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

 From: Deepankar Sent on: Sunday, August 1, 2010 8:06 PM
```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.

On Sun, Aug 1, 2010 at 7:28 PM, Michael Mellinger
> I added a Perl solution. ?It seems I missed something in the problem
> because my code is much longer. ?No ugly Perl shortcuts taken:
>
> http://github.com...­
>
> -Mike
>
>
>
> --
> http://www.meetup...­
> This message was sent by Michael Mellinger ([address removed]) from Algorithms and Data Structures.
> Meetup, PO Box 4668 #37895 New York, New York[masked] | [address removed]
>
>
```

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