The Strong Birthday Problem Revisited

We revisit the Strong Birthday Problem (SBP) introduced in [1]. The problem is stated as follows: what is the minimum number of people we have to choose so that everyone has a shared birthday with probability at least 1/2? We derive recurrence relations to compute the probability, and further show a nice connection to the associated Stirling numbers of the second kind to derive additional recurrences. We implement the recurrences using dynamic programming as well as compute the values using the combinatorial formula, and provide numerical results.