[scheme271]

I think it's slightly different. Consider this problem instead, what's the chances of two people sharing the same birthday in a group. It's (365364...*(365-n+1))/(365^n). If you plot this out, it increases exponentially. At n=23 it's about 50%. At around 60, it's a bit more than 99%. It's similar to the other problems, where a given condition can have an arbitrarily high chance of being present at surprisingly low graph sizes.

[lupire]

That's sigmoid (starts exponential and then smoothly changes into an asymptotically constant)