Maple vs Excel

AIME 1994
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.

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One Response to Maple vs Excel

  1. I used MATLAB and got 312, but only after I played around with its epsilion tolerance settings, as roundoff initally made it 314 (even worse than Maple).

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