Thanks to a large amount of Black Oo Long Tea, the logical side of my brain seems to be functioning again.
This question is similar to the Birthday problem.
How many people do you need in a room to guarantee that you will find someone with the same birthday?
Based on the pigeon hole principle, the answer is 366. Simply because there are 365 days in a year. Statistically even in the unlikely case where all of them had a different birthday from each other, there is an extra person that CANNOT fit outside these constraints and will share a birthday with all the others.
Let's say we just want the probability to be more than half. How many do we need then?
The answer to this question is actually 23. Which is a surprisingly small number.
Unfortunately, I failed discreet maths, so I am gonna let Wiki do some of the talking
https://en.wikipedia.org/wiki/Birthday_problem
This principle might be useful in solving this. Although, I admit that I am not completely sure at this point how to modify this and apply it because the problem feels abit different. Maths was never my forte though I do programming.