Inspired by jd2718’s Thanksgiving Puzzles, here’s a Thanksgiving puzzle created by yours truly (though inspired by one I heard a while back):
It’s Thanksgiving Day and you’re hosting dinner for your large extended family of 30 people. In the interest of organization, you’ve created nametags for each person and placed them around the table. But when everybody goes to sit down at the table, there’s a problem: Great Aunt Ermintrude, who is 104, has already sat down. However, being a bit senile, she has forgotten her own name and just picked a seat at random! Not wanting to disturb her, everybody decides to just let her stay there. Each person, as he comes to the table, will sit at his own seat if it is available, but if it is not, he’ll just pick a seat at random from the ones that are left. You, being the host, are the last one to sit down. What is the probability that you’ll sit at your correct place?
[Note that there is a small possibility Great Aunt Ermintrude has sat at her own place after all.]