One of the first things I do every year when I realize that the new year upon us...

...no, not New Year's resolutions.

No, I always reduce the new year to its prime factorization. Why? Because sometimes I write competition math problems involving the school year, and so it's nice to know how the number factors.

In case you were wondering, 2016 = 2⁵3²7.

It's also, by the way, 2⁵ less than 2¹¹. That's right - in 32 more years, the year number will be a perfect 11^th power.

And if you want to verify that without using a calculator:

2⁵3²7 + 2⁵ = 2⁵(3²7 + 1) = 2⁵(63 + 1) = 2⁵2⁶ = 2¹¹.

Obviously, even when I'm on school vacation, my math mind doesn't shut down. In fact, I just spent a good part of a day writing a math unit that some of my high school students will be working on later on this year: Probability. This unit covers essential concepts like dependent and independent events, mutually exclusive outcomes, complementary outcomes, and compound events. There may eventually be a second probability unit that delves into more topics, such as conditional probability. For now, if you're looking for basic concepts, this is a good starting point.

Meanwhile, a unit on Pythagorean Means has also been added to the site.

It seems that some of you haven't left behind your math brains while on Christmas vacation, either. Professor Puzzler has fielded a handful of math-related questions while on vacation: 

• Why Can't I Divide by Zero?
• Why Does Cryptology Exist?
• What Are Telescoping Series?
• What Does the Upper-Case Pi Mean?

Thanks for all the great questions!

Happy 2¹¹ - 2⁵,
Douglas Twitchell
TPS Admin