Tim Attwood wrote:
> I'm mostly stalled at 43%, I've seen several
> problems that are easy enough to express
> solutions to that are none-the-less difficult
> to compute in any reasonable amount of time. 

Some of the questions state an iterative problem for which there is a 
direct solution.

For instance, the second problem looks iterative, but there is a direct 
formula for any member of the Fibonacci series, there is a direct 
formula for the sum of a power series, and the even-valued members of 
the Fibonacci series occur at every third position starting with 0. 
When you put that together, the sum is

(1/sqrt(5) * ( (phi^(n+3)-1)/(phi-1) - ((1-phi)^(n+3)-1)/(1-phi-1) )

where n is equal to the index of the highest even-valued member of the 
Fibonacci series that is below one million.  It turns out that n is 30 
in this case, and therefore the sum is 5702886.

Regards,
John

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