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