Find n for which
[tex]\lfloor \log_2 1 \rfloor + \lfloor \log_2 2 \rfloor + \lfloor \log_2 3 \rfloor + \ldots + \lfloor \log_2 n \rfloor = 1994[/tex].
A fairly straightforward problem that can be worked out quickly once you see the pattern. 313 was my initial answer which was wrong. (The actual answer is 312.) The funny thing is that I first tried to check it with Maple and it returned an answer that was slightly wrong. My guess is bad code resulting in some round off error.
So I checked with Excel and found the answer and my initial error. Athough admitting that I like a microsoft product will destroy whatever “geek” status I that possess, I have to say that there are few things you cannot do with Excel. It is also an excellent (pun not intended) way to investigate patterns in number theory.