Partition Problem - Alternative Forms of The Problem

Alternative Forms of The Problem

An interesting related problem, somewhat similar to the Birthday paradox is that of determining the size of the input set so that we have a probability of one half that there is a solution, under the assumption that each element in the set is randomly selected with uniform distribution between 1 and some given value.

The problem is interesting in that the solution can be counter-intuitive (not unlike the Birthday paradox). For example, with elements randomly selected in between 1 and one million, many people's intuition is that the answer is in the thousands, tens, or even hundreds of thousands, whereas the correct answer is approximately 23 (see Birthday problem#Partition problem for details).

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