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Simple n-tuple problem - with no simple solution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115785] Simple n-tuple problem - with no simple solution
  • From: Don <donabc at comcast.net>
  • Date: Thu, 20 Jan 2011 06:33:21 -0500 (EST)

Problem: Given an n-tuple  (n >= 1). with each element  able to take
on the values in
Range[0, 1.0, .05] , produce all the n-tuples that sum to 1.0.

The most direct way to solve this problem is to generaate all possible
n-tuples and Select out all those that sum to 1.0.

For example, when n = 2 :

n = 2;
Select[Tuples[Table[Range[0, 1.0, .05], {n}]], Total[#] == 1 &]

The problem with this solution is that the number of n-tuples that are
generated before the Select is used grows exponentially fast as a
function
of n - causing the system to run out of memory (RAM) very quickly.

Is there a more memory efficient way to solve this problem that
doesn't
use so much memory but still is not too slow in terms of processor
time?

Thank you.


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