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.