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I'm working on a distributed system an I need to solve the following problem.

Given N nodes trying to solve N problems. The chance of any node going down is P. What level of redundancy (K) is needed that the chance of any given problem being solved is S.

Just to be clear. Levels of Redundancy is the number of extra problems that each node would have to solve. Eg. 1 level of redundancy is that each node solves 2 problems, its own, and its neighbors. 2 levels would be 3 problems, Its own, neighbors, and step-neighbors.

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    Lets take node 1, node 2 is its neighbor, node3 is its step-neighbor. (Sorry, I know a real word exist for this but I don't know what it is.)2012-04-05

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