ninatoo wrote:But now I realise that when we are dealing with dates constantly, from time to time these things happen and someone more mathematical than I could probably explain why

.
I remember a former work colleague proving statistically that if you have a crowd of 20 or more people, the probability of two people sharing the same birth date is greater than 50%. If I remember rightly, it was:
Assuming a 365 day year, if you have two people, there is a 1 in 365 chance that the second person shares the same birth date as the first. Then a third person joins that two, there is a 1 in 365 chance that he shares the birthday of the first person, and a 1 in 365 chance that he shares the birthday of the second person. Then a fourth person joins the crowd, there is a 1 in 365 chance that he shares the birthday of person 1, 1 in 365 chance that he shares the birthday of person 2, and 1 in 365 chance that he shares a birthday with person 3.
So the probability in a crowd of 'n' people that two people share the same birth date is 1/365 + 2/365 + 3/365 ... to (n-1)/365. On adding up 1/365 + 2/365 + 3/365 + 4/365 etc, when you get to + 19/365 you pass 0.5 (50%). Therefore 19/365 being for a crowd of 20 (n-1=19; n=20), when you have 20 or more people, there is a greater than 50% chance that two will share a birthday.
So if you apply that theory to your family tree, if you have 20 or more people (could be close relatives) then there is a greater than 50% chance that two of them share a birthday. The probability increases if you include dates of marriage and dates of death.

All that arithmetic should be enough to send you to sleep.
The household of a good friend of mine has 5 people in it. The two parents, and three children. There are only three separate birthdays between them. The parents, by coincidence share the same birthday (of the same year). Then there is the older daughter, followed by the son and younger daughter who are twins.
All the best,
AndrewP