Another generalization is to ask what is the probability of finding at least one pair in a group of people have at least one shared birthday], this average is determining the Mean of the distribution, as opposed to the customary formulation which determines the Median.
(In case the sum of all the weights is an odd number of grams, a discrepancy of one gram is allowed.) If there are only two or three weights, the answer is very clearly no; although there are some combinations which work, the majority of randomly selected combinations of three weights do not.
Real-world applications for the birthday paradox include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a collision for a hash function. Let these events respectively be called "Event 2", "Event 3", and so on.
One may also add an "Event 1", corresponding to the event of person 1 having a birthday, which occurs with probability 1.
A related problem is the partition problem, a variant of the knapsack problem from operations research.
Some weights are put on a balance scale; each weight is an integer number of grams randomly chosen between one gram and one million grams (one tonne).
It may be shown people is needed; but on average, only 25 people are required.