If you can construct a number using the digits, 0,1,2,3,4,5,6,7,8, and 9 each exactly once and the operations of addition, subtraction, multiplication, division, exponentiation, and digit concatenation, in any order, we will call that number pandigital. Notice that there are only finitely many pandigital numbers.
How close can you get to the mathematical constant e with a pandigital number?
There are two parts to this logic puzzle. First, try to get the best approximation of e that you can. Then, try to come up with an estimate of how close you can get if you checked all possible pandigital approximations. I will post one particularly good approximation in the comments, but I suggest you think about it for a while before looking.