***
While trying to find the solution to a forwarded email that landed 3 months ago in an email account I don't check, I found:
Kerafyrm: Roflcopter. Computer science win.
"I woke up to a forwarded e-mail in my inbox this morning that read:
It is said that engineers take 3 minutes to resolve this, architects 3 hours and doctors 6 hours.
If you guess which the 6th number is, you'll be able to open the excel file. Once you discover it, put your name, save it and send it on.
Which is the 6th number? 1, 2, 6, 42, 1806, ___???
Once you have found the number open the document and type it in as the password!
After spending a while thinking about it, I still couldn't figure out what the last number in that sequence was. I knew if it were a mathematical sequence and not a trick question, it had to involve powers as the sequence appeared to be growing quadratically.
Alas my patience never quite got down to that. Since they happily provided me with a password protected excel file whose password was the answer, I launched a brute-force attack on the file over the set of 0-9 characters. In less than 3 minutes, I had the answer -- 3263442.
For the curious, I solved the sequence too. Here is the recursive definition of that sequence:
T(1) = 1
T(2) = 2
T(n) = T(n-2) + T(n-2)^2 + T(n-1)^2"
(Emphasis mine)
However, his formulation of the answer is not elegant.
Here's a better one:
n1 = 1
ni = (ni-1)(ni-1 + 1) for i > 1
