ok birthday problem AGAIN?

Question

ok so our textbook has this question where its like f(n) is the number of students in your class whose birthday is on the nth day of the year. and the book wanted us to say if this problem was invertible or not. The answer was that it isn't

Ok so our teacher wanted us to think of a situation when this problem would be invertible. So does that mean what is the smallest amount of people you could gather in a room where no two people would share the same birthday? IS that the only way this problem would be invertible?

And how do u figure that number out? I found somewhere that you could have 28 ppl in a room before the probability was .5 meaning that there are 2 ppl sharing the same birthdays??

AHH...god this problem is so confusing

Answer 1

The function would be invertible if there was only one student in the class. To say a function is invertible means that no two values of the function would be equal. It seems reasonable that there are several occurrences of only 1 student having his birthday on the n-th day of the year. That would mean there are several values of n where f(n) = 1, and that makes it impossible to invert the function.

This has nothing to do with the probability of two people having the same birthday.