Dork Scratchings

In this post I will attempt to show that sitting down and having a nice cup of tea is the best approach to solving any new mathematical problem.  So, here's a problem: A plane has 100 seats and 100 passengers each with an allocated seat number.  The first passenger to get on the plane is blind and chooses a seat at random.  Each subsequent passenger to board chooses their own seat if still available, or a seat at random if not.  What is the probability that the 100th passenger gets their allocated seat? This is more subtle than it seems at first.  The last passenger could get their own seat because the blind passenger chooses the correct seat, or because the 2nd passenger chooses the blind person's seat, or because the first 87 passengers occupy the first 87 seats.  In fact there's a huge number of ways in which it could happen. Knuckleheaded Compsci solution Suppose we've forgotten to have a cup of tea.  Then we might just dive in an...

Queqiao and Chang'e-4 Exciting news from the BBC Website: China Moon mission lands Chang'e-4 spacecraft on far side .  The page includes a video with sinister background music as if to suggest they're the baddies (a la Drax in Moonraker).  However, the part that really intrigued me was the mention of the L2 Lagrange point - the first I've ever seen in a news story! As I described in my post Lagrange Points   there are 5 locations in the Earth-moon-Sun plane in which - in the rotating frame of reference and taking centrifugal forces into account - there is no overall force and an object can be parked indefinitely.  One of them is just beyond the moon and is called L2 . Now the problem with landing a probe on the far side of the moon is that you can't talk directly to it: there's a big rock in the way!  So, according to the BBC article the Chinese Space Agency has parked a satellite Queqiao at L2 to relay messages.  This left me a bit confused...