## Archive for August 20, 2012

### What’s the Difference?

Today is 8/20/12, which makes it a *difference day*, because the difference between the date and the month is equal to the year: 20 – 8 = 12. In general, a day in the form *mm*/*dd*/*yy* is a difference day if *dd* – *mm* = *yy*.

Dates of this type are relatively rare. There will be exactly 12 per year through 2019, but from 2031 through 2099, there won’t be any. So here’s a question:

How many difference days will there be during the 21st century?

The answer is below.

Speaking of differences, here are some math jokes about differences.

**What’s the difference between a narcoleptic and a math professor?**

The narcoleptic is a slumber nut.

**What’s the difference between a math Ph.D. and a large pizza?**

A large pizza can feed a family of four.

**What’s the difference between a lemma and a proposition?
**You’ll never receive a lemma at a bar.

**What’s the difference between a mathematician and a chocolate muffin?
**One is a mathematician, and the other is a chocolate muffin.

Though I believe mathematicians are useful, I would much prefer a machine for turning theorems into coffee.

(Admittedly, that last one is in the wrong format. But it seems weird to ask, “What’s the difference between a mathematician and a machine for turning theorems into coffee?” The answer would be, “Nothing.”)

There will be 281 difference days during the 21st century. There are 12 per year for 2000–19, but then the number per year starts to decrease. You might expect there to be 11 difference days in 2020, 10 difference days in 2021, and so on, with the number decreasing by 1 each year. But February, April, June, September and November cause problems because they have fewer than 31 days. So the total number of difference days during the 21st century is:

20(12) + 10 + 10 + 8 + 8 + 7 + 5 + 5 + 3 + 3 + 1 + 1 = 281