I asked a question for homework in the last 15 minutes of class today:
“How many zeros are there in 100! ?” (not 2 zeros – I mean in the numeral that you get by evaluating the factorial).
Several people correctly said there were 24 “trailing” zeros, but no one was able to find how many total zeros there were (i.e. it seems hard to count the zeros that aren’t at the end).
Turns out it was harder than I thought
There isn’t a known way to compute the value. See here for a short discussion (http://math.stackexchange.com/questions/142126/how-many-zeroes-are-in-100) and here for a list of the number of non-trailing zeros in a bunch of factorials (https://oeis.org/A137581).
So it’s a good thing I told you to only spend 10 minutes on it, eh? It won’t hurt you to do some thinking, and it’s probably a good lesson to learn that some things are solvable (or at least aren’t known to be).
I gave you a 2-page assignment today. Complete it and hand it in by the end of Wednesday, September 17th. Come to see me if you need clarification or help; otherwise, work independently on it.