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).
Read more about this topic: Partition Problem
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