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Bachet's Problem (arxiv) is a famous problem where we have to find the smallest set of positive integers such that they measure every number between 1 and 40. This can be generalized to every integer between 1 and N.

My question is as follows:

  • Assume that we have a set of weights that can "weigh" any positive integer upto N.
  • But our weights are not ideal - as in , they may "fail" or "break". So we decide to build redundancy into the set.
  • Now, what is the minimum set which assures every the measurement up to N in the event of upto m/2 objects in the set failing given that m is the size of the set.

This is my first question here at math.se. Please help me with the tagging, in case I may have blundered. :P

Regards

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Hi rrampage, I've removed the "elementary-set-theory" tag since this isn't set theory. Cheers! –  Antonio Vargas Sep 18 '12 at 22:09
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