## My Son’s New Joke

*September 24, 2013 at 5:10 pm* *
3 comments *

My son is doing his math homework — he’s in first grade, so it involves writing a certain number, spelling that number, and finding all occurrences of that number in a grid of random numbers called a “Number Hunt.” Based on today’s number, he came up with the following joke:

What number is mostly even but not even?

Eleven.

Not a great joke, to be sure… but as good as most jokes on his dad’s blog, and he’s only six years old.

The homework was frustrating (for me), because my sons are capable of much more.

When my sons ride their bikes through the parking lot, they solve problems involving parking space numbers, the digits on license plates, and other numerical things. They ask me to create “math challenges” for them to think about as they ride. Yesterday, they solved the following three challenges:

- Which license plate has the greatest product if you multiply its four digits together? (The license plate format in Virginia is LLL-DDDD, where L is a letter and D is a digit.)
- How many different license plates are possible with the format LLL-DDDD?
- Each of the three rows in our parking lot has a different number of cars. If our parking lot had a fourth row, how many cars would there be in the fourth row?

For Question 1, Eli realized that the license plate with {9, 7, 6, 5} would have a greater product than the license plate with {9, 7, 6, 3}, since 5 > 3. But then he realized that {9, 9, 8, 2} would be even greater, and he correctly determined that the product is 1,296.

For Question 2, Alex thought it would be 144. His argument was that there would be 6 ways to arrange the letters and 24 ways to arrange the digits, and 6 × 24 = 144. We talked about this, and I pointed out that his answer would be correct if we knew *which* three letters and *which* three digits we were using (and they were all different). He and Eli reconvened and eventually claimed there would be 26^{3} x 10^{4} possible license plates… and being the good father that I am, I let them use the calculator on my phone to find the product.

For Question 3, the number of cars in the three rows was 2, 5, and 8. They extended the pattern and concluded that there would be 11 cars in the non-existent fourth row.

So you can understand why I’d be frustrated that Alex’s homework involved writing the number 11 repeatedly. I thought about telling him not to do it, but then I imagined the following conversation:

Alex: Would you punish me for something I didn’t do?

Teacher: Of course not, Alex.

Alex: Good, because I didn’t do my homework.

Or perhaps he’d just fabricate an excuse:

I thought my homework was abelian, so I figured I could turn it in and then do it.

And finally — should abelian be capitalized?

Entry filed under: Uncategorized. Tags: abelian, bike, eleven, homework, joke, license plate, math.

1.xander | September 25, 2013 at 2:43 pmAbelian should be capitalized, as it is in this sentence. However, if abelian is not the first word of the sentence, it should not be capitalized. 😛

Also, what’s purple and commutes?

2.venneblock | October 1, 2013 at 10:19 pmA Minnesota Vikings fan who drives to work?

3.xander | October 2, 2013 at 12:36 amI was thinking of “an abelian grape,” but I might like your answer better. 😦