**Published on** May 21st, 2013 |
*by Jo*

# A number game

By Innes Bigaran

I thought I would make this month’s blog entry a little bit of fun, so I have borrowed something from my tutorial worksheets for my second year university studies of mathematics.

The aim of this exercise is to discover something new and exciting about a particular number. Which number, you may ask? Well, sum the digits representing the month and day of your birthday, for example, for me, the 20^{th} of April 20+4=24.

Now, do a quick Google search on that number and see what you can find.

When I first Googled 24, there were many links to things related to the television show- note to self: refine your search. So, instead I searched for “24 number”. First hit: Wikipedia, of course.

From here I found quite a few things that I thought were pretty cool:

Did you know?

- The SI prefix for 10^24 is “Yotta”
- 24! (factorial) is an approximation of Avogadro’s number
- 24 is a Harshad Number: it is divisible by the sum of its digits.
- 24 is the maximum number of unit spheres that can touch each other without overlapping in four dimensional space: it is termed the “kissing number” in 4D space.
- The product of any four consecutive numbers is divisible by 24 (I’ll leave that to you to look up why this one works)

And probably most interestingly:

- The product of any four consecutive numbers is divisible by 24 (I’ll leave that to you to look up why this one works)

Try it yourself!

You never know, this little piece of knowledge may come in handy one day- if not for anything else, it could be an interesting conversation starter!

** All credit for the framework of this blog entry is given Michael Patterson, the author of this question, which was incorporated into the University of Melbourne Real Analysis with Applications tutorial sheets**[subscribe2]