Thanksgiving Week Challenge! This week's puzzle comes in two parts. The first part will count as the normal puzzle for the week of 11/27. The second part is a challenging bonus question. You have the week of Thanskgiving and the following week to come up with a soluion.
Aditya is hosting Thanksgiving dinner. They have 48 guests coming. Adiyta will seat everyone at a vrey large round table. On the table between each pair of settings is a wine glass with a cloth napkin arranged inside. As each person is seated (by Adiyta), they take a napkin randomly from the left or the right. Adiyta does not see which one they take. In what order should the seats be assigned to maximize the expected number of guests who don't get napkins?
The set up is the same as above, but this time Adiyta is not seating the guests. The seats are occupied in random order. If the number of guests grow to be very large, what fraction of them (asymptotically) will end up without a napkin?