I had to use the symbol "!" to denote the mathematical operation of faculty
We call it "factorial" in English.
My favorite combinatorial problem: How many ways are there to put N identical balls in M distinct buckets? It's cool problem because you won't get it through brute force, but when you look at it the right way, you can just write down the answer, with only a basic background in combinatorics.
Another bit of brain candy for math lovers: How many zeros are on the end of "100!" ? This requires only very basic (pre algebra) math, and insight.
--Glenn