# Re: [algorithms-and-data-structures] Algorithms Meetup Problem #4

 From: Michael M. Sent on: Sunday, August 1, 2010 11:07 PM
```This make sense?

http://docs.googl...­

I'm just looking for a reason to play around with the Latex editor in
Google Docs. :-)  Btw, it only works in the old version of gDocs.  The
broke it in the new version.

-Mike

On Sun, Aug 1, 2010 at 8:06 PM, Deepankar <[address removed]> wrote:
> I think the following substitutions allow it to be simply solved as a
> one line solution
>
> for some i between 1 and n
>
> t(i) = sqrt ( d(i) / (0.5 * g)) ? - lets call this 1
> where t(i) is the time for the ith ball to fall
> d(i) is the height of the ith ball.
>
> t(0) + t(1) .. + t(n) = T - lets call this 2
> where T is the total time which is supplied.
>
> Substituting for t(i) from 1 into 2
> (sqrt(d(1)) + sqrt(d(2)) .... + sqrt(d(n)))/ sqrt(0.5 * g) = T
>
> which gives
> g = (sqrt(d(1)) + sqrt(d(2)) .... + sqrt(d(n)))**2 / (T**2 * 0.5)
>
> where x**n = x raised to n.
>
> hence it collapses down to a single variable.
```

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