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;