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.

翻译：本文重新探讨了文献[1]中提出的强生日问题。该问题表述为：为使每个人至少与另一人生日相同的概率不低于1/2，至少需要选取多少人？我们推导了计算该概率的递推关系，并进一步揭示了其与第二类关联斯特林数的优美联系，从而得到更多递推式。我们采用动态编程实现递推计算，同时利用组合公式进行数值求解，并给出了计算结果。