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        riddles >> easy >> Purple rain
        
(Message started by: alien on Feb 24^th, 2005, 4:16am)

Title: Purple rain
Post by alien on Feb 24^th, 2005, 4:16am

It raines. There is the swimming pool near the house in the form of a cube, with the side 10 meters long. All rain drops fall in exactly one second sequence of time, perpendicullary, and 1 centimeter apart from one another. Those drops nearest to the edge of the swimming pool fall 5 millimeters off the edge. What time is needed for the pool to be full to the brink, if each rain drop containes the volume of 2 cubic millimeters?

Title: Re: Purple rain
Post by Grimbal on Feb 24^th, 2005, 5:16am

Rain is certainly strange on your planet, alien.

- On your planet, do the rain drops fall in a square grid or a triangular grid?
- How far is the swimming pool from the house?
- What about evaporation?
- Is the swimming pool empty at the start?
- Is the pool drain closed? (as you would expect if it is empty)
- Will the rain last for at least [hide] 5 days, 18 hours 53 minutes and 20 seconds [/hide]?

Title: Re: Purple rain
Post by SMQ on Feb 24^th, 2005, 5:24am

If I understood that right :: every cm² of area receives one 2mm³ drop per second, right? So every 1cm²x10m = 1,000,000mm³ column is "filled" in 500,000s = 5 days, 18 hours, 53 minutes and 20 seconds. ::

--SMQ

Title: Re: Purple rain
Post by towr on Feb 24^th, 2005, 1:18pm

on 02/24/05 at 13:08:08, alien wrote:

Quote:"On your planet, do the rain drops fall in a square grid or a triangular grid?"

That's not important.

It does rather substantially influence the answer, so I'd say it is important.

Title: Re: Purple rain
Post by towr on Feb 25^th, 2005, 12:46am

Whether viewed from the top, the drops fall in this pattern:


o   o   o   o   o   o   o
  o   o   o   o   o   o   o
o   o   o   o   o   o   o
  o   o   o   o   o   o   o
o   o   o   o   o   o   o
  o   o   o   o   o   o   o

or this one:


o   o   o   o   o   o   o 

o   o   o   o   o   o   o

o   o   o   o   o   o   o

o   o   o   o   o   o   o

The first one has a higher density of drops, so the pool would be filled quicker (in about sqrt(3)/2 times the time)

Title: Re: Purple rain
Post by alien on Feb 25^th, 2005, 12:52pm

Now I understand. The second pattern is what I had in mind.