Rhetorical question uttered in my presence:
“I wonder if there’s any formula that predicts the probability of finding a common free date as the number of people in the group expands?”
Me (self-entertaining self):
I postulate the probability is the M’th root of the inverse of the N’th prime minus one; where N is the number of people and M is the number of weeks in the date range of interest.
Thus for a population of a 1, probability is 100% for any time period. 1/(2-1) ^ (1/M) = 1.
For a population of 2, within one week: 1/(3-1) ^ (1/1) = 50%. Within the next 4 weeks: 1/(3-1) ^ (1/4) = 85%. For a population of 6, the 6′th prime number is 11, and over 4 weeks: 1/(11-1)^(1/4) = 56%.
“Large” party of 12? The 12th prime is 37, so 3% within 1 week, 41% within 4 weeks.
Just to be thorough: a wedding sized party of 150, would use the 150′th prime, 863. Within one week? 0.1%. Within 52 weeks? 88%.
Note, popular populations can apply up to an M+5 charm effect. Use 2d10 or 1d100.
