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# Final Friday Fix: February Challenge

24 February 2017

On the final Friday of each month, we’re going to set Excel for you to puzzle over so that you can get your “Excel fix”. Challenge your office colleagues to see who can solve the puzzle quickest. There’s no prizes at this stage, you’re playing for bragging rights only!

There’s a Reason for the Exclamation Mark

Nice and simple explanation this Friday: I want to talk about factorials, denoted by n! where

n! = n (n-1)!

i.e. n! = n (n-1) (n-2) … 3 x 2 x 1.

For example, 5! = 5 x 4 x 3 x 2 x 1 = 120. These numbers become astronomical (technical term) very quickly. And it gets worse.

Excel has a function, FACT, which calculates factorials. Except it doesn’t. Consider the following summary:

Using Excel, 23! is 2.5852E+22 (Scientific notation), which when expanded is 25,852,016,738,885,000,000,000. Actually, 23! is really 25,852,016,738,884,976,640,000. Microsoft Excel can only calculate to 15 significant figures and then it starts rounding. Not good.

But it’s even worse than that. The LEN function in Excel counts how many characters there are in a text string. According to Excel, 22! has 20 digits whereas 23! has 19 digits. So 23! is smaller than 22! (yeah, right). What on earth..?

We’ll revisit this on Monday.

The Challenge

Using Excel (unless you fancy a night of long multiplication), calculate 171! precisely (i.e. not just to 15 significant figures).

A clue…

Sound easy? Unless your surname is Gauss you might find this a little awkward. We’ll publish our suggested solution in Monday’s blog. Have a great weekend!