Pi Notation Fun.

My Stats teacher was talking about how a group of 23 people have a 50% chance of having at least two people in the group sharing a B-Day(Day and month, not year). I had seen a bit about summation and asked if there was a multiplicative(holy crap is that spelled right?) equivalent and I ended up with this.

Assuming I didn't already know that it was 23 people, is there an easy way to find x other than churning out every value from 1 onward?
I scarcely remember reading about a formula or something for Sigma Notation...

 Spoiler

I asked a few teachers at school... no real help other than using list n a TI-83. D;

They have the entire summation formula over at Wikipedia. Do a search for "Birthday Paradox" to get the formula.

you know whats more fun? probability of same day and year.

you know whats more fun? probability of same day and year.

But then you have to take into account the portion of the population that's age x.
I doubt there's the same amount of 42 year olds as 52 year olds.