i?"
"Get real!"

Here's the other half:
"What did i say to pi?"
"Be rational!"
[Ok, at least it's not about Math Wars and Learning Styles!]

At that moment I became possessed and asked:
"What did one-half say to one?"
"You're so full of yourself!"

I'm afraid of where this will lead so I'll sign out now. So, do math teachers really have the corniest sense of humor and do they really think they're funny?

Oh No! - Not More Corny Math Jokes!

If interested in purchasing my NEW 2012 Math Challenge Problem/Quiz book, click on BUY NOW at top of right sidebar.  175 problems divided into 35 quizzes with answers at back. Suitable for SAT/Math Contest/Math I/II Subject Tests and Daily/Weekly Problems of the Day. Includes both multiple choice and constructed response items.
Price is $9.95. Secured pdf will be emailed when purchase is verified. DON'T FORGET TO SEND ME AN EMAIL (dmarain "at gmail dot com") FIRST SO THAT I CAN SEND THE ATTACHMENT!
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I can't believe I'm sinking to these depths but it is summer and this may be the time for silliness. Two of my students shared the first couple (I'm doing it from memory so they're not exactly the originals) and the third I saw somewhere in my travels across the web (I forget the site to give proper attribution):

1. Who designed King Arthur's RoundTable?
Sir Cumference, of course. (ugh, groan,...)

2. What did pi say to i?
Get real!

3. Number two said to number three: "Boy, number 6 is really bad news. He's always in trouble."
Number three replied, "What do you expect. He's a product of our times!"

Ok, let me have it!

7-7-07: Your Lucky Day?

Of course, July 7th, 2077 or 7-7-77 will be fun too for those around to enjoy it 70 years from now!

Now you all know the story of the inveterate gambler who waited until the 7th day of the 7th month to bet $777 on horse #7 in the 7th race at 7-1 odds. Of course, the horse finished 7th! Sorry, I couldn't resist telling this groaner...