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Topic: Thought Provoker Help Please
Replies: 7   Last Post: Oct 16, 1998 3:58 PM

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Helena Verrill

Posts: 8
Registered: 12/6/04
Re: Thought Provoker Help Please
Posted: Oct 16, 1998 3:58 PM
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Thoughts provoked:
why is it, I hear this problem over and over,
and the numbers are always exactly the same?

You could ask 'given a 12g container, a 7g
container, and a 5g container, with the 12 full
and the others empty, how do you divide it in two?'

Or take containers with volumes 4a, 2a-1, 2a+1, and
divide the 4a volume of water (starting in the larger
container) into two 2a volumes?
(There is a simple algorithm to do this)

Or what about containers with volumes 2ka, ka+1, ka-k+1
(eg, with k=3,a=5, (30,16,13))
starting with 2ka in the big container that has to be
divded in two?
(should be able to do this in the same way, again)

Generally, what are all the sets (2N,M,K), 2N > M > K where you
can start with 2N g in the 2N container, and divide it
into two equal parts? Or, what sets of volumes are possible
from this starting configuration?

Pity this question isn't really about geometry, whatever
you do with it though, as far as I can see. Maybe you
could make a two dimensional version, with pairs (a_i,b_i)
i=1,2,3; or even n dimensional; but it's still not geometry.

Helena





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