It’s that time of year again and we can play the **2020 Year Game** in our January lessons. You can preview the **2020 game** now, full rules are **here**. Can your students use the digits in the year 2020 and the operations +, -, x, ÷, sqrt (square root),^ (raise to a power), ! (factorial), and !! (double factorial) along with grouping symbols, to write expressions for the counting numbers 1 through 100?

My students have always been curious about the double factorial function.

Excel has a function for computing double factorials, illustrated here.

I like to show my students a few examples and see if they can work out what is going on!

Have a look at **this article **from Wolfram Math World or have a look at this **article on Ask Dr Math**. Note the relationship between the double and single factorial functions.

A great idea for a starter on return to school from Alex Bellos’s Monday Puzzle, note the end of the **solutions post here** where Alex Bellos describes a new New Year challenge from Inder J Taneja, a retired maths professor from Brazil; can your students write 2020 using only single digits? Solutions are provided for the digits 1 to 9.

Once again, Manan Shah has provided us with some puzzles to keep us busy, **20 in fact** to keep us all busy!

I always read **Transum’s Newsletter** with interest, the newsletter published today notes some ideas on the number 2020 including an unusual property, something that last happened in 1210!

See also Weisstein, Eric W. “Self-Descriptive Number.”

From *MathWorld*–A Wolfram Web resource. http://mathworld.wolfram.com/Self-DescriptiveNumber.html

I see MEI has also noted this property in their January **item of the month**, Autobiographical numbers. A little further research led me to **Tanya Khovanova’s 2008 paper on Autobiographical Numbers**. Whilst mentioning Tanya Khovanova, we should of course check her **Number Gossip site for properties of 2020** and from her paper we have a reminder of the **Online Encyclopedia of Integer Sequences**.

We can also look at **WolframAlpha **which provides further information on the number properties of 2020 including what 2020 looks like in **historical numeral** forms. We could use the various **WolframAlpha queries** to learn how Babylonian, for example, numerals work. I have successfully used this as an interesting starter for January lessons.

The **Babylonian system** was a positional base 60 system, though interestingly uses ‘units’ and ‘tens’ symbols to create the 59 symbols needed.

For more on the Babylonian system including how fractions were represented see **History of Fractions** from Nrich.

We could look back and use the excellent **MacTutor History of Mathematics Archive** from the University of St Andrews, Scotland. We could check **today** or **any day** for Mathematicians who were born or died on that day.

The site is searchable in several ways, including the comprehensive index of **History Topics**.

Teacher Resources on Line

On the subject of dates and the new year, from *trol,* Teacher Resources on Line, we can make a **calendar for 2020**. I do like the fold and tuck models – no glue required Scroll down the page.

Wishing educators and students everywhere a very Happy New Year.