Every once in a while you get a puzzle handed to you. This week I was at the scum hole the city of Boulder, Colorado, calls the dog swimming “beach,” and a guy with a black lab said that his dog, Selkie, has five brothers and sisters in town. “But I’ve never run into one of them,” he said. “I wonder what are the chances of that?”
Imagine that each of the six dogs goes out somewhere an average of once every three days. And imagine that between trails and parks and fields and out-and-abouts and algae-choked scum holes there are 200 places a dog can go in and around Boulder, all (let’s say…) with equal probability.
If it’s been exactly two years — 730 days — since Selkie’s owner picked her up from the litter, what are the chances that during this time Selkie would NOT see a doggie sibling?
For extra credit and a second entry into this week’s drawing for the $50 ThinkGeek gift certificate, what are the chances over the same time that any sibling will meet any other sibling? (And if you need a hint, try Googling “birthday problem.”)